pax_global_header00006660000000000000000000000064147417521730014525gustar00rootroot0000000000000052 comment=7accc77a70a08f965a29fdd13515f79cdcab9703 qutip-5.1.1/000077500000000000000000000000001474175217300126735ustar00rootroot00000000000000qutip-5.1.1/.codeclimate.yml000066400000000000000000000013261474175217300157470ustar00rootroot00000000000000version: "2" exclude_patterns: - "doc/" - "dist/" - "**/tests/" checks: argument-count: config: threshold: 10 complex-logic: config: threshold: 20 file-lines: enabled: false method-complexity: config: threshold: 20 method-count: config: threshold: 75 method-lines: config: threshold: 100 nested-control-flow: config: threshold: 4 return-statements: config: threshold: 4 similar-code: config: threshold: 64 identical-code: config: threshold: 64 plugins: fixme: enabled: true pep8: enabled: true duplication: enabled: true config: languages: python: python_version: 3 qutip-5.1.1/.coveragerc000066400000000000000000000005061474175217300150150ustar00rootroot00000000000000[run] source = qutip omit = # QuTiP test files */qutip/tests/* # Tool for tests */qutip/solver/sode/_noise.py [report] exclude_lines = # Skip Python wrappers which help load in C extension modules. __bootstrap__() # Skip empty method that are never meant to be used. raise NotImplementedError qutip-5.1.1/.github/000077500000000000000000000000001474175217300142335ustar00rootroot00000000000000qutip-5.1.1/.github/ISSUE_TEMPLATE/000077500000000000000000000000001474175217300164165ustar00rootroot00000000000000qutip-5.1.1/.github/ISSUE_TEMPLATE/bug_report.yaml000066400000000000000000000043561474175217300214620ustar00rootroot00000000000000name: 🐛 Bug Report description: Spotted a bug? Report it to us! labels: ["bug"] body: - type: textarea id: bug-description attributes: label: Bug Description description: Tell us what went wrong (including what triggered the bug) placeholder: "A clear and concise description of what the bug is, and the steps to reproduce it" validations: required: true - type: textarea id: code-to-reproduce attributes: label: Code to Reproduce the Bug description: Please provide a minimal working example. Paste your code directly (It will be automatically formatted, so there's no need for backticks) placeholder: "from qutip import identity\nprint(identity(2))" render: shell - type: textarea id: bug-output attributes: label: Code Output description: Please paste the relevant output here (automatically formatted) placeholder: "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\nQobj data =\n[[1. 0.]\n[0. 1.]]" render: shell - type: textarea id: expected-behaviour attributes: label: Expected Behaviour description: What should have happened instead? placeholder: "A clear and concise description of what you expected to happen" validations: required: true - type: textarea id: your-environment attributes: label: Your Environment description: Please use `qutip.about()` to get the information about your environment and paste it here (automatically formatted) placeholder: "QuTiP Version: ***\nNumpy Version: ***\nScipy Version: ***\nCython Version: ***\nMatplotlib Version: ***\nPython Version: ***\nNumber of CPUs: ***\nBLAS Info: ***\nOPENMP Installed: ***\nINTEL MKL Ext: ***\nPlatform Info: ***" render: shell validations: required: true - type: textarea id: additional-context attributes: label: Additional Context description: Add anything else you want to tell us. You can include images, plots, etc. placeholder: "Additional information, images, graphs, plots, etc." - type: markdown id: thank-you attributes: value: Thanks for taking the time to fill out this bug report!qutip-5.1.1/.github/ISSUE_TEMPLATE/feature_request.yaml000066400000000000000000000024561474175217300225140ustar00rootroot00000000000000name: 🚀 Feature Request description: Suggest an idea for this project! labels: ["ENH"] body: - type: textarea id: problem-description attributes: label: Problem Description description: Give us a clear and concise description of what the problem is! placeholder: "Example - It would be better if [...]" validations: required: true - type: textarea id: proposed-solution attributes: label: Proposed Solution description: Give us a description of your proposed solution placeholder: "A clear and concise description of what you want to happen" validations: required: true - type: textarea id: alternate-solutions attributes: label: Alternate Solutions description: Are there other ways of implementing this feature? placeholder: "A clear and concise description of any alternative solutions or features you've considered" - type: textarea id: additional-context attributes: label: Additional Context description: You can tell us more about your idea, add code snippets or images, etc. placeholder: "Give us more context or screenshots about the feature request here" - type: markdown id: thank-you attributes: value: Thanks for taking the time to fill out this feature request!qutip-5.1.1/.github/ISSUE_TEMPLATE/others.yaml000066400000000000000000000007511474175217300206110ustar00rootroot00000000000000name: 🤔 Others description: Tell us about issues that aren't exactly bugs or features body: - type: textarea id: issue-description attributes: label: Describe the Issue! description: Tell us about your issue. You can include screenshots, code snippets, etc. placeholder: "Please describe the issue here" validations: required: true - type: markdown id: thank-you attributes: value: Thanks for taking the time to fill out this issue!qutip-5.1.1/.github/pull_request_template.md000066400000000000000000000030201474175217300211670ustar00rootroot00000000000000**Checklist** Thank you for contributing to QuTiP! Please make sure you have finished the following tasks before opening the PR. - [ ] Please read [Contributing to QuTiP Development](http://qutip.org/docs/latest/development/contributing.html) - [ ] Contributions to qutip should follow the [pep8 style](https://www.python.org/dev/peps/pep-0008/). You can use [pycodestyle](http://pycodestyle.pycqa.org/en/latest/index.html) to check your code automatically - [ ] Please add tests to cover your changes if applicable. - [ ] If the behavior of the code has changed or new feature has been added, please also update the documentation in the `doc` folder, and the [notebook](https://github.com/qutip/qutip-tutorials). Feel free to ask if you are not sure. - [ ] Include the changelog in a file named: `doc/changes/.` 'type' can be one of the following: feature, bugfix, doc, removal, misc, or deprecation (see [here](http://qutip.org/docs/latest/development/contributing.html#changelog-generation) for more information). Delete this checklist after you have completed all the tasks. If you have not finished them all, you can also open a [Draft Pull Request](https://github.blog/2019-02-14-introducing-draft-pull-requests/) to let the others know this on-going work and keep this checklist in the PR description. **Description** Describe here the proposed change. **Related issues or PRs** Please mention the related issues or PRs here. If the PR fixes an issue, use the keyword fix/fixes/fixed followed by the issue id, e.g. fix #1184qutip-5.1.1/.github/workflows/000077500000000000000000000000001474175217300162705ustar00rootroot00000000000000qutip-5.1.1/.github/workflows/build.yml000066400000000000000000000163401474175217300201160ustar00rootroot00000000000000name: Build wheels, optionally deploy to PyPI on: workflow_dispatch: inputs: confirm_ref: description: "Confirm chosen branch name to deploy to PyPI (optional):" default: "" override_version: description: "Override version number (optional):" default: "" jobs: # The deploy_test job is part of the test of whether we should deploy to PyPI # or test.PyPI. The job will succeed if either the confirmation reference is # empty, 'test' or if the confirmation is the selected branch or tag name. # It will fail if it is nonempty and does not match. All later jobs depend # on this job, so that they will be immediately cancelled if the confirmation # is bad. The dependency is currently necessary (2021-03) because GitHub # Actions does not have a simpler method of cancelling an entire workflow--- # the normal use-case expects to try and run as much as possible despite one # or two failures. deploy_test: name: Verify PyPI deployment confirmation runs-on: ubuntu-latest env: GITHUB_REF: ${{ github.ref }} CONFIRM_REF: ${{ github.event.inputs.confirm_ref }} steps: - name: Compare confirmation to current reference shell: bash run: | [[ -z $CONFIRM_REF || $GITHUB_REF =~ ^refs/(heads|tags)/$CONFIRM_REF$ || $CONFIRM_REF == "test" ]] if [[ $CONFIRM_REF == "test" ]]; then echo "Build and deploy to test.pypi.org." elif [[ -z $CONFIRM_REF ]]; then echo "Build only. Nothing will be uploaded to PyPI." else echo "Full build and deploy. Wheels and source will be uploaded to PyPI." fi build_sdist: name: Build sdist on Ubuntu needs: deploy_test runs-on: ubuntu-latest env: OVERRIDE_VERSION: ${{ github.event.inputs.override_version }} steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v4 name: Install Python with: # For the sdist we should be as conservative as possible with our # Python version. This should be the lowest supported version. This # means that no unsupported syntax can sneak through. python-version: '3.10' - name: Install pip build run: | python -m pip install 'build' - name: Build sdist tarball shell: bash run: | if [[ ! -z "$OVERRIDE_VERSION" ]]; then echo "$OVERRIDE_VERSION" > VERSION; fi # The build package is the reference PEP 517 package builder. All # dependencies are specified by our setup code. python -m build --sdist . # Zip files are not part of PEP 517, so we need to make our own. - name: Create zipfile from tarball shell: bash working-directory: dist run: | # First assert that there is exactly one tarball, and find its name. shopt -s failglob tarball_pattern="*.tar.gz" tarballs=($tarball_pattern) [[ ${#tarballs[@]} == 1 ]] tarball="${tarballs[0]}" # Get the stem and make the zipfile name. stem="${tarball%.tar.gz}" zipfile="${stem}.zip" # Extract the tarball and rezip it. tar -xzf "$tarball" zip "$zipfile" -r "$stem" rm -r "$stem" - uses: actions/upload-artifact@v4 with: name: sdist path: | dist/*.tar.gz dist/*.zip if-no-files-found: error build_wheels: name: Build wheels on ${{ matrix.os }} needs: deploy_test runs-on: ${{ matrix.os }} strategy: matrix: # between 13 and 14, mac changed from intel chip to apple silicon os: [ubuntu-latest, windows-latest, macos-13, macos-latest] env: # Set up wheels matrix. This is CPython 3.10--3.13 for all OS targets. CIBW_BUILD: "cp3{10,11,12,13}-*" # Numpy and SciPy do not supply wheels for i686 or win32 for # Python 3.10+, so we skip those: CIBW_SKIP: "*-musllinux* *-manylinux_i686 *-win32" OVERRIDE_VERSION: ${{ github.event.inputs.override_version }} steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v4 name: Install Python with: # This is about the build environment, not the released wheel version. python-version: '3.10' - name: Install cibuildwheel run: | # cibuildwheel does the heavy lifting for us. Tested on # 2.22, but should be fine at least up to any minor new release. python -m pip install 'cibuildwheel==2.22.*' - name: Build wheels shell: bash run: | # If the version override was specified, then write it the VERSION # file with it. if [[ ! -z "$OVERRIDE_VERSION" ]]; then echo "$OVERRIDE_VERSION" > VERSION; fi python -m cibuildwheel --output-dir wheelhouse - uses: actions/upload-artifact@v4 with: name: wheels-${{ matrix.os }} path: ./wheelhouse/*.whl deploy: name: "Deploy to PyPI if desired" needs: [deploy_test, build_sdist, build_wheels] runs-on: ubuntu-latest env: TWINE_USERNAME: __token__ TWINE_NON_INTERACTIVE: 1 steps: - name: Download build artifacts to local runner uses: actions/download-artifact@v4 with: path: wheels merge-multiple: true # Check that all .whl, .tar.gz and .zip have been properly build # and downloaded. - name: Check wheels run: | ls -R wheels if ! [[ $(ls wheels/*.whl | wc -l) == 16 ]]; then exit 1; fi if ! ls wheels/*.tar.gz 1> /dev/null 2>&1; then exit 1; fi if ! ls wheels/*.zip 1> /dev/null 2>&1; then exit 1; fi - uses: actions/setup-python@v4 name: Install Python with: python-version: '3.10' - name: Verify this is not a dev version shell: bash run: | python -m pip install wheels/*-cp310-cp310-manylinux*.whl python -c 'import qutip; print(qutip.__version__); assert "dev" not in qutip.__version__; assert "+" not in qutip.__version__' # We built the zipfile for convenience distributing to Windows users on # our end, but PyPI only needs the tarball. - name: Upload sdist and wheels to PyPI run: | # The confirmation is tested explicitly in `deploy_test`, so we know # it is either a missing confirmation (so we shouldn't run this job), # 'test' or a valid confirmation. We don't need to retest the value # of the confirmation, beyond checking that one existed. if [ '${{ github.event.inputs.confirm_ref }}' == 'test' ]; then export TWINE_REPOSITORY=testpypi export TWINE_PASSWORD=${{ secrets.TESTPYPI_TOKEN }} elif [ '${{ github.event.inputs.confirm_ref }}' != '' ]; then export TWINE_REPOSITORY=pypi export TWINE_PASSWORD=${{ secrets.PYPI_TOKEN }} else # Exit without deploying echo "Don't update wheels" exit 0 fi echo "Deploy to $TWINE_REPOSITORY" python -m pip install "twine" python -m twine upload --verbose wheels/*.whl wheels/*.tar.gz qutip-5.1.1/.github/workflows/build_documentation.yml000066400000000000000000000041711474175217300230460ustar00rootroot00000000000000name: Build documentation on: [push, pull_request] jobs: build: name: Build documentation runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v4 name: Install Python with: python-version: '3.11' - name: Install documentation dependencies run: | pip install pip --upgrade python -mpip install -r doc/requirements.txt sudo apt-get update sudo apt-get install texlive-full - name: Install QuTiP from GitHub run: | # Build without build isolation so that we use the build # dependencies already installed from doc/requirements.txt. python -m pip install -e .[full] --no-build-isolation --config-settings editable_mode=compat # Install in editable mode so it doesn't matter if we import from # inside the installation directory, otherwise we can get some errors # because we're importing from the wrong location. python -c 'import qutip; qutip.about()' - name: Build PDF documentation working-directory: doc run: | make latexpdf SPHINXOPTS="-W --keep-going -T" # Above flags are: # -W : turn warnings into errors # --keep-going : do not stop after the first error # -T : display a full traceback if a Python exception occurs - name: Upload built PDF files uses: actions/upload-artifact@v4 with: name: qutip_pdf_docs path: doc/_build/latex/* if-no-files-found: error - name: Build HTML documentation working-directory: doc run: | make html SPHINXOPTS="-W --keep-going -T" # Above flags are: # -W : turn warnings into errors # --keep-going : do not stop after the first error # -T : display a full traceback if a Python exception occurs - name: Upload built HTML files uses: actions/upload-artifact@v4 with: name: qutip_html_docs path: doc/_build/html/* if-no-files-found: error qutip-5.1.1/.github/workflows/tests.yml000066400000000000000000000276201474175217300201640ustar00rootroot00000000000000# The name is short because we mostly care how it appears in the pull request # "checks" dialogue box - it looks like # Tests / ubuntu-latest, python-3.9, defaults # or similar. name: Tests on: [push, pull_request] defaults: run: # The slightly odd shell call is to force bash to read .bashrc, which is # necessary for having conda behave sensibly. We use bash as the shell even # on Windows, since we don't run anything much complicated, and it makes # things much simpler. shell: bash -l -e {0} jobs: cases: name: ${{ matrix.os }}, python${{ matrix.python-version }}, ${{ matrix.case-name }} runs-on: ${{ matrix.os }} env: MPLBACKEND: Agg # Explicitly define matplotlib backend for Windows tests strategy: fail-fast: false matrix: os: [ubuntu-latest] # Test other versions of Python in special cases to avoid exploding the # matrix size; make sure to test all supported versions in some form. python-version: ["3.11"] case-name: [defaults] # Version 2 not yet available on conda's default channel condaforge: [1] numpy-build: [""] numpy-requirement: [""] scipy-requirement: [">=1.9"] coverage-requirement: ["==6.5"] # Extra special cases. In these, the new variable defined should always # be a truth-y value (hence 'nomkl: 1' rather than 'mkl: 0'), because # the lack of a variable is _always_ false-y, and the defaults lack all # the special cases. include: - case-name: p313 numpy 2 os: ubuntu-latest python-version: "3.13" numpy-build: ">=2.0.0" numpy-requirement: ">=2.0.0" pypi: 1 - case-name: p310 numpy 1.22 os: ubuntu-latest python-version: "3.10" numpy-build: ">=1.22.0,<1.23.0" numpy-requirement: ">=1.22.0,<1.23.0" scipy-requirement: ">=1.10,<1.11" semidefinite: 1 oldcython: 1 pypi: 1 coveralls: 1 pytest-extra-options: "-W ignore:dep_util:DeprecationWarning -W \"ignore:The 'renderer' parameter of do_3d_projection\"" # Python 3.12 and latest numpy # Use conda-forge to provide Python 3.11 and latest numpy - case-name: p312, numpy fallback os: ubuntu-latest python-version: "3.12" numpy-requirement: ">=1.26,<1.27" scipy-requirement: ">=1.11,<1.12" condaforge: 1 # Install mpi4py to test mpi_pmap # Should be enough to include this in one of the runs includempi: 1 coveralls: 1 # Python 3.10, no mkl, scipy 1.9, numpy 1.23 # Scipy 1.9 did not support cython 3.0 yet. # cython#17234 - case-name: p310 no mkl os: ubuntu-latest python-version: "3.10" numpy-requirement: ">=1.23,<1.24" scipy-requirement: ">=1.9,<1.10" semidefinite: 1 condaforge: 1 oldcython: 1 nomkl: 1 coveralls: 1 pytest-extra-options: "-W ignore:dep_util:DeprecationWarning -W \"ignore:The 'renderer' parameter of do_3d_projection\"" # Mac # Mac has issues with MKL since september 2022. - case-name: macos os: macos-latest python-version: "3.13" numpy-build: ">=2.0.0" numpy-requirement: ">=2.0.0" condaforge: 1 nomkl: 1 - case-name: macos - numpy fallback os: macos-13 # Test on intel cpus python-version: "3.11" numpy-build: ">=2.0.0" numpy-requirement: ">=1.25,<1.26" condaforge: 1 nomkl: 1 coveralls: 1 - case-name: Windows os: windows-latest python-version: "3.13" numpy-build: ">=2.0.0" numpy-requirement: ">=2.0.0" pypi: 1 - case-name: Windows - numpy fallback os: windows-latest python-version: "3.10" numpy-build: ">=2.0.0" numpy-requirement: ">=1.24,<1.25" semidefinite: 1 oldcython: 1 nocython: 1 condaforge: 1 nomkl: 1 coveralls: 1 pytest-extra-options: "-W ignore:dep_util:DeprecationWarning -W \"ignore:The 'renderer' parameter of do_3d_projection\"" steps: - uses: actions/checkout@v4 - uses: conda-incubator/setup-miniconda@v3 with: auto-update-conda: true python-version: ${{ matrix.python-version }} channels: ${{ matrix.condaforge == 1 && 'conda-forge' || 'defaults' }} - name: Install QuTiP and dependencies # In the run, first we handle any special cases. We do this in bash # rather than in the GitHub Actions file directly, because bash gives us # a proper programming language to use. # We install without build isolation so qutip is compiled with the # version of cython, scipy, numpy in the test matrix, not a temporary # version use in the installation virtual environment. run: | # Install the extra requirement python -m pip install pytest>=5.2 pytest-rerunfailures # tests python -m pip install ipython # ipython python -m pip install loky tqdm mpmath # extras python -m pip install "coverage${{ matrix.coverage-requirement }}" chardet python -m pip install pytest-cov coveralls pytest-fail-slow python -m pip install setuptools if [[ "${{ matrix.pypi }}" ]]; then pip install "numpy${{ matrix.numpy-build }}" pip install "scipy${{ matrix.scipy-requirement }}" elif [[ -z "${{ matrix.nomkl }}" ]]; then conda install blas=*=mkl "numpy${{ matrix.numpy-build }}" "scipy${{ matrix.scipy-requirement }}" elif [[ "${{ matrix.os }}" =~ ^windows.*$ ]]; then # Conda doesn't supply forced nomkl builds on Windows, so we rely on # pip not automatically linking to MKL. pip install "numpy${{ matrix.numpy-build }}" "scipy${{ matrix.scipy-requirement }}" else conda install nomkl "numpy${{ matrix.numpy-build }}" "scipy${{ matrix.scipy-requirement }}" fi if [[ -n "${{ matrix.conda-extra-pkgs }}" ]]; then conda install "${{ matrix.conda-extra-pkgs }}" fi if [[ "${{ matrix.includempi }}" ]]; then # Use openmpi because mpich causes problems. Note, environment variable names change in v5 conda install "openmpi<5" mpi4py fi if [[ "${{ matrix.oldcython }}" ]]; then python -m pip install cython==0.29.36 filelock matplotlib==3.5 else python -m pip install cython filelock fi python -m pip install -e . -v --no-build-isolation if [[ "${{ matrix.nocython }}" ]]; then python -m pip uninstall cython -y fi if [[ "${{ matrix.pypi }}" ]]; then python -m pip install "numpy${{ matrix.numpy-requirement }}" elif [[ -z "${{ matrix.nomkl }}" ]]; then conda install "numpy${{ matrix.numpy-requirement }}" elif [[ "${{ matrix.os }}" =~ ^windows.*$ ]]; then python -m pip install "numpy${{ matrix.numpy-requirement }}" else conda install nomkl "numpy${{ matrix.numpy-requirement }}" fi if [[ -n "${{ matrix.semidefinite }}" ]]; then python -m pip install cvxpy>=1.0 cvxopt fi python -m pip install matplotlib>=1.2.1 # graphics - name: Package information run: | conda list python -c "import qutip; qutip.about()" python -c "import qutip; print(qutip.settings)" - name: Environment information run: | uname -a if [[ "ubuntu-latest" == "${{ matrix.os }}" ]]; then hostnamectl lscpu free -h fi - name: Run tests # If our tests are running for longer than an hour, _something_ is wrong # somewhere. The GitHub default is 6 hours, which is a bit long to wait # to see if something hung. timeout-minutes: 60 run: | export MKL_VERBOSE=2 if [[ -n "${{ matrix.openmp }}" ]]; then # Force OpenMP runs to use more threads, even if there aren't # actually that many CPUs. We have to check any dispatch code is # truly being executed. export QUTIP_NUM_PROCESSES=2 fi if [[ "${{ matrix.includempi }}" ]]; then # By default, the max. number of allowed worker processes in openmpi is # (number of physical cpu cores) - 1. # We only have 2 physical cores, but we want to test mpi_pmap with 2 workers. export OMPI_MCA_rmaps_base_oversubscribe=true fi pytest -Werror --strict-config --strict-markers --fail-slow=300 --durations=0 --durations-min=1.0 --verbosity=1 --cov=qutip --cov-report= --color=yes ${{ matrix.pytest-extra-options }} qutip/tests # Above flags are: # -Werror # treat warnings as errors # --strict-config # error out if the configuration file is not parseable # --strict-markers # error out if a marker is used but not defined in the # configuration file # --timeout=300 # error any individual test that goes longer than the given time # --durations=0 --durations-min=1.0 # at the end, show a list of all the tests that took longer than a # second to run # --verbosity=1 # turn the verbosity up so pytest prints the names of the tests # it's currently working on # --cov=qutip # limit coverage reporting to code that's within the qutip package # --cov-report= # don't print the coverage report to the terminal---it just adds # cruft, and we're going to upload the .coverage file to Coveralls # --color=yes # force coloured output in the terminal - name: Upload to Coveralls if: ${{ matrix.coveralls }} env: GITHUB_TOKEN: ${{ secrets.github_token }} COVERALLS_FLAG_NAME: ${{ matrix.os }}-${{ matrix.python-version }}-${{ matrix.case-name }} COVERALLS_PARALLEL: true run: coveralls --service=github towncrier-check: name: Verify Towncrier entry added runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Install Towncrier run: | python -m venv towncrier_check source towncrier_check/bin/activate python -m pip install towncrier - name: Verify Towncrier entry added if: github.event_name == 'pull_request' env: BASE_BRANCH: ${{ github.base_ref }} run: | # Fetch the pull request' base branch so towncrier will be able to # compare the current branch with the base branch. # Source: https://github.com/actions/checkout/#fetch-all-branches. git fetch --no-tags origin +refs/heads/${BASE_BRANCH}:refs/remotes/origin/${BASE_BRANCH} source towncrier_check/bin/activate towncrier check --compare-with origin/${BASE_BRANCH} towncrier build --version "$(cat VERSION)" --draft finalise: name: Finalise coverage reporting needs: cases runs-on: ubuntu-latest container: python:3-slim steps: - name: Finalise coverage reporting env: GITHUB_TOKEN: ${{ secrets.github_token }} run: | python -m pip install coveralls coveralls --service=github --finish qutip-5.1.1/.gitignore000066400000000000000000000006211474175217300146620ustar00rootroot00000000000000*~ *.py[cod] *.so .DS_Store .f2py_f2cmap .idea/ .vscode/ # Packages *.egg .eggs *.egg-info dist build eggs parts bin var sdist develop-eggs .installed.cfg lib lib64 qutip/version.py qutip/__config__.py rhs*.pyx qutip/cy/*.c *.cpp !qutip/core/data/src/*.cpp *.dat qutip/core/*.h qutip/**/*.html qutip/solver/ode/*.c *.qo benchmark/benchmark_data.js *-tasks.txt *compiled_coeff* result_images/ qutip-5.1.1/.mailmap000066400000000000000000000026111474175217300143140ustar00rootroot00000000000000Markus Baden Ivan Carvalho Ben Criger Simon Cross Kevin Fischer Eric Giguère Canoming Canoming <36161480+Canoming@users.noreply.github.com> Christopher Granade Christopher Granade Arne Grimsmo Stefan Krastanov Neill Lambert Boxi Li Jake Lishman Paul Nation Paul Nation Alexander Pitchford Alexander Pitchford Alexander James Pitchford Nicolas Quesada Tarun Raheja Tarun Raheja <31796197+tehruhn@users.noreply.github.com> Sidhant Saraogi Sidhant Saraogi sid Anubhav Vardhan Lucas Verney Florestan Ziem qutip-5.1.1/.readthedocs.yaml000066400000000000000000000005171474175217300161250ustar00rootroot00000000000000# .readthedocs.yaml # Read the Docs configuration file # See https://docs.readthedocs.io/en/stable/config-file/v2.html for details version: 2 formats: - pdf build: os: ubuntu-22.04 tools: python: "mambaforge-4.10" conda: environment: doc/rtd-environment.yml sphinx: configuration: doc/conf.py fail_on_warning: truequtip-5.1.1/CITATION.bib000066400000000000000000000027121474175217300145650ustar00rootroot00000000000000@misc{qutip5, title = {{QuTiP} 5: The Quantum Toolbox in {Python}}, author = { Lambert, Neill and Giguère, Eric and Menczel, Paul and Li, Boxi and Hopf, Patrick and SuĂĄrez, Gerardo and Gali, Marc and Lishman, Jake and Gadhvi, Rushiraj and Agarwal, Rochisha and Galicia, Asier and Shammah, Nathan and Nation, Paul D. and Johansson, J. R. and Ahmed, Shahnawaz and Cross, Simon and Pitchford, Alexander and Nori, Franco }, year={2024}, eprint={2412.04705}, archivePrefix={arXiv}, primaryClass={quant-ph}, url={https://arxiv.org/abs/2412.04705}, doi={10.48550/arXiv.2412.04705}, } @article{qutip2, doi = {10.1016/j.cpc.2012.11.019}, url = {https://doi.org/10.1016/j.cpc.2012.11.019}, year = {2013}, month = {apr}, publisher = {Elsevier {BV}}, volume = {184}, number = {4}, pages = {1234--1240}, author = {J.R. Johansson and P.D. Nation and F. Nori}, title = {{QuTiP} 2: A {P}ython framework for the dynamics of open quantum systems}, journal = {Computer Physics Communications} } @article{qutip1, doi = {10.1016/j.cpc.2012.02.021}, url = {https://doi.org/10.1016/j.cpc.2012.02.021}, year = {2012}, month = {aug}, publisher = {Elsevier {BV}}, volume = {183}, number = {8}, pages = {1760--1772}, author = {J.R. Johansson and P.D. Nation and F. Nori}, title = {{QuTiP}: An open-source {P}ython framework for the dynamics of open quantum systems}, journal = {Computer Physics Communications} } qutip-5.1.1/CODE_OF_CONDUCT.md000066400000000000000000000037641474175217300155040ustar00rootroot00000000000000# Contributor Covenant Code of Conduct As contributors and maintainers of this project, and in the interest of fostering an open and welcoming community, we pledge to respect all people who contribute through reporting issues, posting feature requests, updating documentation, submitting pull requests or patches, and other activities. We are committed to making participation in this project a harassment-free experience for everyone, regardless of level of experience, gender, gender identity and expression, sexual orientation, disability, personal appearance, body size, race, ethnicity, age, religion, or nationality. Examples of unacceptable behavior by participants include: * The use of sexualized language or imagery * Personal attacks * Trolling or insulting/derogatory comments * Public or private harassment * Publishing other's private information, such as physical or electronic addresses, without explicit permission * Other unethical or unprofessional conduct Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct. By adopting this Code of Conduct, project maintainers commit themselves to fairly and consistently applying these principles to every aspect of managing this project. Project maintainers who do not follow or enforce the Code of Conduct may be permanently removed from the project team. This code of conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by opening an issue or contacting one or more of the project maintainers. This Code of Conduct is adapted from the Contributor Covenant , version 1.2.0, available at https://www.contributor-covenant.org/version/1/2/0/code-of-conduct.html [homepage]: https://contributor-covenant.org [version]: https://contributor-covenant.org/version/1/2/ qutip-5.1.1/CONTRIBUTING.md000066400000000000000000000013251474175217300151250ustar00rootroot00000000000000# Contributing to QuTiP Development You are most welcome to contribute to QuTiP development by forking this repository and sending pull requests, or filing bug reports at the [issues page](https://github.com/qutip/qutip/issues). You can also help out with users' questions, or discuss proposed changes in the [QuTiP discussion group](https://groups.google.com/g/qutip). All code contributions are acknowledged in the [contributors](https://qutip.readthedocs.io/en/stable/contributors.html) section in the documentation. For more information, including technical advice, please see the ["contributing to QuTiP development" section of the documentation](https://qutip.readthedocs.io/en/stable/development/contributing.html). qutip-5.1.1/LICENSE.txt000066400000000000000000000030021474175217300145110ustar00rootroot00000000000000Copyright (c) 2011 to 2022 inclusive, QuTiP developers and contributors. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. qutip-5.1.1/MANIFEST.in000066400000000000000000000004541474175217300144340ustar00rootroot00000000000000include README.md include LICENSE.txt include VERSION include requirements.txt include CITATION.bib include pyproject.toml recursive-include qutip *.pyx recursive-include qutip *.pxd recursive-include qutip *.hpp recursive-include qutip *.cpp recursive-include qutip *.ini recursive-include qutip *.hqutip-5.1.1/README.md000066400000000000000000000145651474175217300141650ustar00rootroot00000000000000QuTiP: Quantum Toolbox in Python ================================ [A. Pitchford](https://github.com/ajgpitch), [C. Granade](https://github.com/cgranade), [A. Grimsmo](https://github.com/arnelg), [N. Shammah](https://github.com/nathanshammah), [S. Ahmed](https://github.com/quantshah), [N. Lambert](https://github.com/nwlambert), [E. Giguère](https://github.com/ericgig), [B. Li](https://github.com/boxili), [J. Lishman](https://github.com/jakelishman), [S. Cross](https://github.com/hodgestar), [A. Galicia](https://github.com/AGaliciaMartinez), [P. Menczel](https://github.com/pmenczel), [P. Hopf](https://github.com/flowerthrower/), [P. D. Nation](https://github.com/nonhermitian), and [J. R. Johansson](https://github.com/jrjohansson) [![Build Status](https://github.com/qutip/qutip/actions/workflows/tests.yml/badge.svg?branch=master)](https://github.com/qutip/qutip/actions/workflows/tests.yml) [![Coverage Status](https://img.shields.io/coveralls/qutip/qutip.svg?logo=Coveralls)](https://coveralls.io/r/qutip/qutip) [![Maintainability](https://api.codeclimate.com/v1/badges/df502674f1dfa1f1b67a/maintainability)](https://codeclimate.com/github/qutip/qutip/maintainability) [![license](https://img.shields.io/badge/license-New%20BSD-blue.svg)](https://opensource.org/licenses/BSD-3-Clause) [![PyPi Downloads](https://img.shields.io/pypi/dm/qutip?label=downloads%20%7C%20pip&logo=PyPI)](https://pypi.org/project/qutip) [![Conda-Forge Downloads](https://img.shields.io/conda/dn/conda-forge/qutip?label=downloads%20%7C%20conda&logo=Conda-Forge)](https://anaconda.org/conda-forge/qutip) QuTiP is open-source software for simulating the dynamics of closed and open quantum systems. It uses the excellent Numpy, Scipy, and Cython packages as numerical backends, and graphical output is provided by Matplotlib. QuTiP aims to provide user-friendly and efficient numerical simulations of a wide variety of quantum mechanical problems, including those with Hamiltonians and/or collapse operators with arbitrary time-dependence, commonly found in a wide range of physics applications. QuTiP is freely available for use and/or modification, and it can be used on all Unix-based platforms and on Windows. Being free of any licensing fees, QuTiP is ideal for exploring quantum mechanics in research as well as in the classroom. Support ------- [![Unitary Fund](https://img.shields.io/badge/Supported%20By-UNITARY%20FUND-brightgreen.svg?style=flat)](https://unitary.fund) [![Powered by NumFOCUS](https://img.shields.io/badge/powered%20by-NumFOCUS-orange.svg?style=flat&colorA=E1523D&colorB=007D8A)](https://numfocus.org) We are proud to be affiliated with [Unitary Fund](https://unitary.fund) and [numFOCUS](https://numfocus.org). We are grateful for [Nori's lab](https://dml.riken.jp/) at RIKEN and [Blais' lab](https://www.physique.usherbrooke.ca/blais/) at the Institut Quantique for providing developer positions to work on QuTiP. We also thank Google for supporting us by financing GSoC students to work on the QuTiP as well as [other supporting organizations](https://qutip.org/#supporting-organizations) that have been supporting QuTiP over the years. Installation ------------ [![Pip Package](https://img.shields.io/pypi/v/qutip?logo=PyPI)](https://pypi.org/project/qutip) [![Conda-Forge Package](https://img.shields.io/conda/vn/conda-forge/qutip?logo=Conda-Forge)](https://anaconda.org/conda-forge/qutip) QuTiP is available on both `pip` and `conda` (the latter in the `conda-forge` channel). You can install QuTiP from `pip` by doing ```bash pip install qutip ``` to get the minimal installation. You can instead use the target `qutip[full]` to install QuTiP with all its optional dependencies. For more details, including instructions on how to build from source, see [the detailed installation guide in the documentation](https://qutip.readthedocs.io/en/stable/installation.html). All back releases are also available for download in the [releases section of this repository](https://github.com/qutip/qutip/releases), where you can also find per-version changelogs. For the most complete set of release notes and changelogs for historic versions, see the [changelog](https://qutip.readthedocs.io/en/stable/changelog.html) section in the documentation. The pre-release of QuTiP 5.0 is available on PyPI and can be installed using pip: ```bash pip install --pre qutip ``` This version breaks compatibility with QuTiP 4.7 in many small ways. Please see the [changelog](https://github.com/qutip/qutip/blob/master/doc/changelog.rst) for a list of changes, new features and deprecations. This version should be fully working. If you find any bugs, confusing documentation or missing features, please create a GitHub issue. Documentation ------------- [![Documentation Status - Latest](https://readthedocs.org/projects/qutip/badge/?version=latest)](https://qutip.readthedocs.io/en/latest/?badge=latest) The documentation for the latest [stable release](https://qutip.readthedocs.io/en/latest/) and the [master](https://qutip.readthedocs.io/en/master/) branch is available for reading on Read The Docs. The documentation for official releases, in HTML and PDF formats, can be found in the [documentation section of the QuTiP website](https://qutip.org/documentation.html). The latest development documentation is available in this repository in the `doc` folder. A [selection of demonstration notebooks is available](https://qutip.org/tutorials.html), which demonstrate some of the many features of QuTiP. These are stored in the [qutip/qutip-tutorials repository](https://github.com/qutip/qutip-tutorials) here on GitHub. Contribute ---------- You are most welcome to contribute to QuTiP development by forking this repository and sending pull requests, or filing bug reports at the [issues page](https://github.com/qutip/qutip/issues). You can also help out with users' questions, or discuss proposed changes in the [QuTiP discussion group](https://groups.google.com/g/qutip). All code contributions are acknowledged in the [contributors](https://qutip.readthedocs.io/en/stable/contributors.html) section in the documentation. For more information, including technical advice, please see the ["contributing to QuTiP development" section of the documentation](https://qutip.readthedocs.io/en/stable/development/contributing.html). Citing QuTiP ------------ If you use QuTiP in your research, please cite the original QuTiP papers that are available [here](https://dml.riken.jp/?s=QuTiP). qutip-5.1.1/VERSION000066400000000000000000000000061474175217300137370ustar00rootroot000000000000005.1.1 qutip-5.1.1/doc/000077500000000000000000000000001474175217300134405ustar00rootroot00000000000000qutip-5.1.1/doc/.gitattributes000066400000000000000000000000751474175217300163350ustar00rootroot00000000000000# Force Windows batch files to use \r\n. *.bat text eol=crlf qutip-5.1.1/doc/.gitignore000066400000000000000000000001101474175217300154200ustar00rootroot00000000000000.DS_Store *.pyc *.pyx *.dat *.qu *.dat *~ _build _images gallery/build qutip-5.1.1/doc/LICENSE_cc-by-3.0.txt000066400000000000000000000437561474175217300166550ustar00rootroot00000000000000THE WORK (AS DEFINED BELOW) IS PROVIDED UNDER THE TERMS OF THIS CREATIVE COMMONS PUBLIC LICENSE ("CCPL" OR "LICENSE"). 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If the standard suite of rights granted under applicable copyright law includes additional rights not granted under this License, such additional rights are deemed to be included in the License; this License is not intended to restrict the license of any rights under applicable law. qutip-5.1.1/doc/Makefile000066400000000000000000000126701474175217300151060ustar00rootroot00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line. SPHINXOPTS = SPHINXBUILD = sphinx-build PAPER = BUILDDIR = _build # Internal variables. 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For pre-built documentation, see https://www.qutip.org/documentation.html Building -------- The main Python requirements for the documentation are `sphinx`, `sphinx-gallery`, `sphinx_rtd_theme`, `numpydoc` and `ipython`. You should build or install the version of QuTiP you want to build the documentation against in the same environment. You will also need a sensible copy of `make`, and if you want to build the LaTeX documentation then also a `pdflatex` distribution. As of 2021-04-20, the `conda` recipe for `sphinx_rtd_theme` is rather old compared to the `pip` version, so it's recommended to use a mostly `pip`-managed environment to do the documentation build. The simplest way to get a functional build environment is to use the `requirements.txt` file in this repository, which completely defines a known-good `pip` environment (tested on Python 3.8, but not necessarily limited to it). If you typically use conda, the way to do this is ```bash $ conda create -n qutip-doc-build python=3.8 $ conda activate qutip-doc-build $ pip install -r /path/to/qutip/doc/requirements.txt ``` You will also need to build or install the main QuTiP library in the same environment. If you simply want to build the documentation without editing the main library, you can install a release version of QuTiP with `pip install qutip`. Otherwise, refer to [the main repository](https://github.com/qutip/qutip) for the current process to build from source. You need to have the optional QuTiP dependency `Cython` to build the documentation, but this is included in this repository's `requirements.txt` so you do not need to do anything separately. After you have done this, you can effect the build with `make`. The targets you might want are `html`, `latexpdf` and `clean`, which build the HTML pages, build the PDFs, and delete all built files respectively. For example, to build the HTML files only, use ```bash $ make html ``` *Note (2021-04-20):* the documentation build is currently broken on Windows due to incompatibilities in the main library in multiprocessing components. Writing User Guides ------------------- The user guide provides an overview of QuTiP's functionality. The guide is composed of individual reStructuredText (`.rst`) files which each get rendered as a webpage. Each page typically tackles one area of functionality. To learn more about how to write `.rst` files, it is useful to follow the [Sphinx Guide](https://www.sphinx-doc.org/en/master/usage/index.html). The documentation build also utilizes a number of [Sphinx Extensions](https://www.sphinx-doc.org/en/master/usage/extensions/index.html) including but not limited to [doctest](https://www.sphinx-doc.org/en/master/usage/extensions/doctest.html), [autodoc](https://www.sphinx-doc.org/en/master/usage/extensions/autodoc.html), [sphinx gallery](https://sphinx-gallery.github.io/stable/index.html), [plot](https://matthew-brett.github.io/nb2plots/nbplots.html#module-nb2plots.nbplots). Additional extensions can be configured in the `conf.py` file. Tests can also be run on examples in the documentation using the doctest extension and plots are generated using the `plot` directive. For more specific guidelines on how to incorporate code examples into the guide, refer to (insert reference). qutip-5.1.1/doc/apidoc/000077500000000000000000000000001474175217300146775ustar00rootroot00000000000000qutip-5.1.1/doc/apidoc/apidoc.rst000066400000000000000000000006001474175217300166640ustar00rootroot00000000000000.. _apidoc: ***************** API documentation ***************** This chapter contains automatically generated API documentation, including a complete list of QuTiP's public classes and functions. .. toctree:: :maxdepth: 3 quantumobject.rst time_dep.rst solver.rst environments.rst heom.rst piqs.rst visualization.rst utilities.rst experimental.rst qutip-5.1.1/doc/apidoc/environments.rst000066400000000000000000000024701474175217300201630ustar00rootroot00000000000000************ Environments ************ Bosonic Environments -------------------- .. autoclass:: qutip.core.BosonicEnvironment :members: .. autoclass:: qutip.core.DrudeLorentzEnvironment :members: :inherited-members: :show-inheritance: :exclude-members: from_correlation_function, from_power_spectrum, from_spectral_density .. autoclass:: qutip.core.UnderDampedEnvironment :members: :inherited-members: :show-inheritance: :exclude-members: from_correlation_function, from_power_spectrum, from_spectral_density .. autoclass:: qutip.core.OhmicEnvironment :members: :inherited-members: :show-inheritance: :exclude-members: from_correlation_function, from_power_spectrum, from_spectral_density .. autoclass:: qutip.core.CFExponent :members: .. autoclass:: qutip.core.ExponentialBosonicEnvironment :members: :show-inheritance: .. autofunction:: qutip.core.environment.system_terminator Fermionic Environments ---------------------- .. autoclass:: qutip.core.FermionicEnvironment :members: :exclude-members: from_correlation_function, from_power_spectrum, from_spectral_density .. autoclass:: qutip.core.LorentzianEnvironment :members: :show-inheritance: .. autoclass:: qutip.core.ExponentialFermionicEnvironment :members: :show-inheritance: qutip-5.1.1/doc/apidoc/experimental.rst000066400000000000000000000015741474175217300201350ustar00rootroot00000000000000 ************ Experimental ************ .. note:: Functions here are untested and under-documented. Continuous Variables -------------------- .. automodule:: qutip.continuous_variables :members: correlation_matrix, covariance_matrix, correlation_matrix_field, correlation_matrix_quadrature, wigner_covariance_matrix, logarithmic_negativity Distribution functions ---------------------- .. autoclass:: qutip.distributions.Distribution :members: .. Docstrings are empty... .. autoclass:: qutip.distributions.WignerDistribution :members: .. autoclass:: qutip.distributions.QDistribution :members: .. autoclass:: qutip.distributions.TwoModeQuadratureCorrelation :members: .. autoclass:: qutip.distributions.HarmonicOscillatorWaveFunction :members: .. autoclass:: qutip.distributions.HarmonicOscillatorProbabilityFunction :members: qutip-5.1.1/doc/apidoc/heom.rst000066400000000000000000000020531474175217300163610ustar00rootroot00000000000000******************************** Hierarchical Equations of Motion ******************************** HEOM Solvers ------------ .. automodule:: qutip.solver.heom :members: heomsolve .. autoclass:: qutip.solver.heom.HEOMSolver :members: .. autoclass:: qutip.solver.heom.HSolverDL :members: .. autoclass:: qutip.solver.heom.HierarchyADOs :members: .. autoclass:: qutip.solver.heom.HierarchyADOsState :members: .. autoclass:: qutip.solver.heom.HEOMResult :members: Baths ----- .. autoclass:: qutip.solver.heom.BathExponent :members: .. autoclass:: qutip.solver.heom.Bath :members: .. autoclass:: qutip.solver.heom.BosonicBath :members: .. autoclass:: qutip.solver.heom.DrudeLorentzBath :members: .. autoclass:: qutip.solver.heom.DrudeLorentzPadeBath :members: .. autoclass:: qutip.solver.heom.UnderDampedBath :members: .. autoclass:: qutip.solver.heom.FermionicBath :members: .. autoclass:: qutip.solver.heom.LorentzianBath :members: .. autoclass:: qutip.solver.heom.LorentzianPadeBath :members: qutip-5.1.1/doc/apidoc/piqs.rst000066400000000000000000000011001474175217300163750ustar00rootroot00000000000000************************ Permutational Invariance ************************ .. autoclass:: qutip.piqs.piqs.Dicke :members: .. autoclass:: qutip.piqs.piqs.Pim :members: .. automodule:: qutip.piqs.piqs :members: num_dicke_states, num_dicke_ladders, num_tls, isdiagonal, dicke_blocks, dicke_blocks_full, dicke_function_trace, purity_dicke, entropy_vn_dicke, state_degeneracy, m_degeneracy, energy_degeneracy, ap, am, spin_algebra, jspin, collapse_uncoupled, dicke_basis, dicke, excited, superradiant, css, ghz, ground, identity_uncoupled, block_matrix, tau_column, qutip-5.1.1/doc/apidoc/quantumobject.rst000066400000000000000000000073631474175217300203230ustar00rootroot00000000000000.. _api_qobj: *************** Quantum Objects *************** .. _classes-qobj: Qobj ---- .. autoclass:: qutip.core.qobj.Qobj :members: :special-members: __call__ .. automodule:: qutip.core.properties :members: issuper, isoper, isoperket, isoperbra, isket, isbra, isherm CoreOptions ----------- .. autoclass:: qutip.core.options.CoreOptions :members: ******************************** Creation of States and Operators ******************************** Quantum States -------------- .. automodule:: qutip.core.states :members: basis, bell_state, bra, coherent, coherent_dm, fock, fock_dm, ghz_state, maximally_mixed_dm, ket, ket2dm, phase_basis, projection, qutrit_basis, singlet_state, spin_state, spin_coherent, state_number_enumerate, state_number_index, state_index_number, state_number_qobj, thermal_dm, triplet_states, w_state, zero_ket Quantum Operators ----------------- .. automodule:: qutip.core.operators :members: charge, commutator, create, destroy, displace, fcreate, fdestroy, jmat, num, qeye, identity, momentum, phase, position, qdiags, qutrit_ops, qzero, sigmam, sigmap, sigmax, sigmay, sigmaz, spin_Jx, spin_Jy, spin_Jz, spin_Jm, spin_Jp, squeeze, squeezing, tunneling, qeye_like, qzero_like Quantum Gates ------------- .. automodule:: qutip.core.gates :members: rx, ry, rz, sqrtnot, snot, phasegate, qrot, cy_gate, cz_gate, s_gate, t_gate, cs_gate, ct_gate, cphase, cnot, csign, berkeley, swapalpha, swap, iswap, sqrtswap, sqrtiswap, fredkin, molmer_sorensen, toffoli, hadamard_transform, qubit_clifford_group, globalphase Energy Restricted Operators --------------------------- .. automodule:: qutip.core.energy_restricted :members: enr_state_dictionaries, enr_thermal_dm, enr_fock, enr_destroy, enr_identity .. _api-rand: Random Operators and States --------------------------- .. automodule:: qutip.random_objects :members: rand_dm, rand_herm, rand_ket, rand_stochastic, rand_unitary, rand_super, rand_super_bcsz, rand_kraus_map ******************** Manipulation of Qobj ******************** Tensor ------ .. automodule:: qutip.core.tensor :members: tensor, super_tensor, composite, tensor_contract .. automodule:: qutip.core.qobj :members: ptrace .. automodule:: qutip.partial_transpose :members: partial_transpose Superoperators and Liouvillians ------------------------------- .. automodule:: qutip.core.superoperator :members: operator_to_vector, vector_to_operator, liouvillian, spost, spre, sprepost, lindblad_dissipator Superoperator Representations ----------------------------- .. automodule:: qutip.core.superop_reps :members: kraus_to_choi, kraus_to_super, to_choi, to_chi, to_super, to_kraus, to_stinespring :undoc-members: Operators and Superoperator Dimensions -------------------------------------- .. automodule:: qutip.core.dimensions :members: to_tensor_rep, from_tensor_rep Miscellaneous ------------- .. automodule:: qutip.simdiag :members: simdiag ************************* Extracting data from Qobj ************************* Expectation Values ------------------ .. automodule:: qutip.core.expect :members: expect, variance Entropy Functions ----------------- .. automodule:: qutip.entropy :members: concurrence, entropy_conditional, entropy_linear, entropy_mutual, entropy_relative, entropy_vn Density Matrix Metrics ---------------------- .. automodule:: qutip.core.metrics :members: fidelity, tracedist, bures_dist, bures_angle, hellinger_dist, hilbert_dist, average_gate_fidelity, process_fidelity, unitarity, dnorm Measurement of quantum states ----------------------------- .. automodule:: qutip.measurement :members: measure, measure_povm, measure_observable, measurement_statistics, measurement_statistics_observable, measurement_statistics_povm qutip-5.1.1/doc/apidoc/solver.rst000066400000000000000000000131551474175217300167500ustar00rootroot00000000000000*************************** Dynamics and Time-Evolution *************************** SchrĂśdinger Equation -------------------- .. automodule:: qutip.solver.sesolve :members: sesolve .. automodule:: qutip.solver.krylovsolve :members: krylovsolve .. autoclass:: qutip.solver.sesolve.SESolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator Master Equation --------------- .. automodule:: qutip.solver.mesolve :members: mesolve .. autoclass:: qutip.solver.mesolve.MESolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator .. autoclass:: qutip.solver.result.Result :members: :inherited-members: :exclude-members: add_processor, add Monte Carlo Evolution --------------------- .. automodule:: qutip.solver.mcsolve :members: mcsolve .. autoclass:: qutip.solver.mcsolve.MCSolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator .. automodule:: qutip.solver.nm_mcsolve :members: nm_mcsolve .. autoclass:: qutip.solver.nm_mcsolve.NonMarkovianMCSolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator .. autoclass:: qutip.solver.multitrajresult.McResult :show-inheritance: :members: .. autoclass:: qutip.solver.multitrajresult.NmmcResult :show-inheritance: :members: Bloch-Redfield Master Equation ------------------------------ .. automodule:: qutip.solver.brmesolve :members: brmesolve .. autoclass:: qutip.solver.brmesolve.BRSolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator Floquet States and Floquet-Markov Master Equation ------------------------------------------------- .. automodule:: qutip.solver.floquet :members: fmmesolve, fsesolve, floquet_tensor .. autoclass:: qutip.solver.floquet.FMESolver :members: :inherited-members: :show-inheritance: :exclude-members: add_integrator .. autoclass:: qutip.solver.floquet.FloquetBasis :members: Stochastic SchrĂśdinger Equation and Master Equation --------------------------------------------------- .. automodule:: qutip.solver.stochastic :members: ssesolve, smesolve .. autoclass:: qutip.solver.stochastic.SMESolver :members: :inherited-members: :exclude-members: add_integrator .. autoclass:: qutip.solver.stochastic.SSESolver :members: :inherited-members: :exclude-members: add_integrator .. autoclass:: qutip.solver.multitrajresult.MultiTrajResult :members: :inherited-members: :exclude-members: add_processor, add, add_end_condition Non-Markovian Solvers --------------------- .. automodule:: qutip.solver.nonmarkov.transfertensor :members: ttmsolve .. _api-ode: Integrator ---------- Different ODE solver from many sources (scipy, diffrax, home made, etc.) used by qutip solvers. Their options are added to the solver options: .. autoclass:: qutip.solver.integrator.scipy_integrator.IntegratorScipyAdams :members: options .. autoclass:: qutip.solver.integrator.scipy_integrator.IntegratorScipyBDF :members: options .. autoclass:: qutip.solver.integrator.scipy_integrator.IntegratorScipylsoda :members: options .. autoclass:: qutip.solver.integrator.scipy_integrator.IntegratorScipyDop853 :members: options .. autoclass:: qutip.solver.integrator.qutip_integrator.IntegratorVern7 :members: options .. autoclass:: qutip.solver.integrator.qutip_integrator.IntegratorVern9 :members: options .. autoclass:: qutip.solver.integrator.qutip_integrator.IntegratorDiag :members: options .. autoclass:: qutip.solver.integrator.krylov.IntegratorKrylov :members: options .. _classes-sode: Stochastic Integrator --------------------- .. autoclass:: qutip.solver.sode.rouchon.RouchonSODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.EulerSODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.Milstein_SODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.Taylor1_5_SODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.Implicit_Milstein_SODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.Implicit_Taylor1_5_SODE :members: options .. autoclass:: qutip.solver.sode.sode.PlatenSODE :members: options .. autoclass:: qutip.solver.sode.itotaylor.Explicit1_5_SODE :members: options .. autoclass:: qutip.solver.sode.sode.PredCorr_SODE :members: options Parallelization --------------- .. automodule:: qutip.solver.parallel :members: parallel_map, serial_map, loky_pmap, mpi_pmap *********** Propagators *********** .. automodule:: qutip.solver.propagator :members: propagator, propagator_steadystate :undoc-members: .. autoclass:: qutip.solver.propagator.Propagator :members: :inherited-members: :special-members: __call__ ************************ Other dynamics functions ************************ Correlation Functions --------------------- .. automodule:: qutip.solver.correlation :members: correlation_2op_1t, correlation_2op_2t, correlation_3op_1t, correlation_3op_2t, correlation_3op, coherence_function_g1, coherence_function_g2 .. automodule:: qutip.solver.spectrum :members: spectrum, spectrum_correlation_fft Steady-state Solvers -------------------- .. automodule:: qutip.solver.steadystate :members: steadystate, pseudo_inverse, steadystate_floquet :undoc-members: Scattering in Quantum Optical Systems ------------------------------------- .. automodule:: qutip.solver.scattering :members: temporal_basis_vector, temporal_scattered_state, scattering_probability :undoc-members: qutip-5.1.1/doc/apidoc/time_dep.rst000066400000000000000000000006251474175217300172220ustar00rootroot00000000000000*********************************** Constructing time dependent systems *********************************** QobjEvo ------- .. autoclass:: qutip.core.cy.qobjevo.QobjEvo :members: :special-members: __call__ Coefficient ----------- .. automodule:: qutip.core.coefficient :members: coefficient CompilationOptions ------------------ .. autoclass:: qutip.core.coefficient.CompilationOptions qutip-5.1.1/doc/apidoc/utilities.rst000066400000000000000000000010331474175217300174410ustar00rootroot00000000000000Utility Functions ================= .. _utilities: Utility Functions ----------------- .. automodule:: qutip.utilities :members: n_thermal, clebsch, convert_unit, iterated_fit .. _fileio: File I/O Functions ------------------ .. automodule:: qutip.fileio :members: file_data_read, file_data_store, qload, qsave .. _ipython: IPython Notebook Tools ---------------------- .. automodule:: qutip.ipynbtools :members: version_table .. _misc: Miscellaneous ------------- .. automodule:: qutip.about :members: about qutip-5.1.1/doc/apidoc/visualization.rst000066400000000000000000000021271474175217300203340ustar00rootroot00000000000000*************************** Visualization and animation *************************** Bloch sphere ------------ .. autoclass:: qutip.bloch.Bloch :members: Graphs and Visualization ------------------------ .. automodule:: qutip.visualization :members: hinton, matrix_histogram, plot_energy_levels, plot_fock_distribution, plot_wigner, sphereplot, plot_schmidt, plot_qubism, plot_expectation_values, plot_wigner_sphere, plot_spin_distribution :undoc-members: .. automodule:: qutip.animation :members: anim_hinton, anim_matrix_histogram, anim_fock_distribution, anim_wigner, anim_sphereplot, anim_schmidt, anim_qubism, anim_wigner_sphere, anim_spin_distribution .. automodule:: qutip.matplotlib_utilities :members: wigner_cmap, complex_phase_cmap Pseudoprobability Functions --------------------------- .. automodule:: qutip.wigner :members: qfunc, spin_q_function, spin_wigner, wigner .. autoclass:: qutip.QFunc :members: Quantum Process Tomography -------------------------- .. automodule:: qutip.tomography :members: qpt, qpt_plot, qpt_plot_combined :undoc-members: qutip-5.1.1/doc/biblio.rst000066400000000000000000000114001474175217300154260ustar00rootroot00000000000000.. _biblo: Bibliography ============ .. Note: first letter of entries must be escaped to avoid rst parsing as enumerated list https://docutils.sourceforge.io/docs/ref/rst/restructuredtext.html#enumerated-lists .. [BCSZ08] \W. Bruzda, V. Cappellini, H.-J. Sommers, K. Ĺťyczkowski, *Random Quantum Operations*, Phys. Lett. A **373**, 320-324 (2009). :doi:`10.1016/j.physleta.2008.11.043`. .. [Hav03] \T. Havel, *Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups*, J. Math. Phys. **44** 2, 534 (2003). :doi:`10.1063/1.1518555`. .. [Wat13] \J. Watrous, |theory-qi|_, lecture notes. .. [Mez07] \F. Mezzadri, *How to generate random matrices from the classical compact groups*, Notices of the AMS **54**, 592-604 (2007). :arxiv:`math-ph/0609050`. .. [Moh08] \M. Mohseni, A. T. Rezakhani, D. A. Lidar, *Quantum-process tomography: Resource analysis of different strategies*, Phys. Rev. A **77**, 032322 (2008). :doi:`10.1103/PhysRevA.77.032322`. .. [Gri98] \M. Grifoni, P. Hänggi, *Driven quantum tunneling*, Phys. Rep. **304**, 299 (1998). :doi:`10.1016/S0370-1573(98)00022-2`. .. [Gar03] Gardiner and Zoller, *Quantum Noise* (Springer, 2004). .. [Bre02] H.-P. Breuer and F. Petruccione, *The Theory of Open Quantum Systems* (Oxford, 2002). .. [Coh92] \C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, *Atom-Photon Interactions: Basic Processes and Applications*, (Wiley, 1992). .. [WBC11] \C. Wood, J. Biamonte, D. G. Cory, *Tensor networks and graphical calculus for open quantum systems*. :arxiv:`1111.6950` .. [AKN98] \D. Aharonov, A. Kitaev, N. Nisan, *Quantum circuits with mixed states*, in Proceedings of the Thirtieth Annual ACM STOC, 20-30 (1998). :arxiv:`quant-ph/9806029` .. [dAless08] \D. d’Alessandro, *Introduction to Quantum Control and Dynamics*, (Chapman & Hall/CRC, 2008). .. [Byrd95] \R. H. Byrd, P. Lu, J. Nocedal, C. Zhu, *A Limited Memory Algorithm for Bound Constrained Optimization*, SIAM J. Sci. Comput. **16**, 1190 (1995). :doi:`10.1137/0916069` .. [Flo12] \F. F. Floether, P. de Fouquieres, S. G. Schirmer, *Robust quantum gates for open systems via optimal control: Markovian versus non-Markovian dynamics*, New J. Phys. **14**, 073023 (2012). :doi:`10.1088/1367-2630/14/7/073023` .. [Lloyd14] \S. Lloyd, S. Montangero, *Information theoretical analysis of quantum optimal control*, Phys. Rev. Lett. **113**, 010502 (2014). :doi:`10.1103/PhysRevLett.113.010502` .. [Doria11] \P. Doria, T. Calarco, S. Montangero, *Optimal Control Technique for Many-Body Quantum Dynamics*, Phys. Rev. Lett. **106**, 190501 (2011). :doi:`10.1103/PhysRevLett.106.190501` .. [Caneva11] \T. Caneva, T. Calarco, S. Montangero, *Chopped random-basis quantum optimization*, Phys. Rev. A **84**, 022326 (2011). :doi:`10.1103/PhysRevA.84.022326` .. [Rach15] \N. Rach, M. M. MĂźller, T. Calarco, S. Montangero, *Dressing the chopped-random-basis optimization: A bandwidth-limited access to the trap-free landscape*, Phys. Rev. A. **92**, 062343 (2015). :doi:`10.1103/PhysRevA.92.062343` .. [Wis09] \H. M. Wiseman, G. J. Milburn, *Quantum Measurement and Control*, (Cambridge University Press, 2009). .. [NKanej] \N. Khaneja *et al.*, *Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms.* J. Magn. Reson. **172**, 296–305 (2005). :doi:`10.1016/j.jmr.2004.11.004` .. [Donvil22] \B. Donvil, P. Muratore-Ginanneschi, *Quantum trajectory framework for general time-local master equations*, Nat Commun **13**, 4140 (2022). :doi:`10.1038/s41467-022-31533-8`. .. [Abd19] \M. Abdelhafez, D. I. Schuster, J. Koch, *Gradient-based optimal control of open quantum systems using quantumtrajectories and automatic differentiation*, Phys. Rev. A **99**, 052327 (2019). :doi:`10.1103/PhysRevA.99.052327`. .. [BoFiN23] \N. Lambert, T. Raheja, S. Cross, P. Menczel, S. Ahmed, A. Pitchford, D. Burgarth, F. Nori, *QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics*, Phys. Rev. Research **5**, 013181 (2023). :doi:`10.1103/PhysRevResearch.5.013181`. .. [Lambert19] \N. Lambert, S. Ahmed, M. Cirio, F. Nori, *Modelling the ultra-strongly coupled spin-boson model with unphysical modes*, Nat Commun **10**, 3721 (2019). :doi:`10.1038/s41467-019-11656-1`. .. The trick with |text|_ is to get an italic link, and is described in the Docutils FAQ at https://docutils.sourceforge.net/FAQ.html#is-nested-inline-markup-possible. This is at the bottom of the source file to avoid extra whitespace. .. |theory-qi| replace:: *Theory of Quantum Information* .. _theory-qi: https://cs.uwaterloo.ca/~watrous/TQI-notes/qutip-5.1.1/doc/changelog.rst000066400000000000000000003573651474175217300161440ustar00rootroot00000000000000.. _changelog: ********** Change Log ********** .. towncrier release notes start QuTiP 5.1.1 (2025-01-10) ========================= Patch to add support for scipy 1.15. Features -------- - qutip.cite() now cites the QuTiP 5 paper, https://arxiv.org/abs/2412.04705. - Added QuTiP family package information to qutip.about(). (#2604) Bug Fixes --------- - Fix support for calculating the eigenstates of ENR operators (#2595). - Update various functions to use `sph_harm_y` when using scipy >= 1.15. - Update mkl finding to support the 'emscripten' sys.platform. (#2606) QuTiP 5.1.0 (2024-12-12) ======================== Features -------- - It adds odd parity support to HEOM's fermionic solver (#2261, by Gerardo Jose Suarez) - Create `SMESolver.run_from_experiment`, which allows to run stochastic evolution from know noise or measurements. (#2318) - Add types hints. (#2327, #2473) - Weighted trajectories in trajectory solvers (enables improved sampling for nm_mcsolve) (#2369, by Paul Menczel) - Updated `qutip.core.metrics.dnorm` to have an efficient speedup when finding the difference of two unitaries. We use a result on page 18 of D. Aharonov, A. Kitaev, and N. Nisan, (1998). (#2416, by owenagnel) - Allow mixed initial conditions for mcsolve and nm_mcsolve. (#2437, by Paul Menczel) - Add support for `jit` and `grad` in qutip.core.metrics (#2461, by Rochisha Agarwal) - Allow merging results from stochastic solvers. (#2474) - Support measurement statistics for `jax` and `jaxdia` dtypes (#2493, by Rochisha Agarwal) - Enable mcsolve with jax.grad using numpy_backend (#2499, by Rochisha Agarwal) - Add propagator method to steadystate (#2508) - Introduces the qutip.core.environment module, which contains classes that characterize bosonic and fermionic thermal environments. (#2534, by Gerardo Jose Suarez) - Implements a `einsum` function for Qobj dimensions (Evaluates the Einstein summation convention on the operands.) (#2545, by Franco Mayo) - Wave function calculations have been sped up with a Cython implementation. It optimizes the update method of the HarmonicOscillatorWaveFunction class in distribution.py. (#2553, by Matheus Gomes Cordeiro) - Speed up `kraus_to_super` by adding a `sparse` option. (#2569, by Sola85) Bug Fixes --------- - Fix a dimension problem for the argument color of Bloch.add_states Clean-up of the code in Bloch.add_state Add Bloch.add_arc and Bloch.add_line in the guide on Bloch class (#2445, by PositroniumJS) - Fix HTMLProgressBar display (#2475) - Make expm, cosm, sinm work with jax. (#2484, by Rochisha Agarwal) - Fix stochastic solver step method (#2491) - `clip` gives deprecation warning, that might be a problem in the future. Hence switch to `where` (#2507, by Rochisha Agarwal) - Fix brmesolve detection of contant vs time-dependent system. (#2530) - `propagator` now accepts list format `c_ops` like `mesolve` does. (#2532) - Fix compatibility issue with matplotlib>=3.9 in matrix_histogram (#2544, by Andreas Maeder) - Resolve incompatibility of TwoModeQuadratureCorrelation class (#2548, by quantum-menace) - Fix sparse eigen solver issue with many degenerate eigen values. (#2586) - Fix getting tensor permutation for uneven super operators. (#2561) Documentation ------------- - Improve guide-settings page. (#2403) - Tidy up formatting of type aliases in the api documentation (#2436, by Paul Menczel) - Update documentation - Update contributors - Improve apidoc readability (#2523) - Fix error in simdiag docstring (#2585, by Sola85) Miscellaneous ------------- - Add auto_real_casting options. (#2329) - Add dispatcher for sqrtm (#2453, by Rochisha Agarwal) - Make `e_ops`, `args` and `options` keyword only. Solver were inconsistent with `e_ops` usually following `c_ops` but sometime preceding it. Setting it as keyword only remove the need to memorize the signature of each solver. (#2489) - Introduces a new `NumpyBackend `class that enables dynamic selection of the numpy_backend used in `qutip`. The class facilitates switching between different numpy implementations ( `numpy` and `jax.numpy` mainly ) based on the configuration specified in `settings.core`. (#2490, by Rochisha Agarwal) - Improve mkl lookup function. (#2497) - Deterministic trajectories are not counted in ``ntraj``. (#2502) - Allow tests to be executed multiple times in one Python session (#2538, by Zhang Maiyun) - Improve performance of qutip.Qobj by using static numpy version check (#2557, by Pieter Eendebak) - Fix towncrier check (#2542) QuTiP 5.0.4 (2024-08-30) ======================== Micro release to add support for numpy 2.1 Bug Fixes --------- - Fixed rounding error in dicke_trace_function that resulted in negative eigenvalues. (#2466, by Andrey Nikitin) QuTiP 5.0.3 (2024-06-20) ======================== Micro release to add support for numpy 2. Bug Fixes --------- - Bug Fix in Process Matrix Rendering. (#2400, by Anush Venkatakrishnan) - Fix steadystate permutation being reversed. (#2443) - Add parallelizing support for `vernN` methods with `mcsolve`. (#2454 by Utkarsh) Documentation ------------- - Added `qutip.core.gates` to apidoc/functions.rst and a Gates section to guide-states.rst. (#2441, by alan-nala) Miscellaneous ------------- - Add support for numpy 2 (#2421, #2457) - Add support for scipy 1.14 (#2469) QuTiP 5.0.2 (2024-05-16) ======================== Bug Fixes --------- - Use CSR as the default for expand_operator (#2380, by BoxiLi) - Fix import of the partial_transpose function. Ensures that the negativity function can handle both kets and density operators as input. (#2371, by vikas-chaudhary-2802) - Ensure that end_condition of mcsolve result doesn't say target tolerance reached when it hasn't (#2382, by magzpavz) - Fix two bugs in steadystate floquet solver, and adjust tests to be sensitive to this issue. (#2393, by Neill Lambert) Documentation ------------- - Correct a mistake in the doc (#2401, by PositroniumJS) - Fix #2156: Correct a sample of code in the doc (#2409, by PositroniumJS) Miscellaneous ------------- - Better metadata management in operators creation functions (#2388) - Implicitly set minimum python version to 3.9 (#2413) - Qobj.__eq__ uses core's settings rtol. (#2425) - Only normalize solver states when the initial state is already normalized. (#2427) QuTiP 5.0.1 (2024-04-03) ======================== Patch update fixing small issues with v5.0.0 release - Fix broken links in the documentation when migrating to readthedocs - Fix readthedocs search feature - Add setuptools to runtime compilation requirements - Fix mcsolve documentation for open systems - Fix OverFlowError in progress bars QuTiP 5.0.0 (2024-03-26) ======================== QuTiP 5 is a redesign of many of the core components of QuTiP (``Qobj``, ``QobjEvo``, solvers) to make them more consistent and more flexible. ``Qobj`` may now be stored in either sparse or dense representations, and the two may be mixed sensibly as needed. ``QobjEvo`` is now used consistently throughout QuTiP, and the implementation has been substantially cleaned up. A new ``Coefficient`` class is used to represent the time-dependent factors inside ``QobjEvo``. The solvers have been rewritten to work well with the new data layer and the concept of ``Integrators`` which solve ODEs has been introduced. In future, new data layers may provide their own ``Integrators`` specialized to their representation of the underlying data. Much of the user-facing API of QuTiP remains familiar, but there have had to be many small breaking changes. If we can make changes to easy migrating code from QuTiP 4 to QuTiP 5, please let us know. An extensive list of changes follows. Contributors ------------ QuTiP 5 has been a large effort by many people over the last three years. In particular: - Jake Lishman led the implementation of the new data layer and coefficients. - Eric Giguère led the implementation of the new QobjEvo interface and solvers. - Boxi Li led the updating of QuTiP's QIP support and the creation of ``qutip_qip``. Other members of the QuTiP Admin team have been heavily involved in reviewing, testing and designing QuTiP 5: - Alexander Pitchford - Asier Galicia - Nathan Shammah - Shahnawaz Ahmed - Neill Lambert - Simon Cross - Paul Menczel Two Google Summer of Code contributors updated the tutorials and benchmarks to QuTiP 5: - Christian Staufenbiel updated many of the tutorials (``). - Xavier Sproken update the benchmarks (``). During an internship at RIKEN, Patrick Hopf created a new quantum control method and improved the existing methods interface: - Patrick Hopf created new quantum control package (``). Four experimental data layers backends were written either as part of Google Summer of Code or as separate projects. While these are still alpha quality, they helped significantly to test the data layer API: - ``qutip-tensorflow``: a TensorFlow backend by Asier Galicia (``) - ``qutip-cupy``: a CuPy GPU backend by Felipe Bivort Haiek (``)` - ``qutip-tensornetwork``: a TensorNetwork backend by Asier Galicia (``) - ``qutip-jax``: a JAX backend by Eric Giguère (``) Finally, Yuji Tamakoshi updated the visualization function and added animation functions as part of Google Summer of Code project. We have also had many other contributors, whose specific contributions are detailed below: - Pieter Eendebak (updated the required SciPy to 1.5+, `#1982 `). - Pieter Eendebak (reduced import times by setting logger names, `#1981 `) - Pieter Eendebak (Allow scipy 1.12 to be used with qutip, `#2354 `) - Xavier Sproken (included C header files in the source distribution, `#1971 `) - Christian Staufenbiel (added support for multiple collapse operators to the Floquet solver, `#1962 `) - Christian Staufenbiel (fixed the basis used in the Floquet Master Equation solver, `#1952 `) - Christian Staufenbiel (allowed the ``bloch_redfield_tensor`` function to accept strings and callables for `a_ops`, `#1951 `) - Christian Staufenbiel (Add a guide on Superoperators, Pauli Basis and Channel Contraction, `#1984 `) - Henrique SilvĂŠro (allowed ``qutip_qip`` to be imported as ``qutip.qip``, `#1920 `) - Florian Hopfmueller (added a vastly improved implementations of ``process_fidelity`` and ``average_gate_fidelity``, `#1712 `, `#1748 `, `#1788 `) - Felipe Bivort Haiek (fixed inaccuracy in docstring of the dense implementation of negation, `#1608 `) - Rajath Shetty (added support for specifying colors for individual points, vectors and states display by `qutip.Bloch`, `#1335 `) - Rochisha Agarwal (Add dtype to printed ouput of qobj, `#2352 `) - Kosuke Mizuno (Add arguments of plot_wigner() and plot_wigner_fock_distribution() to specify parameters for wigner(), `#2057 `) - Matt Ord (Only pre-compute density matrices if keep_runs_results is False, `#2303 `) - Daniel Moreno GalĂĄn (Add the possibility to customize point colors as in V4 and fix point plot behavior for 'l' style, `#2303 `) - Sola85 (Fixed simdiag not returning orthonormal eigenvectors, `#2269 `) - Edward Thomas (Fix LaTeX display of Qobj state in Jupyter cell outputs, `#2272 `) - Bogdan Reznychenko (Rework `kraus_to_choi` making it faster, `#2284 `) - gabbence95 (Fix typos in `expect` documentation, `#2331 `) - lklivingstone (Added __repr__ to QobjEvo, `#2111 `) - Yuji Tamakoshi (Improve print(qutip.settings) by make it shorter, `#2113 `) - khnikhil (Added fermionic annihilation and creation operators, `#2166 `) - Daniel Weiss (Improved sampling algorithm for mcsolve, `#2218 `) - SJUW (Increase missing colorbar padding for matrix_histogram_complex() from 0 to 0.05, `#2181 `) - Valan Baptist Mathuranayagam (Changed qutip-notebooks to qutip-tutorials and fixed the typo in the link redirecting to the changelog section in the PR template, `#2107 `) - Gerardo Jose Suarez (Added information on sec_cutoff to the documentation, `#2136 `) - Cristian Emiliano Godinez Ramirez (Added inherited members to API doc of MESolver, SMESolver, SSESolver, NonMarkovianMCSolver, `#2167 `) - Andrey Rakhubovsky (Corrected grammar in Bloch-Redfield master equation documentation, `#2174 `) - Rushiraj Gadhvi (qutip.ipynbtools.version_table() can now be called without Cython installed, `#2110 `) - Harsh Khilawala (Moved HTMLProgressBar from qutip/ipynbtools.py to qutip/ui/progressbar.py, `#2112 `) - Avatar Srinidhi P V (Added new argument bc_type to take boundary conditions when creating QobjEvo, `#2114 `) - Andrey Rakhubovsky (Fix types in docstring of projection(), `#2363 `) Qobj changes ------------ Previously ``Qobj`` data was stored in a SciPy-like sparse matrix. Now the representation is flexible. Implementations for dense and sparse formats are included in QuTiP and custom implementations are possible. QuTiP's performance on dense states and operators is significantly improved as a result. Some highlights: - The data is still acessible via the ``.data`` attribute, but is now an instance of the underlying data type instead of a SciPy-like sparse matrix. The operations available in ``qutip.core.data`` may be used on ``.data``, regardless of the data type. - ``Qobj`` with different data types may be mixed in arithmetic and other operations. A sensible output type will be automatically determined. - The new ``.to(...)`` method may be used to convert a ``Qobj`` from one data type to another. E.g. ``.to("dense")`` will convert to the dense representation and ``.to("csr")`` will convert to the sparse type. - Many ``Qobj`` methods and methods that create ``Qobj`` now accepted a ``dtype`` parameter that allows the data type of the returned ``Qobj`` to specified. - The new ``&`` operator may be used to obtain the tensor product. - The new ``@`` operator may be used to obtain the matrix / operator product. ``bar @ ket`` returns a scalar. - The new ``.contract()`` method will collapse 1D subspaces of the dimensions of the ``Qobj``. - The new ``.logm()`` method returns the matrix logarithm of an operator. - The methods ``.set_data``, ``.get_data``, ``.extract_state``, ``.eliminate_states``, ``.evaluate`` and ``.check_isunitary`` have been removed. - The property ``dtype`` return the representation of the data used. - The new ``data_as`` allow to obtain the data as a common python formats: numpy array, scipy sparse matrix, JAX Array, etc. QobjEvo changes --------------- The ``QobjEvo`` type for storing time-dependent quantum objects has been significantly expanded, standardized and extended. The time-dependent coefficients are now represented using a new ``Coefficient`` type that may be independently created and manipulated if required. Some highlights: - The ``.compile()`` method has been removed. Coefficients specified as strings are automatically compiled if possible and the compilation is cached across different Python runs and instances. - Mixing coefficient types within a single ``Qobj`` is now supported. - Many new attributes were added to ``QobjEvo`` for convenience. Examples include ``.dims``, ``.shape``, ``.superrep`` and ``.isconstant``. - Many old attributes such as ``.cte``, ``.use_cython``, ``.type``, ``.const``, and ``.coeff_file`` were removed. - A new ``Spline`` coefficient supports spline interpolations of different orders. The old ``Cubic_Spline`` coefficient has been removed. - The new ``.arguments(...)`` method allows additional arguments to the underlying coefficient functions to be updated. - The ``_step_func_coeff`` argument has been replaced by the ``order`` parameter. ``_step_func_coeff=False`` is equivalent to ``order=3``. ``_step_func_coeff=True`` is equivalent to ``order=0``. Higher values of ``order`` gives spline interpolations of higher orders. - The spline type can take ``bc_type`` to control the boundary conditions. - QobjEvo can be creating from the multiplication of a Qobj with a coefficient: ``oper * qutip.coefficient(f, args=args)`` is equivalent to ``qutip.QobjEvo([[oper, f]], args=args)``. - Coefficient function can be defined in a pythonic manner: ``def f(t, A, w)``. The dictionary ``args`` second argument is no longer needed. Function using the exact ``f(t, args)`` signature will use the old method for backward compatibility. Solver changes -------------- The solvers in QuTiP have been heavily reworked and standardized. Under the hood solvers now make use of swappable ODE ``Integrators``. Many ``Integrators`` are included (see the list below) and custom implementations are possible. Solvers now consistently accept a ``QobjEvo`` instance at the Hamiltonian or Liouvillian, or any object which can be passed to the ``QobjEvo`` constructor. A breakdown of highlights follows. All solvers: - Solver options are now supplied in an ordinary Python dict. ``qutip.Options`` is deprecated and returns a dict for backwards compatibility. - A specific ODE integrator may be selected by supplying a ``method`` option. - Each solver provides a class interface. Creating an instance of the class allows a solver to be run multiple times for the same system without having to repeatedly reconstruct the right-hand side of the ODE to be integrated. - A ``QobjEvo`` instance is accepted for most operators, e.g., ``H``, ``c_ops``, ``e_ops``, ``a_ops``. - The progress bar is now selected using the ``progress_bar`` option. A new progess bar using the ``tqdm`` Python library is provided. - Dynamic arguments, where the value of an operator depends on the current state of the evolution interface reworked. Now a property of the solver is to be used as an arguments: ``args={"state": MESolver.StateFeedback(default=rho0)}`` Integrators: - The SciPy zvode integrator is available with the BDF and Adams methods as ``bdf`` and ``adams``. - The SciPy dop853 integrator (an eighth order Runge-Kutta method by Dormand & Prince) is available as ``dop853``. - The SciPy lsoda integrator is available as ``lsoda``. - QuTiP's own implementation of Verner's "most efficient" Runge-Kutta methods of order 7 and 9 are available as ``vern7`` and ``vern9``. See http://people.math.sfu.ca/~jverner/ for a description of the methods. - QuTiP's own implementation of a solver that directly diagonalizes the the system to be integrated is available as ``diag``. It only works on time-independent systems and is slow to setup, but once the diagonalization is complete, it generates solutions very quickly. - QuTiP's own implementatoin of an approximate Krylov subspace integrator is available as ``krylov``. This integrator is only usable with ``sesolve``. Result class: - A new ``.e_data`` attribute provides expectation values as a dictionary. Unlike ``.expect``, the values are provided in a Python list rather than a numpy array, which better supports non-numeric types. - The contents of the ``.stats`` attribute changed significantly and is now more consistent across solvers. Monte-Carlo Solver (mcsolve): - The system, H, may now be a super-operator. - The ``seed`` parameter now supports supplying numpy ``SeedSequence`` or ``Generator`` types. - The new ``timeout`` and ``target_tol`` parameters allow the solver to exit early if a timeout or target tolerance is reached. - The ntraj option no longer supports a list of numbers of trajectories. Instead, just run the solver multiple times and use the class ``MCSolver`` if setting up the solver uses a significant amount of time. - The ``map_func`` parameter has been replaced by the ``map`` option. - A loky based parallel map as been added. - A mpi based parallel map as been added. - The result returned by ``mcsolve`` now supports calculating photocurrents and calculating the steady state over N trajectories. - The old ``parfor`` parallel execution function has been removed from ``qutip.parallel``. Use ``parallel_map``, ``loky_map`` or ``mpi_pmap`` instead. - Added improved sampling options which converge much faster when the probability of collapse is small. Non Markovian Monte-Carlo Solver (nm_mcsolve): - New Monte-Carlo Solver supporting negative decay rates. - Based on the influence martingale approach, Donvil et al., Nat Commun 13, 4140 (2022). - Most of the improvements made to the regular Monte-Carlo solver are also available here. - The value of the influence martingale is available through the ``.trace`` attribute of the result. Stochastic Equation Solvers (ssesolve, smesolve) - Function call greatly changed: many keyword arguments are now options. - m_ops and dW_factors are now changed from the default from the new class interface only. - Use the same parallel maps as mcsolve: support for loky and mpi map added. - End conditions ``timeout`` and ``target_tol`` added. - The ``seed`` parameter now supports supplying numpy ``SeedSequence``. - Wiener function is now available as a feedback. Bloch-Redfield Master Equation Solver (brmesolve): - The ``a_ops`` and ``spectra`` support implementations been heavily reworked to reuse the techniques from the new Coefficient and QobjEvo classes. - The ``use_secular`` parameter has been removed. Use ``sec_cutoff=-1`` instead. - The required tolerance is now read from ``qutip.settings``. Krylov Subspace Solver (krylovsolve): - The Krylov solver is now implemented using ``SESolver`` and the ``krylov`` ODE integrator. The function ``krylovsolve`` is maintained for convenience and now supports many more options. - The ``sparse`` parameter has been removed. Supply a sparse ``Qobj`` for the Hamiltonian instead. Floquet Solver (fsesolve and fmmesolve): - The Floquet solver has been rewritten to use a new ``FloquetBasis`` class which manages the transformations from lab to Floquet basis and back. - Many of the internal methods used by the old Floquet solvers have been removed. The Floquet tensor may still be retried using the function ``floquet_tensor``. - The Floquet Markov Master Equation solver has had many changes and new options added. The environment temperature may be specified using ``w_th``, and the result states are stored in the lab basis and optionally in the Floquet basis using ``store_floquet_state``. - The spectra functions supplied to ``fmmesolve`` must now be vectorized (i.e. accept and return numpy arrays for frequencies and densities) and must accept negative frequence (i.e. usually include a ``w > 0`` factor so that the returned densities are zero for negative frequencies). - The number of sidebands to keep, ``kmax`` may only be supplied when using the ``FMESolver`` - The ``Tsteps`` parameter has been removed from both ``fsesolve`` and ``fmmesolve``. The ``precompute`` option to ``FloquetBasis`` may be used instead. Evolution of State Solver (essovle): - The function ``essolve`` has been removed. Use the ``diag`` integration method with ``sesolve`` or ``mesolve`` instead. Steady-state solvers (steadystate module): - The ``method`` parameter and ``solver`` parameters have been separated. Previously they were mixed together in the ``method`` parameter. - The previous options are now passed as parameters to the steady state solver and mostly passed through to the underlying SciPy functions. - The logging and statistics have been removed. Correlation functions (correlation module): - A new ``correlation_3op`` function has been added. It supports ``MESolver`` or ``BRMESolver``. - The ``correlation``, ``correlation_4op``, and ``correlation_ss`` functions have been removed. - Support for calculating correlation with ``mcsolve`` has been removed. Propagators (propagator module): - A class interface, ``qutip.Propagator``, has been added for propagators. - Propagation of time-dependent systems is now supported using ``QobjEvo``. - The ``unitary_mode`` and ``parallel`` options have been removed. Correlation spectra (spectrum module): - The functions ``spectrum_ss`` and ``spectrum_pi`` have been removed and are now internal functions. - The ``use_pinv`` parameter for ``spectrum`` has been removed and the functionality merged into the ``solver`` parameter. Use ``solver="pi"`` instead. Hierarchical Equation of Motion Solver (HEOM) - Updated the solver to use the new QuTiP integrators and data layer. - Updated all the HEOM tutorials to QuTiP 5. - Added support for combining bosonic and fermionic baths. - Sped up the construction of the RHS of the HEOM solver by a factor of 4x. - As in QuTiP 4, the HEOM supports arbitrary spectral densities, bosonic and fermionic baths, PĂĄde and Matsubara expansions of the correlation functions, calculating the Matsubara terminator and inspection of the ADOs (auxiliary density operators). QuTiP core ---------- There have been numerous other small changes to core QuTiP features: - ``qft(...)`` the function that returns the quantum Fourier transform operator was moved from ``qutip.qip.algorithm`` into ``qutip``. - The Bloch-Redfield solver tensor, ``brtensor``, has been moved into ``qutip.core``. See the section above on the Bloch-Redfield solver for details. - The functions ``mat2vec`` and ``vec2mat`` for transforming states to and from super-operator states have been renamed to ``stack_columns`` and ``unstack_columns``. - The function ``liouvillian_ref`` has been removed. Used ``liouvillian`` instead. - The superoperator transforms ``super_to_choi``, ``choi_to_super``, ``choi_to_kraus``, ``choi_to_chi`` and ``chi_to_choi`` have been removed. Used ``to_choi``, ``to_super``, ``to_kraus`` and ``to_chi`` instead. - All of the random object creation functions now accepted a numpy ``Generator`` as a seed. - The ``dims`` parameter of all random object creation functions has been removed. Supply the dimensions as the first parameter if explicit dimensions are required. - The function ``rand_unitary_haar`` has been removed. Use ``rand_unitary(distribution="haar")`` instead. - The functions ``rand_dm_hs`` and ``rand_dm_ginibre`` have been removed. Use ``rand_dm(distribution="hs")`` and ``rand_dm(distribution="ginibre")`` instead. - The function ``rand_ket_haar`` has been removed. Use ``rand_ket(distribution="haar")`` instead. - The measurement functions have had the ``target`` parameter for expanding the measurement operator removed. Used ``expand_operator`` to expand the operator instead. - ``qutip.Bloch`` now supports applying colours per-point, state or vector in ``add_point``, ``add_states``, and ``add_vectors``. - Dimensions use a class instead of layered lists. - Allow measurement functions to support degenerate operators. - Add ``qeye_like`` and ``qzero_like``. - Added fermionic annihilation and creation operators. QuTiP settings -------------- Previously ``qutip.settings`` was an ordinary module. Now ``qutip.settings`` is an instance of a settings class. All the runtime modifiable settings for core operations are in ``qutip.settings.core``. The other settings are not modifiable at runtime. - Removed ``load``. ``reset`` and ``save`` functions. - Removed ``.debug``, ``.fortran``, ``.openmp_thresh``. - New ``.compile`` stores the compilation options for compiled coefficients. - New ``.core["rtol"]`` core option gives the default relative tolerance used by QuTiP. - The absolute tolerance setting ``.atol`` has been moved to ``.core["atol"]``. Visualization ------------- - Added arguments to ``plot_wigner`` and ``plot_wigner_fock_distribution`` to specify parameters for ``wigner``. - Removed ``Bloch3D``. The same functionality is provided by ``Bloch``. - Added ``fig``, ``ax`` and ``cmap`` keyword arguments to all visualization functions. - Most visualization functions now respect the ``colorblind_safe`` setting. - Added new functions to create animations from a list of ``Qobj`` or directly from solver results with saved states. Package reorganization ---------------------- - ``qutip.qip`` has been moved into its own package, qutip-qip. Once installed, qutip-qip is available as either ``qutip.qip`` or ``qutip_qip``. Some widely useful gates have been retained in ``qutip.gates``. - ``qutip.control`` has been moved to qutip-qtrl and once installed qutip-qtrl is available as either ``qutip.control`` or ``qutip_qtrl``. Note that ``quitp_qtrl`` is provided primarily for backwards compatibility. Improvements to optimal control will take place in the new ``qutip_qoc`` package. - ``qutip.lattice`` has been moved into its own package, qutip-lattice. It is available from ``. - ``qutip.sparse`` has been removed. It contained the old sparse matrix representation and is replaced by the new implementation in ``qutip.data``. - ``qutip.piqs`` functions are no longer available from the ``qutip`` namespace. They are accessible from ``qutip.piqs`` instead. Miscellaneous ------------- - Support has been added for 64-bit integer sparse matrix indices, allowing sparse matrices with up to 2**63 rows and columns. This support needs to be enabled at compilation time by calling ``setup.py`` and passing ``--with-idxint-64``. Feature removals ---------------- - Support for OpenMP has been removed. If there is enough demand and a good plan for how to organize it, OpenMP support may return in a future QuTiP release. - The ``qutip.parfor`` function has been removed. Use ``qutip.parallel_map`` instead. - ``qutip.graph`` has been removed and replaced by SciPy's graph functions. - ``qutip.topology`` has been removed. It contained only one function ``berry_curvature``. - The ``~/.qutip/qutiprc`` config file is no longer supported. It contained settings for the OpenMP support. - Deprecate ``three_level_atom`` - Deprecate ``orbital`` Changes from QuTiP 5.0.0b1: --------------------------- Features -------- - Add dtype to printed ouput of qobj (#2352 by Rochisha Agarwal) Miscellaneous ------------- - Allow scipy 1.12 to be used with qutip. (#2354 by Pieter Eendebak) QuTiP 5.0.0b1 (2024-03-04) ========================== Features -------- - Create a Dimension class (#1996) - Add arguments of plot_wigner() and plot_wigner_fock_distribution() to specify parameters for wigner(). (#2057, by Kosuke Mizuno) - Restore feedback to solvers (#2210) - Added mpi_pmap, which uses the mpi4py module to run computations in parallel through the MPI interface. (#2296, by Paul) - Only pre-compute density matrices if keep_runs_results is False (#2303, by Matt Ord) Bug Fixes --------- - Add the possibility to customize point colors as in V4 and fix point plot behavior for 'l' style (#1974, by Daniel Moreno GalĂĄn) - Disabled broken "improved sampling" for `nm_mcsolve`. (#2234, by Paul) - Fixed result objects storing a reference to the solver through options._feedback. (#2262, by Paul) - Fixed simdiag not returning orthonormal eigenvectors. (#2269, by Sola85) - Fix LaTeX display of Qobj state in Jupyter cell outputs (#2272, by Edward Thomas) - Improved behavior of `parallel_map` and `loky_pmap` in the case of timeouts, errors or keyboard interrupts (#2280, by Paul) - Ignore deprecation warnings from cython 0.29.X in tests. (#2288) - Fixed two problems with the steady_state() solver in the HEOM method. (#2333) Miscellaneous ------------- - Improve fidelity doc-string (#2257) - Improve documentation in guide/dynamics (#2271) - Improve states and operator parameters documentation. (#2289) - Rework `kraus_to_choi` making it faster (#2284, by Bogdan Reznychenko) - Remove Bloch3D: redundant to Bloch (#2306) - Allow tests to run without matplotlib and ipython. (#2311) - Add too small step warnings in fixed dt SODE solver (#2313) - Add `dtype` to `Qobj` and `QobjEvo` (#2325) - Fix typos in `expect` documentation (#2331, by gabbence95) - Allow measurement functions to support degenerate operators. (#2342) QuTiP 5.0.0a2 (2023-09-06) ========================== Features -------- - Add support for different spectra types for bloch_redfield_tensor (#1951) - Improve qutip import times by setting logger names explicitly. (#1981, by Pieter Eendebak) - Change the order of parameters in expand_operator (#1991) - Add `svn` and `solve` to dispatched (#2002) - Added nm_mcsolve to provide support for Monte-Carlo simulations of master equations with possibly negative rates. The method implemented here is described in arXiv:2209.08958 [quant-ph]. (#2070 by pmenczel) - Add support for combining bosonic and fermionic HEOM baths (#2089) - Added __repr__ to QobjEvo (#2111 by lklivingstone) - Improve print(qutip.settings) by make it shorter (#2113 by tamakoshi2001) - Create the `trace_oper_ket` operation (#2126) - Speed up the construction of the RHS of the HEOM solver by a factor of 4x by converting the final step to Cython. (#2128) - Rewrite the stochastic solver to use the v5 solver interface. (#2131) - Add `Qobj.get` to extract underlying data in original format. (#2141) - Add qeye_like and qzero_like (#2153) - Add capacity to dispatch on ``Data`` (#2157) - Added fermionic annihilation and creation operators. (#2166 by khnikhil) - Changed arguments and applied colorblind_safe to functions in visualization.py (#2170 by Yuji Tamakoshi) - Changed arguments and applied colorblind_safe to plot_wigner_sphere and matrix_histogram in visualization.py (#2193 by Yuji Tamakoshi) - Added Dia data layer which represents operators as multi-diagonal matrices. (#2196) - Added support for animated plots. (#2203 by Yuji Tamakoshi) - Improved sampling algorithm for mcsolve (#2218 by Daniel Weiss) - Added support for early termination of map functions. (#2222) Bug Fixes --------- - Add missing state transformation to floquet_markov_mesolve (#1952 by christian512) - Added default _isherm value (True) for momentum and position operators. (#2032 by Asier Galicia) - Changed qutip-notebooks to qutip-tutorials and fixed the typo in the link redirecting to the changelog section in the PR template. (#2107 by Valan Baptist Mathuranayagam) - Increase missing colorbar padding for matrix_histogram_complex() from 0 to 0.05. (#2181 by SJUW) - Raise error on insufficient memory. (#2224) - Fixed fallback to fsesolve call in fmmesolve (#2225) Removals -------- - Remove qutip.control and replace with qutip_qtrl. (#2116) - Deleted _solve in countstat.py and used _data.solve. (#2120 by Yuji Tamakoshi) - Deprecate three_level_atom (#2221) - Deprecate orbital (#2223) Documentation ------------- - Add a guide on Superoperators, Pauli Basis and Channel Contraction. (#1984 by christian512) - Added information on sec_cutoff to the documentation (#2136 by Gerardo Jose Suarez) - Added inherited members to API doc of MESolver, SMESolver, SSESolver, NonMarkovianMCSolver (#2167 by Cristian Emiliano Godinez Ramirez) - Corrected grammar in Bloch-Redfield master equation documentation (#2174 by Andrey Rakhubovsky) Miscellaneous ------------- - Update scipy version requirement to 1.5+ (#1982 by Pieter Eendebak) - Added __all__ to qutip/measurements.py and qutip/core/semidefinite.py (#2103 by Rushiraj Gadhvi) - Restore towncrier check (#2105) - qutip.ipynbtools.version_table() can now be called without Cython installed (#2110 by Rushiraj Gadhvi) - Moved HTMLProgressBar from qutip/ipynbtools.py to qutip/ui/progressbar.py (#2112 by Harsh Khilawala) - Added new argument bc_type to take boundary conditions when creating QobjEvo (#2114 by Avatar Srinidhi P V ) - Remove Windows build warning suppression. (#2119) - Optimize dispatcher by dispatching on positional only args. (#2135) - Clean semidefinite (#2138) - Migrate `transfertensor.py` to solver (#2142) - Add a test for progress_bar (#2150) - Enable cython 3 (#2151) - Added tests for visualization.py (#2192 by Yuji Tamakoshi) - Sorted arguments of sphereplot so that the order is similar to those of plot_spin_distribution (#2219 by Yuji Tamakoshi) QuTiP 5.0.0a1 (2023-02-07) ========================== QuTiP 5 is a redesign of many of the core components of QuTiP (``Qobj``, ``QobjEvo``, solvers) to make them more consistent and more flexible. ``Qobj`` may now be stored in either sparse or dense representations, and the two may be mixed sensibly as needed. ``QobjEvo`` is now used consistently throughout QuTiP, and the implementation has been substantially cleaned up. A new ``Coefficient`` class is used to represent the time-dependent factors inside ``QobjEvo``. The solvers have been rewritten to work well with the new data layer and the concept of ``Integrators`` which solve ODEs has been introduced. In future, new data layers may provide their own ``Integrators`` specialized to their representation of the underlying data. Much of the user-facing API of QuTiP remains familiar, but there have had to be many small breaking changes. If we can make changes to easy migrating code from QuTiP 4 to QuTiP 5, please let us know. Any extensive list of changes follows. Contributors ------------ QuTiP 5 has been a large effort by many people over the last three years. In particular: - Jake Lishman led the implementation of the new data layer and coefficients. - Eric Giguère led the implementation of the new QobjEvo interface and solvers. - Boxi Li led the updating of QuTiP's QIP support and the creation of ``qutip_qip``. Other members of the QuTiP Admin team have been heavily involved in reviewing, testing and designing QuTiP 5: - Alexander Pitchford - Asier Galicia - Nathan Shammah - Shahnawaz Ahmed - Neill Lambert - Simon Cross Two Google Summer of Code contributors updated the tutorials and benchmarks to QuTiP 5: - Christian Staufenbiel updated many of the tutorials (``). - Xavier Sproken update the benchmarks (``). Four experimental data layers backends were written either as part of Google Summer of Code or as separate projects. While these are still alpha quality, the helped significantly to test the data layer API: - ``qutip-tensorflow``: a TensorFlow backend by Asier Galicia (``) - ``qutip-cupy``: a CuPy GPU backend by Felipe Bivort Haiek (``)` - ``qutip-tensornetwork``: a TensorNetwork backend by Asier Galicia (``) - ``qutip-jax``: a JAX backend by Eric Giguère (``) We have also had many other contributors, whose specific contributions are detailed below: - Pieter Eendebak (updated the required SciPy to 1.4+, `#1982 `). - Pieter Eendebak (reduced import times by setting logger names, `#1981 `) - Xavier Sproken (included C header files in the source distribution, `#1971 `) - Christian Staufenbiel (added support for multiple collapse operators to the Floquet solver, `#1962 `) - Christian Staufenbiel (fixed the basis used in the Floquet Master Equation solver, `#1952 `) - Christian Staufenbiel (allowed the ``bloch_redfield_tensor`` function to accept strings and callables for `a_ops`, `#1951 `) - Henrique SilvĂŠro (allowed ``qutip_qip`` to be imported as ``qutip.qip``, `#1920 `) - Florian Hopfmueller (added a vastly improved implementations of ``process_fidelity`` and ``average_gate_fidelity``, `#1712 `, `#1748 `, `#1788 `) - Felipe Bivort Haiek (fixed inaccuracy in docstring of the dense implementation of negation, `#1608 `) - Rajath Shetty (added support for specifying colors for individual points, vectors and states display by `qutip.Bloch`, `#1335 `) Qobj changes ------------ Previously ``Qobj`` data was stored in a SciPy-like sparse matrix. Now the representation is flexible. Implementations for dense and sparse formats are included in QuTiP and custom implementations are possible. QuTiP's performance on dense states and operators is significantly improved as a result. Some highlights: - The data is still acessible via the ``.data`` attribute, but is now an instance of the underlying data type instead of a SciPy-like sparse matrix. The operations available in ``qutip.core.data`` may be used on ``.data``, regardless of the data type. - ``Qobj`` with different data types may be mixed in arithmetic and other operations. A sensible output type will be automatically determined. - The new ``.to(...)`` method may be used to convert a ``Qobj`` from one data type to another. E.g. ``.to("dense")`` will convert to the dense representation and ``.to("csr")`` will convert to the sparse type. - Many ``Qobj`` methods and methods that create ``Qobj`` now accepted a ``dtype`` parameter that allows the data type of the returned ``Qobj`` to specified. - The new ``&`` operator may be used to obtain the tensor product. - The new ``@`` operator may be used to obtain the matrix / operator product. ``bar @ ket`` returns a scalar. - The new ``.contract()`` method will collapse 1D subspaces of the dimensions of the ``Qobj``. - The new ``.logm()`` method returns the matrix logarithm of an operator. - The methods ``.set_data``, ``.get_data``, ``.extract_state``, ``.eliminate_states``, ``.evaluate`` and ``.check_isunitary`` have been removed. QobjEvo changes --------------- The ``QobjEvo`` type for storing time-dependent quantum objects has been significantly expanded, standardized and extended. The time-dependent coefficients are now represented using a new ``Coefficient`` type that may be independently created and manipulated if required. Some highlights: - The ``.compile()`` method has been removed. Coefficients specified as strings are automatically compiled if possible and the compilation is cached across different Python runs and instances. - Mixing coefficient types within a single ``Qobj`` is now supported. - Many new attributes were added to ``QobjEvo`` for convenience. Examples include ``.dims``, ``.shape``, ``.superrep`` and ``.isconstant``. - Many old attributes such as ``.cte``, ``.use_cython``, ``.type``, ``.const``, and ``.coeff_file`` were removed. - A new ``Spline`` coefficient supports spline interpolations of different orders. The old ``Cubic_Spline`` coefficient has been removed. - The new ``.arguments(...)`` method allows additional arguments to the underlying coefficient functions to be updated. - The ``_step_func_coeff`` argument has been replaced by the ``order`` parameter. ``_step_func_coeff=False`` is equivalent to ``order=3``. ``_step_func_coeff=True`` is equivalent to ``order=0``. Higher values of ``order`` gives spline interpolations of higher orders. Solver changes -------------- The solvers in QuTiP have been heavily reworked and standardized. Under the hood solvers now make use of swappable ODE ``Integrators``. Many ``Integrators`` are included (see the list below) and custom implementations are possible. Solvers now consistently accept a ``QobjEvo`` instance at the Hamiltonian or Liouvillian, or any object which can be passed to the ``QobjEvo`` constructor. A breakdown of highlights follows. All solvers: - Solver options are now supplied in an ordinary Python dict. ``qutip.Options`` is deprecated and returns a dict for backwards compatibility. - A specific ODE integrator may be selected by supplying a ``method`` option. - Each solver provides a class interface. Creating an instance of the class allows a solver to be run multiple times for the same system without having to repeatedly reconstruct the right-hand side of the ODE to be integrated. - A ``QobjEvo`` instance is accepted for most operators, e.g., ``H``, ``c_ops``, ``e_ops``, ``a_ops``. - The progress bar is now selected using the ``progress_bar`` option. A new progess bar using the ``tqdm`` Python library is provided. - Dynamic arguments, where the value of an operator depends on the current state of the evolution, have been removed. They may be re-implemented later if there is demand for them. Integrators: - The SciPy zvode integrator is available with the BDF and Adams methods as ``bdf`` and ``adams``. - The SciPy dop853 integrator (an eighth order Runge-Kutta method by Dormand & Prince) is available as ``dop853``. - The SciPy lsoda integrator is available as ``lsoda``. - QuTiP's own implementation of Verner's "most efficient" Runge-Kutta methods of order 7 and 9 are available as ``vern7`` and ``vern9``. See http://people.math.sfu.ca/~jverner/ for a description of the methods. - QuTiP's own implementation of a solver that directly diagonalizes the the system to be integrated is available as ``diag``. It only works on time-independent systems and is slow to setup, but once the diagonalization is complete, it generates solutions very quickly. - QuTiP's own implementatoin of an approximate Krylov subspace integrator is available as ``krylov``. This integrator is only usable with ``sesolve``. Result class: - A new ``.e_data`` attribute provides expectation values as a dictionary. Unlike ``.expect``, the values are provided in a Python list rather than a numpy array, which better supports non-numeric types. - The contents of the ``.stats`` attribute changed significantly and is now more consistent across solvers. Monte-Carlo Solver (mcsolve): - The system, H, may now be a super-operator. - The ``seed`` parameter now supports supplying numpy ``SeedSequence`` or ``Generator`` types. - The new ``timeout`` and ``target_tol`` parameters allow the solver to exit early if a timeout or target tolerance is reached. - The ntraj option no longer supports a list of numbers of trajectories. Instead, just run the solver multiple times and use the class ``MCSolver`` if setting up the solver uses a significant amount of time. - The ``map_func`` parameter has been replaced by the ``map`` option. In addition to the existing ``serial`` and ``parallel`` values, the value ``loky`` may be supplied to use the loky package to parallelize trajectories. - The result returned by ``mcsolve`` now supports calculating photocurrents and calculating the steady state over N trajectories. - The old ``parfor`` parallel execution function has been removed from ``qutip.parallel``. Use ``parallel_map`` or ``loky_map`` instead. Bloch-Redfield Master Equation Solver (brmesolve): - The ``a_ops`` and ``spectra`` support implementaitons been heavily reworked to reuse the techniques from the new Coefficient and QobjEvo classes. - The ``use_secular`` parameter has been removed. Use ``sec_cutoff=-1`` instead. - The required tolerance is now read from ``qutip.settings``. Krylov Subspace Solver (krylovsolve): - The Krylov solver is now implemented using ``SESolver`` and the ``krylov`` ODE integrator. The function ``krylovsolve`` is maintained for convenience and now supports many more options. - The ``sparse`` parameter has been removed. Supply a sparse ``Qobj`` for the Hamiltonian instead. Floquet Solver (fsesolve and fmmesolve): - The Floquet solver has been rewritten to use a new ``FloquetBasis`` class which manages the transformations from lab to Floquet basis and back. - Many of the internal methods used by the old Floquet solvers have been removed. The Floquet tensor may still be retried using the function ``floquet_tensor``. - The Floquet Markov Master Equation solver has had many changes and new options added. The environment temperature may be specified using ``w_th``, and the result states are stored in the lab basis and optionally in the Floquet basis using ``store_floquet_state``. - The spectra functions supplied to ``fmmesolve`` must now be vectorized (i.e. accept and return numpy arrays for frequencies and densities) and must accept negative frequence (i.e. usually include a ``w > 0`` factor so that the returned densities are zero for negative frequencies). - The number of sidebands to keep, ``kmax`` may only be supplied when using the ``FMESolver`` - The ``Tsteps`` parameter has been removed from both ``fsesolve`` and ``fmmesolve``. The ``precompute`` option to ``FloquetBasis`` may be used instead. Evolution of State Solver (essovle): - The function ``essolve`` has been removed. Use the ``diag`` integration method with ``sesolve`` or ``mesolve`` instead. Steady-state solvers (steadystate module): - The ``method`` parameter and ``solver`` parameters have been separated. Previously they were mixed together in the ``method`` parameter. - The previous options are now passed as parameters to the steady state solver and mostly passed through to the underlying SciPy functions. - The logging and statistics have been removed. Correlation functions (correlation module): - A new ``correlation_3op`` function has been added. It supports ``MESolver`` or ``BRMESolver``. - The ``correlation``, ``correlation_4op``, and ``correlation_ss`` functions have been removed. - Support for calculating correlation with ``mcsolve`` has been removed. Propagators (propagator module): - A class interface, ``qutip.Propagator``, has been added for propagators. - Propagation of time-dependent systems is now supported using ``QobjEvo``. - The ``unitary_mode`` and ``parallel`` options have been removed. Correlation spectra (spectrum module): - The functions ``spectrum_ss`` and ``spectrum_pi`` have been removed and are now internal functions. - The ``use_pinv`` parameter for ``spectrum`` has been removed and the functionality merged into the ``solver`` parameter. Use ``solver="pi"`` instead. QuTiP core ---------- There have been numerous other small changes to core QuTiP features: - ``qft(...)`` the function that returns the quantum Fourier transform operator was moved from ``qutip.qip.algorithm`` into ``qutip``. - The Bloch-Redfield solver tensor, ``brtensor``, has been moved into ``qutip.core``. See the section above on the Bloch-Redfield solver for details. - The functions ``mat2vec`` and ``vec2mat`` for transforming states to and from super-operator states have been renamed to ``stack_columns`` and ``unstack_columns``. - The function ``liouvillian_ref`` has been removed. Used ``liouvillian`` instead. - The superoperator transforms ``super_to_choi``, ``choi_to_super``, ``choi_to_kraus``, ``choi_to_chi`` and ``chi_to_choi`` have been removed. Used ``to_choi``, ``to_super``, ``to_kraus`` and ``to_chi`` instead. - All of the random object creation functions now accepted a numpy ``Generator`` as a seed. - The ``dims`` parameter of all random object creation functions has been removed. Supply the dimensions as the first parameter if explicit dimensions are required. - The function ``rand_unitary_haar`` has been removed. Use ``rand_unitary(distribution="haar")`` instead. - The functions ``rand_dm_hs`` and ``rand_dm_ginibre`` have been removed. Use ``rand_dm(distribution="hs")`` and ``rand_dm(distribution="ginibre")`` instead. - The function ``rand_ket_haar`` has been removed. Use ``rand_ket(distribution="haar")`` instead. - The measurement functions have had the ``target`` parameter for expanding the measurement operator removed. Used ``expand_operator`` to expand the operator instead. - ``qutip.Bloch`` now supports applying colours per-point, state or vector in ``add_point``, ``add_states``, and ``add_vectors``. QuTiP settings -------------- Previously ``qutip.settings`` was an ordinary module. Now ``qutip.settings`` is an instance of a settings class. All the runtime modifiable settings for core operations are in ``qutip.settings.core``. The other settings are not modifiable at runtime. - Removed ``load``. ``reset`` and ``save`` functions. - Removed ``.debug``, ``.fortran``, ``.openmp_thresh``. - New ``.compile`` stores the compilation options for compiled coefficients. - New ``.core["rtol"]`` core option gives the default relative tolerance used by QuTiP. - The absolute tolerance setting ``.atol`` has been moved to ``.core["atol"]``. Package reorganization ---------------------- - ``qutip.qip`` has been moved into its own package, qutip-qip. Once installed, qutip-qip is available as either ``qutip.qip`` or ``qutip_qip``. Some widely useful gates have been retained in ``qutip.gates``. - ``qutip.lattice`` has been moved into its own package, qutip-lattice. It is available from ``. - ``qutip.sparse`` has been removed. It contained the old sparse matrix representation and is replaced by the new implementation in ``qutip.data``. - ``qutip.piqs`` functions are no longer available from the ``qutip`` namespace. They are accessible from ``qutip.piqs`` instead. Miscellaneous ------------- - Support has been added for 64-bit integer sparse matrix indices, allowing sparse matrices with up to 2**63 rows and columns. This support needs to be enabled at compilation time by calling ``setup.py`` and passing ``--with-idxint-64``. Feature removals ---------------- - Support for OpenMP has been removed. If there is enough demand and a good plan for how to organize it, OpenMP support may return in a future QuTiP release. - The ``qutip.parfor`` function has been removed. Use ``qutip.parallel_map`` instead. - ``qutip.graph`` has been removed and replaced by SciPy's graph functions. - ``qutip.topology`` has been removed. It contained only one function ``berry_curvature``. - The ``~/.qutip/qutiprc`` config file is no longer supported. It contained settings for the OpenMP support. QuTiP 4.7.5 (2024-01-29) ======================== Patch release for QuTiP 4.7. It adds support for SciPy 1.12. Bug Fixes --------- - Remove use of scipy. in parallel.py, incompatible with scipy==1.12 (#2305 by Evan McKinney) QuTiP 4.7.4 (2024-01-15) ======================== Bug Fixes --------- - Adapt to deprecation from matplotlib 3.8 (#2243, reported by Bogdan Reznychenko) - Fix name of temp files for removal after use. (#2251, reported by Qile Su) - Avoid integer overflow in Qobj creation. (#2252, reported by KianHwee-Lim) - Ignore DeprecationWarning from pyximport (#2287) - Add partial support and tests for python 3.12. (#2294) Miscellaneous ------------- - Rework `choi_to_kraus`, making it rely on an eigenstates solver that can choose `eigh` if the Choi matrix is Hermitian, as it is more numerically stable. (#2276, by Bogdan Reznychenko) - Rework `kraus_to_choi`, making it faster (#2283, by Bogdan Reznychenko and Rafael Haenel) QuTiP 4.7.3 (2023-08-22) ======================== Bug Fixes --------- - Non-oper qobj + scalar raise an error. (#2208 reported by vikramkashyap) - Fixed issue where `extract_states` did not preserve hermiticity. Fixed issue where `rand_herm` did not set the private attribute _isherm to True. (#2214 by AGaliciaMartinez) - ssesolve average states to density matrices (#2216 reported by BenjaminDAnjou) Miscellaneous ------------- - Exclude cython 3.0.0 from requirement (#2204) - Run in no cython mode with cython >=3.0.0 (#2207) QuTiP 4.7.2 (2023-06-28) ======================== This is a bugfix release for QuTiP 4.7.X. It adds support for numpy 1.25 and scipy 1.11. Bug Fixes --------- - Fix setting of sso.m_ops in heterodyne smesolver and passing through of sc_ops to photocurrent solver. (#2081 by Bogdan Reznychenko and Simon Cross) - Update calls to SciPy eigvalsh and eigsh to pass the range of eigenvalues to return using ``subset_by_index=``. (#2081 by Simon Cross) - Fixed bug where some matrices were wrongly found to be hermitian. (#2082 by AGaliciaMartinez) Miscellaneous ------------- - Fixed typo in stochastic.py (#2049, by eltociear) - `ptrace` always return density matrix (#2185, issue by udevd) - `mesolve` can support mixed callable and Qobj for `e_ops` (#2184 issue by balopat) QuTiP 4.7.1 (2022-12-11) ======================== This is a bugfix release for QuTiP 4.7.X. In addition to the minor fixes listed below, the release adds builds for Python 3.11 and support for packaging 22.0. Features -------- - Improve qutip import times by setting logger names explicitly. (#1980) Bug Fixes --------- - Change floquet_master_equation_rates(...) to use an adaptive number of time steps scaled by the number of sidebands, kmax. (#1961) - Change fidelity(A, B) to use the reduced fidelity formula for pure states which is more numerically efficient and accurate. (#1964) - Change ``brmesolve`` to raise an exception when ode integration is not successful. (#1965) - Backport fix for IPython helper Bloch._repr_svg_ from dev.major. Previously the print_figure function returned bytes, but since ipython/ipython#5452 (in 2014) it returns a Unicode string. This fix updates QuTiP's helper to match. (#1970) - Fix correlation for case where only the collapse operators are time dependent. (#1979) - Fix the hinton visualization method to plot the matrix instead of its transpose. (#2011) - Fix the hinton visualization method to take into account all the matrix coefficients to set the squares scale, instead of only the diagonal coefficients. (#2012) - Fix parsing of package versions in setup.py to support packaging 22.0. (#2037) - Add back .qu suffix to objects saved with qsave and loaded with qload. The suffix was accidentally removed in QuTiP 4.7.0. (#2038) - Add a default max_step to processors. (#2040) Documentation ------------- - Add towncrier for managing the changelog. (#1927) - Update the version of numpy used to build documentation to 1.22.0. (#1940) - Clarify returned objects from bloch_redfield_tensor(). (#1950) - Update Floquet Markov solver docs. (#1958) - Update the roadmap and ideas to show completed work as of August 2022. (#1967) Miscellaneous ------------- - Return TypeError instead of Exception for type error in sesolve argument. (#1924) - Add towncrier draft build of changelog to CI tests. (#1946) - Add Python 3.11 to builds. (#2041) - Simplify version parsing by using packaging.version.Version. (#2043) - Update builds to use cibuildwheel 2.11, and to build with manylinux2014 on Python 3.8 and 3.9, since numpy and SciPy no longer support manylinux2010 on those versions of Python. (#2047) QuTiP 4.7.0 (2022-04-13) ======================== This release sees the addition of two new solvers -- ``qutip.krylovsolve`` based on the Krylov subspace approximation and ``qutip.nonmarkov.heom`` that reimplements the BoFiN HEOM solver. Bloch sphere rendering gained support for drawing arcs and lines on the sphere, and for setting the transparency of rendered points and vectors, Hinton plots gained support for specifying a coloring style, and matrix histograms gained better default colors and more flexible styling options. Other significant improvements include better scaling of the Floquet solver, support for passing ``Path`` objects when saving and loading files, support for passing callable functions as ``e_ops`` to ``mesolve`` and ``sesolve``, and faster state number enumeration and Husimi Q functions. Import bugfixes include some bugs affecting plotting with matplotlib 3.5 and fixing support for qutrits (and other non-qubit) quantum circuits. The many other small improvements, bug fixes, documentation enhancements, and behind the scenese development changes are included in the list below. QuTiP 4.7.X will be the last series of releases for QuTiP 4. Patch releases will continue for the 4.7.X series but the main development effort will move to QuTiP 5. The many, many contributors who filed issues, submitted or reviewed pull requests, and improved the documentation for this release are listed next to their contributions below. Thank you to all of you. Improvements ------------ - **MAJOR** Added krylovsolve as a new solver based on krylov subspace approximation. (`#1739 `_ by Emiliano Fortes) - **MAJOR** Imported BoFiN HEOM (https://github.com/tehruhn/bofin/) into QuTiP and replaced the HEOM solver with a compatibility wrapper around BoFiN bosonic solver. (`#1601 `_, `#1726 `_, and `#1724 `_ by Simon Cross, Tarun Raheja and Neill Lambert) - **MAJOR** Added support for plotting lines and arcs on the Bloch sphere. (`#1690 `_ by Gaurav Saxena, Asier Galicia and Simon Cross) - Added transparency parameter to the add_point, add_vector and add_states methods in the Bloch and Bloch3d classes. (`#1837 `_ by Xavier Spronken) - Support ``Path`` objects in ``qutip.fileio``. (`#1813 `_ by AdriĂ  Labay) - Improved the weighting in steadystate solver, so that the default weight matches the documented behaviour and the dense solver applies the weights in the same manner as the sparse solver. (`#1275 `_ and `#1802 `_ by NS2 Group at LPS and Simon Cross) - Added a ``color_style`` option to the ``hinton`` plotting function. (`#1595 `_ by Cassandra Granade) - Improved the scaling of ``floquet_master_equation_rates`` and ``floquet_master_equation_tensor`` and fixed transposition and basis change errors in ``floquet_master_equation_tensor`` and ``floquet_markov_mesolve``. (`#1248 `_ by Camille Le Calonnec, Jake Lishman and Eric Giguère) - Removed ``linspace_with`` and ``view_methods`` from ``qutip.utilities``. For the former it is far better to use ``numpy.linspace`` and for the later Python's in-built ``help`` function or other tools. (`#1680 `_ by Eric Giguère) - Added support for passing callable functions as ``e_ops`` to ``mesolve`` and ``sesolve``. (`#1655 `_ by Marek NaroĹźniak) - Added the function ``steadystate_floquet``, which returns the "effective" steadystate of a periodic driven system. (`#1660 `_ by Alberto Mercurio) - Improved mcsolve memory efficiency by not storing final states when they are not needed. (`#1669 `_ by Eric Giguère) - Improved the default colors and styling of matrix_histogram and provided additional styling options. (`#1573 `_ and `#1628 `_ by Mahdi Aslani) - Sped up ``state_number_enumerate``, ``state_number_index``, ``state_index_number``, and added some error checking. ``enr_state_dictionaries`` now returns a list for ``idx2state``. (`#1604 `_ by Johannes Feist) - Added new Husimi Q algorithms, improving the speed for density matrices, and giving a near order-of-magnitude improvement when calculating the Q function for many different states, using the new ``qutip.QFunc`` class, instead of the ``qutip.qfunc`` function. (`#934 `_ and `#1583 `_ by Daniel Weigand and Jake Lishman) - Updated licence holders with regards to new governance model, and remove extraneous licensing information from source files. (`#1579 `_ by Jake Lishman) - Removed the vendored copy of LaTeX's qcircuit package which is GPL licensed. We now rely on the package being installed by user. It is installed by default with TexLive. (`#1580 `_ by Jake Lishman) - The signatures of rand_ket and rand_ket_haar were changed to allow N (the size of the random ket) to be determined automatically when dims are specified. (`#1509 `_ by Purva Thakre) Bug Fixes --------- - Fix circuit index used when plotting circuits with non-reversed states. (`#1847 `_ by Christian Staufenbiel) - Changed implementation of ``qutip.orbital`` to use ``scipy.special.spy_harm`` to remove bugs in angle interpretation. (`#1844 `_ by Christian Staufenbiel) - Fixed ``QobjEvo.tidyup`` to use ``settings.auto_tidyup_atol`` when removing small elements in sparse matrices. (`#1832 `_ by Eric Giguère) - Ensured that tidyup's default tolerance is read from settings at each call. (`#1830 `_ by Eric Giguère) - Fixed ``scipy.sparse`` deprecation warnings raised by ``qutip.fast_csr_matrix``. (`#1827 `_ by Simon Cross) - Fixed rendering of vectors on the Bloch sphere when using matplotlib 3.5 and above. (`#1818 `_ by Simon Cross) - Fixed the displaying of ``Lattice1d`` instances and their unit cells. Previously calling them raised exceptions in simple cases. (`#1819 `_, `#1697 `_ and `#1702 `_ by Simon Cross and Saumya Biswas) - Fixed the displaying of the title for ``hinton`` and ``matrix_histogram`` plots when a title is given. Previously the supplied title was not displayed. (`#1707 `_ by Vladimir Vargas-CalderĂłn) - Removed an incorrect check on the initial state dimensions in the ``QubitCircuit`` constructor. This allows, for example, the construction of qutrit circuits. (`#1807 `_ by Boxi Li) - Fixed the checking of ``method`` and ``offset`` parameters in ``coherent`` and ``coherent_dm``. (`#1469 `_ and `#1741 `_ by Joseph Fox-Rabinovitz and Simon Cross) - Removed the Hamiltonian saved in the ``sesolve`` solver results. (`#1689 `_ by Eric Giguère) - Fixed a bug in rand_herm with ``pos_def=True`` and ``density>0.5`` where the diagonal was incorrectly filled. (`#1562 `_ by Eric Giguère) Documentation Improvements -------------------------- - Added contributors image to the documentation. (`#1828 `_ by Leonard Assis) - Fixed the Theory of Quantum Information bibliography link. (`#1840 `_ by Anto Luketina) - Fixed minor grammar errors in the dynamics guide. (`#1822 `_ by Victor Omole) - Fixed many small documentation typos. (`#1569 `_ by Ashish Panigrahi) - Added Pulser to the list of libraries that use QuTiP. (`#1570 `_ by Ashish Panigrahi) - Corrected typo in the states and operators guide. (`#1567 `_ by Laurent Ajdnik) - Converted http links to https. (`#1555 `_ by Jake Lishamn) Developer Changes ----------------- - Add GitHub actions test run on windows-latest. (`#1853 `_ and `#1855 `_ by Simon Cross) - Bumped the version of pillow used to build documentation from 9.0.0 to 9.0.1. (`#1835 `_ by dependabot) - Migrated the ``qutip.superop_reps`` tests to pytest. (`#1825 `_ by Felipe Bivort Haiek) - Migrated the ``qutip.steadystates`` tests to pytest. (`#1679 `_ by Eric Giguère) - Changed the README.md CI badge to the GitHub Actions badge. (`#1581 `_ by Jake Lishman) - Updated CodeClimate configuration to treat our Python source files as Python 3. (`#1577 `_ by Jake Lishman) - Reduced cyclomatic complexity in ``qutip._mkl``. (`#1576 `_ by Jake Lishman) - Fixed PEP8 warnings in ``qutip.control``, ``qutip.mcsolve``, ``qutip.random_objects``, and ``qutip.stochastic``. (`#1575 `_ by Jake Lishman) - Bumped the version of urllib3 used to build documentation from 1.26.4 to 1.26.5. (`#1563 `_ by dependabot) - Moved tests to GitHub Actions. (`#1551 `_ by Jake Lishman) - The GitHub contributing guidelines were re-added and updated to point to the more complete guidelines in the documentation. (`#1549 `_ by Jake Lishman) - The release documentation was reworked after the initial 4.6.1 to match the actual release process. (`#1544 `_ by Jake Lishman) QuTiP 4.6.3 (2022-02-9) ======================= This minor release adds support for numpy 1.22 and Python 3.10 and removes some blockers for running QuTiP on the Apple M1. The performance of the ``enr_destroy``, ``state_number_enumerate`` and ``hadamard_transform`` functions was drastically improved (up to 70x or 200x faster in some common cases), and support for the drift Hamiltonian was added to the ``qutip.qip`` ``Processor``. The ``qutip.hardware_info`` module was removed as part of adding support for the Apple M1. We hope the removal of this little-used module does not adversely affect many users -- it was largely unrelated to QuTiP's core functionality and its presence was a continual source of blockers to importing ``qutip`` on new or changed platforms. A new check on the dimensions of ``Qobj``'s were added to prevent segmentation faults when invalid shape and dimension combinations were passed to Cython code. In addition, there were many small bugfixes, documentation improvements, and improvements to our building and testing processes. Improvements ------------ - The ``enr_destroy`` function was made ~200x faster in many simple cases. (`#1593 `_ by Johannes Feist) - The ``state_number_enumerate`` function was made significantly faster. (`#1594 `_ by Johannes Feist) - Added the missing drift Hamiltonian to the method run_analytically of ``Processor``. (`#1603 `_ Boxi Li) - The ``hadamard_transform`` was made much faster, e.g., ~70x faster for N=10. (`#1688 `_ by Asier Galicia) - Added support for computing the power of a scalar-like Qobj. (`#1692 `_ by Asier Galicia) - Removed the ``hardware_info`` module. This module wasn't used inside QuTiP and regularly broke when new operating systems were released, and in particular prevented importing QuTiP on the Apple M1. (`#1754 `_, `#1758 `_ by Eric Giguère) Bug Fixes --------- - Fixed support for calculating the propagator of a density matrix with collapse operators. QuTiP 4.6.2 introduced extra sanity checks on the dimensions of inputs to mesolve (Fix mesolve segfault with bad initial state `#1459 `_), but the propagator function's calls to mesolve violated these checks by supplying initial states with the dimensions incorrectly set. ``propagator`` now calls mesolve with the correct dimensions set on the initial state. (`#1588 `_ by Simon Cross) - Fixed support for calculating the propagator for a superoperator without collapse operators. This functionality was not tested by the test suite and appears to have broken sometime during 2019. Tests have now been added and the code breakages fixed. (`#1588 `_ by Simon Cross) - Fixed the ignoring of the random number seed passed to ``rand_dm`` in the case where ``pure`` was set to true. (`#1600 `_ Pontus WikstĂĽhl) - Fixed qutip.control.optimize_pulse support for sparse eigenvector decomposition with the Qobj oper_dtype (the Qobj oper_dtype is the default for large systems). (`#1621 `_ by Simon Cross) - Removed qutip.control.optimize_pulse support for scipy.sparse.csr_matrix and generic ndarray-like matrices. Support for these was non-functional. (`#1621 `_ by Simon Cross) - Fixed errors in the calculation of the Husimi spin_q_function and spin_wigner functions and added tests for them. (`#1632 `_ by Mark Johnson) - Fixed setting of OpenMP compilation flag on Linux. Previously when compiling the OpenMP functions were compiled without parallelization. (`#1693 `_ by Eric Giguère) - Fixed tracking the state of the Bloch sphere figure and axes to prevent exceptions during rendering. (`#1619 `_ by Simon Cross) - Fixed compatibility with numpy configuration in numpy's 1.22.0 release. (`#1752 `_ by Matthew Treinish) - Added dims checks for e_ops passed to solvers to prevent hanging the calling process when e_ops of the wrong dimensions were passed. (`#1778 `_ by Eric Giguère) - Added a check in Qobj constructor that the respective members of data.shape cannot be larger than what the corresponding dims could contain to prevent a segmentation fault caused by inconsistencies between dims and shapes. (`#1783 `_, `#1785 `_, `#1784 `_ by Lajos Palanki & Eric Giguère) Documentation Improvements -------------------------- - Added docs for the num_cbits parameter of the QubitCircuit class. (`#1652 `_ by Jon Crall) - Fixed the parameters in the call to fsesolve in the Floquet guide. (`#1675 `_ by Simon Cross) - Fixed the description of random number usage in the Monte Carlo solver guide. (`#1677 `_ by Ian Thorvaldson) - Fixed the rendering of equation numbers in the documentation (they now appear on the right as expected, not above the equation). (`#1678 `_ by Simon Cross) - Updated the installation requirements in the documentation to match what is specified in setup.py. (`#1715 `_ by Asier Galicia) - Fixed a typo in the ``chi_to_choi`` documentation. Previously the documentation mixed up chi and choi. (`#1731 `_ by Pontus WikstĂĽhl) - Improved the documentation for the stochastic equation solvers. Added links to notebooks with examples, API doumentation and external references. (`#1743 `_ by Leonardo Assis) - Fixed a typo in ``qutip.settings`` in the settings guide. (`#1786 `_ by Mahdi Aslani) - Made numerous small improvements to the text of the QuTiP basics guide. (`#1768 `_ by Anna Naden) - Made a small phrasing improvement to the README. (`#1790 `_ by Rita Abani) Developer Changes ----------------- - Improved test coverage of states and operators functions. (`#1578 `_ by Eric Giguère) - Fixed test_interpolate mcsolve use (`#1645 `_ by Eric Giguère) - Ensured figure plots are explicitly closed during tests so that the test suite passes when run headless under Xvfb. (`#1648 `_ by Simon Cross) - Bumped the version of pillow used to build documentation from 8.2.0 to 9.0.0. (`#1654 `_, `#1760 `_ by dependabot) - Bumped the version of babel used to build documentation from 2.9.0 to 2.9.1. (`#1695 `_ by dependabot) - Bumped the version of numpy used to build documentation from 1.19.5 to 1.21.0. (`#1767 `_ by dependabot) - Bumped the version of ipython used to build documentation from 7.22.0 to 7.31.1. (`#1780 `_ by dependabot) - Rename qutip.bib to CITATION.bib to enable GitHub's citation support. (`#1662 `_ by Ashish Panigrahi) - Added tests for simdiags. (`#1681 `_ by Eric Giguère) - Added support for specifying the numpy version in the CI test matrix. (`#1696 `_ by Simon Cross) - Fixed the skipping of the dnorm metric tests if cvxpy is not installed. Previously all metrics tests were skipped by accident. (`#1704 `_ by Florian Hopfmueller) - Added bug report, feature request and other options to the GitHub issue reporting template. (`#1728 `_ by Aryaman Kolhe) - Updated the build process to support building on Python 3.10 by removing the build requirement for numpy < 1.20 and replacing it with a requirement on oldest-supported-numpy. (`#1747 `_ by Simon Cross) - Updated the version of cibuildwheel used to build wheels to 2.3.0. (`#1747 `_, `#1751 `_ by Simon Cross) - Added project urls to linking to the source repository, issue tracker and documentation to setup.cfg. (`#1779 `_ by Simon Cross) - Added a numpy 1.22 and Python 3.10 build to the CI test matrix. (`#1777 `_ by Simon Cross) - Ignore deprecation warnings from SciPy 1.8.0 scipy.sparse.X imports in CI tests. (`#1797 `_ by Simon Cross) - Add building of wheels for Python 3.10 to the cibuildwheel job. (`#1796 `_ by Simon Cross) QuTiP 4.6.2 (2021-06-02) ======================== This minor release adds a function to calculate the quantum relative entropy, fixes a corner case in handling time-dependent Hamiltonians in ``mesolve`` and adds back support for a wider range of matplotlib versions when plotting or animating Bloch spheres. It also adds a section in the README listing the papers which should be referenced while citing QuTiP. Improvements ------------ - Added a "Citing QuTiP" section to the README, containing a link to the QuTiP papers. (`#1554 `_) - Added ``entropy_relative`` which returns the quantum relative entropy between two density matrices. (`#1553 `_) Bug Fixes --------- - Fixed Bloch sphere distortion when using Matplotlib >= 3.3.0. (`#1496 `_) - Removed use of integer-like floats in math.factorial since it is deprecated as of Python 3.9. (`#1550 `_) - Simplified call to ffmpeg used in the the Bloch sphere animation tutorial to work with recent versions of ffmpeg. (`#1557 `_) - Removed blitting in Bloch sphere FuncAnimation example. (`#1558 `_) - Added a version checking condition to handle specific functionalities depending on the matplotlib version. (`#1556 `_) - Fixed ``mesolve`` handling of time-dependent Hamiltonian with a custom tlist and ``c_ops``. (`#1561 `_) Developer Changes ----------------- - Read documentation version and release from the VERSION file. QuTiP 4.6.1 (2021-05-04) ======================== This minor release fixes bugs in QIP gate definitions, fixes building from the source tarball when git is not installed and works around an MKL bug in versions of SciPy <= 1.4. It also adds the ``[full]`` pip install target so that ``pip install qutip[full]`` installs qutip and all of its optional and developer dependencies. Improvements ------------ - Add the ``[full]`` pip install target (by **Jake Lishman**) Bug Fixes --------- - Work around pointer MKL eigh bug in SciPy <= 1.4 (by **Felipe Bivort Haiek**) - Fix berkeley, swapalpha and cz gate operations (by **Boxi Li**) - Expose the CPHASE control gate (by **Boxi Li**) - Fix building from the sdist when git is not installed (by **Jake Lishman**) Developer Changes ----------------- - Move the qutip-doc documentation into the qutip repository (by **Jake Lishman**) - Fix warnings in documentation build (by **Jake Lishman**) - Fix warnings in pytest runs and make pytest treat warnings as errors (by **Jake Lishman**) - Add Simon Cross as author (by **Simon Cross**) QuTiP 4.6.0 (2021-04-11) ======================== This release brings improvements for qubit circuits, including a pulse scheduler, measurement statistics, reading/writing OpenQASM and optimisations in the circuit simulations. This is the first release to have full binary wheel releases on pip; you can now do ``pip install qutip`` on almost any machine to get a correct version of the package without needing any compilers set up. The support for Numpy 1.20 that was first added in QuTiP 4.5.3 is present in this version as well, and the same build considerations mentioned there apply here too. If building using the now-supported PEP 517 mechanisms (e.g. ``python -mbuild /path/to/qutip``), all build dependencies will be correctly satisfied. Improvements ------------ - **MAJOR** Add saving, loading and resetting functionality to ``qutip.settings`` for easy re-configuration. (by **Eric Giguère**) - **MAJOR** Add a quantum gate scheduler in ``qutip.qip.scheduler``, to help parallelise the operations of quantum gates. This supports two scheduling modes: as late as possible, and as soon as possible. (by **Boxi Li**) - **MAJOR** Improved qubit circuit simulators, including OpenQASM support and performance optimisations. (by **Sidhant Saraogi**) - **MAJOR** Add tools for quantum measurements and their statistics. (by **Simon Cross** and **Sidhant Saraogi**) - Add support for Numpy 1.20. QuTiP should be compiled against a version of Numpy ``>= 1.16.6`` and ``< 1.20`` (note: does _not_ include 1.20 itself), but such an installation is compatible with any modern version of Numpy. Source installations from ``pip`` understand this constraint. - Improve the error message when circuit plotting fails. (by **Boxi Li**) - Add support for parsing M1 Mac hardware information. (by **Xiaoliang Wu**) - Add more single-qubit gates and controlled gates. (by **Mateo Laguna** and **MartĂ­n Sande Costa**) - Support decomposition of ``X``, ``Y`` and ``Z`` gates in circuits. (by **Boxi Li**) - Refactor ``QubitCircuit.resolve_gate()`` (by **MartĂ­n Sande Costa**) Bug Fixes --------- - Fix ``dims`` in the returns from ``Qobj.eigenstates`` on superoperators. (by **Jake Lishman**) - Calling Numpy ufuncs on ``Qobj`` will now correctly raise a ``TypeError`` rather than returning a nonsense ``ndarray``. (by **Jake Lishman**) - Convert segfault into Python exception when creating too-large tensor products. (by **Jake Lishman**) - Correctly set ``num_collapse`` in the output of ``mesolve``. (by **Jake Lishman**) - Fix ``ptrace`` when all subspaces are being kept, or the subspaces are passed in order. (by **Jake Lishman**) - Fix sorting bug in ``Bloch3d.add_points()``. (by **pschindler**) - Fix invalid string literals in docstrings and some unclosed files. (by **Élie Gouzien**) - Fix Hermicity tests for matrices with values that are within the tolerance of 0. (by **Jake Lishman**) - Fix the trace norm being incorrectly reported as 0 for small matrices. (by **Jake Lishman**) - Fix issues with ``dnorm`` when using CVXPy 1.1 with sparse matrices. (by **Felipe Bivort Haiek**) - Fix segfaults in ``mesolve`` when passed a bad initial ``Qobj`` as the state. (by **Jake Lishman**) - Fix sparse matrix construction in PIQS when using Scipy 1.6.1. (by **Drew Parsons**) - Fix ``zspmv_openmp.cpp`` missing from the pip sdist. (by **Christoph Gohlke**) - Fix correlation functions throwing away imaginary components. (by **Asier Galicia Martinez**) - Fix ``QubitCircuit.add_circuit()`` for SWAP gate. (by **Canoming**) - Fix the broken LaTeX image conversion. (by **Jake Lishman**) - Fix gate resolution of the FREDKIN gate. (by **Bo Yang**) - Fix broken formatting in docstrings. (by **Jake Lishman**) Deprecations ------------ - ``eseries``, ``essolve`` and ``ode2es`` are all deprecated, pending removal in QuTiP 5.0. These are legacy functions and classes that have been left unmaintained for a long time, and their functionality is now better achieved with ``QobjEvo`` or ``mesolve``. Developer Changes ----------------- - **MAJOR** Overhaul of setup and packaging code to make it satisfy PEP 517, and move the build to a matrix on GitHub Actions in order to release binary wheels on pip for all major platforms and supported Python versions. (by **Jake Lishman**) - Default arguments in ``Qobj`` are now ``None`` rather than mutable types. (by **Jake Lishman**) - Fixed comsumable iterators being used to parametrise some tests, preventing the testing suite from being re-run within the same session. (by **Jake Lishman**) - Remove unused imports, simplify some floats and remove unnecessary list conversions. (by **jakobjakobson13**) - Improve Travis jobs matrix for specifying the testing containers. (by **Jake Lishman**) - Fix coverage reporting on Travis. (by **Jake Lishman**) - Added a ``pyproject.toml`` file. (by **Simon Humpohl** and **Eric Giguère**) - Add doctests to documentation. (by **Sidhant Saraogi**) - Fix all warnings in the documentation build. (by **Jake Lishman**) QuTiP 4.5.3 (2021-02-19) ======================== This patch release adds support for Numpy 1.20, made necessary by changes to how array-like objects are handled. There are no other changes relative to version 4.5.2. Users building from source should ensure that they build against Numpy versions >= 1.16.6 and < 1.20 (not including 1.20 itself), but after that or for those installing from conda, an installation will support any current Numpy version >= 1.16.6. Improvements ------------ - Add support for Numpy 1.20. QuTiP should be compiled against a version of Numpy ``>= 1.16.6`` and ``< 1.20`` (note: does _not_ include 1.20 itself), but such an installation is compatible with any modern version of Numpy. Source installations from ``pip`` understand this constraint. QuTiP 4.5.2 (2020-07-14) ======================== This is predominantly a hot-fix release to add support for Scipy 1.5, due to changes in private sparse matrix functions that QuTiP also used. Improvements ------------ - Add support for Scipy 1.5. (by **Jake Lishman**) - Improved speed of ``zcsr_inner``, which affects ``Qobj.overlap``. (by **Jake Lishman**) - Better error messages when installation requirements are not satisfied. (by **Eric Giguère**) Bug Fixes --------- - Fix ``zcsr_proj`` acting on matrices with unsorted indices. (by **Jake Lishman**) - Fix errors in Milstein's heterodyne. (by **Eric Giguère**) - Fix datatype bug in ``qutip.lattice`` module. (by **Boxi Li**) - Fix issues with ``eigh`` on Mac when using OpenBLAS. (by **Eric Giguère**) Developer Changes ----------------- - Converted more of the codebase to PEP 8. - Fix several instances of unsafe mutable default values and unsafe ``is`` comparisons. QuTiP 4.5.1 (2020-05-15) ======================== Improvements ------------ - ``husimi`` and ``wigner`` now accept half-integer spin (by **maij**) - Better error messages for failed string coefficient compilation. (issue raised by **nohchangsuk**) Bug Fixes --------- - Safer naming for temporary files. (by **Eric Giguère**) - Fix ``clebsch`` function for half-integer (by **Thomas Walker**) - Fix ``randint``'s dtype to ``uint32`` for compatibility with Windows. (issue raised by **Boxi Li**) - Corrected stochastic's heterodyne's m_ops (by **eliegenois**) - Mac pool use spawn. (issue raised by **goerz**) - Fix typos in ``QobjEvo._shift``. (by **Eric Giguère**) - Fix warning on Travis CI. (by **Ivan Carvalho**) Deprecations ------------ - ``qutip.graph`` functions will be deprecated in QuTiP 5.0 in favour of ``scipy.sparse.csgraph``. Developer Changes ----------------- - Add Boxi Li to authors. (by **Alex Pitchford**) - Skip some tests that cause segfaults on Mac. (by **Nathan Shammah** and **Eric Giguère**) - Use Python 3.8 for testing on Mac and Linux. (by **Simon Cross** and **Eric Giguère**) QuTiP 4.5.0 (2020-01-31) ======================== Improvements ------------ - **MAJOR FEATURE**: Added `qip.noise`, a module with pulse level description of quantum circuits allowing to model various types of noise and devices (by **Boxi Li**). - **MAJOR FEATURE**: Added `qip.lattice`, a module for the study of lattice dynamics in 1D (by **Saumya Biswas**). - Migrated testing from Nose to PyTest (by **Tarun Raheja**). - Optimized testing for PyTest and removed duplicated test runners (by **Jake Lishman**). - Deprecated importing `qip` functions to the qutip namespace (by **Boxi Li**). - Added the possibility to define non-square superoperators relevant for quantum circuits (by **Arne Grimsmo** and **Josh Combes**). - Implicit tensor product for `qeye`, `qzero` and `basis` (by **Jake Lishman**). - QObjEvo no longer requires Cython for string coefficient (by **Eric Giguère**). - Added marked tests for faster tests in `testing.run()` and made faster OpenMP benchmarking in CI (by **Eric Giguère**). - Added entropy and purity for Dicke density matrices, refactored into more general dicke_trace (by **Nathan Shammah**). - Added option for specifying resolution in Bloch.save function (by **Tarun Raheja**). - Added information related to the value of hbar in `wigner` and `continuous_variables` (by **Nicolas Quesada**). - Updated requirements for `scipy 1.4` (by **Eric Giguère**). - Added previous lead developers to the qutip.about() message (by **Nathan Shammah**). - Added improvements to `Qobj` introducing the `inv` method and making the partial trace, `ptrace`, faster, keeping both sparse and dense methods (by **Eric Giguère**). - Allowed general callable objects to define a time-dependent Hamiltonian (by **Eric Giguère**). - Added feature so that `QobjEvo` no longer requires Cython for string coefficients (by **Eric Giguère**). - Updated authors list on Github and added `my binder` link (by **Nathan Shammah**). Bug Fixes --------- - Fixed `PolyDataMapper` construction for `Bloch3d` (by **Sam Griffiths**). - Fixed error checking for null matrix in essolve (by **Nathan Shammah**). - Fixed name collision for parallel propagator (by **Nathan Shammah**). - Fixed dimensional incongruence in `propagator` (by **Nathan Shammah**) - Fixed bug by rewriting clebsch function based on long integer fraction (by **Eric Giguère**). - Fixed bugs in QobjEvo's args depending on state and added solver tests using them (by **Eric Giguère**). - Fixed bug in `sesolve` calculation of average states when summing the timeslot states (by **Alex Pitchford**). - Fixed bug in `steadystate` solver by removing separate arguments for MKL and Scipy (by **Tarun Raheja**). - Fixed `Bloch.add_ponts` by setting `edgecolor = None` in `plot_points` (by **Nathan Shammah**). - Fixed error checking for null matrix in `essolve` solver affecting also `ode2es` (by **Peter Kirton**). - Removed unnecessary shebangs in .pyx and .pxd files (by **Samesh Lakhotia**). - Fixed `sesolve` and import of `os` in `codegen` (by **Alex Pitchford**). - Updated `plot_fock_distribution` by removing the offset value 0.4 in the plot (by **Rajiv-B**). QuTiP 4.4.1 (2019-08-29) ======================== Improvements ------------ - QobjEvo do not need to start from 0 anymore (by **Eric Giguère**). - Add a quantum object purity function (by **Nathan Shammah** and **Shahnawaz Ahmed**). - Add step function interpolation for array time-coefficient (by **Boxi Li**). - Generalize expand_oper for arbitrary dimensions, and new method for cyclic permutations of given target cubits (by **Boxi Li**). Bug Fixes --------- - Fixed the pickling but that made solver unable to run in parallel on Windows (Thank **lrunze** for reporting) - Removed warning when mesolve fall back on sesolve (by **Michael Goerz**). - Fixed dimension check and confusing documentation in random ket (by **Yariv Yanay**). - Fixed Qobj isherm not working after using Qobj.permute (Thank **llorz1207** for reporting). - Correlation functions call now properly handle multiple time dependant functions (Thank **taw181** for reporting). - Removed mutable default values in mesolve/sesolve (by **Michael Goerz**). - Fixed simdiag bug (Thank **Croydon-Brixton** for reporting). - Better support of constant QobjEvo (by **Boxi Li**). - Fixed potential cyclic import in the control module (by **Alexander Pitchford**). QuTiP 4.4.0 (2019-07-03) ======================== Improvements ------------ - **MAJOR FEATURE**: Added methods and techniques to the stochastic solvers (by **Eric Giguère**) which allows to use a much broader set of solvers and much more efficiently. - **MAJOR FEATURE**: Optimization of the montecarlo solver (by **Eric Giguère**). Computation are faster in many cases. Collapse information available to time dependant information. - Added the QObjEvo class and methods (by **Eric Giguère**), which is used behind the scenes by the dynamical solvers, making the code more efficient and tidier. More built-in function available to string coefficients. - The coefficients can be made from interpolated array with variable timesteps and can obtain state information more easily. Time-dependant collapse operator can have multiple terms. - New wigner_transform and plot_wigner_sphere function. (by **Nithin Ramu**). - ptrace is faster and work on bigger systems, from 15 Qbits to 30 Qbits. - QIP module: added the possibility for user-defined gates, added the possibility to remove or add gates in any point of an already built circuit, added the molmer_sorensen gate, and fixed some bugs (by **Boxi Li**). - Added the quantum Hellinger distance to qutip.metrics (by **Wojciech Rzadkowski**). - Implemented possibility of choosing a random seed (by **Marek Marekyggdrasil**). - Added a code of conduct to Github. Bug Fixes --------- - Fixed bug that made QuTiP incompatible with SciPy 1.3. QuTiP 4.3.0 (2018-07-14) ======================== Improvements ------------ - **MAJOR FEATURE**: Added the Permutational Invariant Quantum Solver (PIQS) module (by **Nathan Shammah** and **Shahnawaz Ahmed**) which allows the simluation of large TLSs ensembles including collective and local Lindblad dissipation. Applications range from superradiance to spin squeezing. - **MAJOR FEATURE**: Added a photon scattering module (by **Ben Bartlett**) which can be used to study scattering in arbitrary driven systems coupled to some configuration of output waveguides. - Cubic_Spline functions as time-dependent arguments for the collapse operators in mesolve are now allowed. - Added a faster version of bloch_redfield_tensor, using components from the time-dependent version. About 3x+ faster for secular tensors, and 10x+ faster for non-secular tensors. - Computing Q.overlap() [inner product] is now ~30x faster. - Added projector method to Qobj class. - Added fast projector method, ``Q.proj()``. - Computing matrix elements, ``Q.matrix_element`` is now ~10x faster. - Computing expectation values for ket vectors using ``expect`` is now ~10x faster. - ``Q.tr()`` is now faster for small Hilbert space dimensions. - Unitary operator evolution added to sesolve - Use OPENMP for tidyup if installed. Bug Fixes --------- - Fixed bug that stopped simdiag working for python 3. - Fixed semidefinite cvxpy Variable and Parameter. - Fixed iterative lu solve atol keyword issue. - Fixed unitary op evolution rhs matrix in ssesolve. - Fixed interpolating function to return zero outside range. - Fixed dnorm complex casting bug. - Fixed control.io path checking issue. - Fixed ENR fock dimension. - Fixed hard coded options in propagator 'batch' mode - Fixed bug in trace-norm for non-Hermitian operators. - Fixed bug related to args not being passed to coherence_function_g2 - Fixed MKL error checking dict key error QuTiP 4.2.0 (2017-07-28) ======================== Improvements ------------ - **MAJOR FEATURE**: Initial implementation of time-dependent Bloch-Redfield Solver. - Qobj tidyup is now an order of magnitude faster. - Time-dependent codegen now generates output NumPy arrays faster. - Improved calculation for analytic coefficients in coherent states (Sebastian Kramer). - Input array to correlation FFT method now checked for validity. - Function-based time-dependent mesolve and sesolve routines now faster. - Codegen now makes sure that division is done in C, as opposed to Python. - Can now set different controls for a each timeslot in quantum optimization. This allows time-varying controls to be used in pulse optimisation. Bug Fixes --------- - rcsolve importing old Odeoptions Class rather than Options. - Non-int issue in spin Q and Wigner functions. - Qobj's should tidyup before determining isherm. - Fixed time-dependent RHS function loading on Win. - Fixed several issues with compiling with Cython 0.26. - Liouvillian superoperators were hard setting isherm=True by default. - Fixed an issue with the solver safety checks when inputing a list with Python functions as time-dependence. - Fixed non-int issue in Wigner_cmap. - MKL solver error handling not working properly. QuTiP 4.1.0 (2017-03-10) ======================== Improvements ------------ *Core libraries* - **MAJOR FEATURE**: QuTiP now works for Python 3.5+ on Windows using Visual Studio 2015. - **MAJOR FEATURE**: Cython and other low level code switched to C++ for MS Windows compatibility. - **MAJOR FEATURE**: Can now use interpolating cubic splines as time-dependent coefficients. - **MAJOR FEATURE**: Sparse matrix - vector multiplication now parallel using OPENMP. - Automatic tuning of OPENMP threading threshold. - Partial trace function is now up to 100x+ faster. - Hermitian verification now up to 100x+ faster. - Internal Qobj objects now created up to 60x faster. - Inplace conversion from COO -> CSR sparse formats (e.g. Memory efficiency improvement.) - Faster reverse Cuthill-Mckee and sparse one and inf norms. Bug Fixes --------- - Cleanup of temp. Cython files now more robust and working under Windows. QuTiP 4.0.2 (2017-01-05) ======================== Bug Fixes --------- - td files no longer left behind by correlation tests - Various fast sparse fixes QuTiP 4.0.0 (2016-12-22) ======================== Improvements ------------ *Core libraries* - **MAJOR FEATURE**: Fast sparse: New subclass of csr_matrix added that overrides commonly used methods to avoid certain checks that incurr execution cost. All Qobj.data now fast_csr_matrix - HEOM performance enhancements - spmv now faster - mcsolve codegen further optimised *Control modules* - Time dependent drift (through list of pwc dynamics generators) - memory optimisation options provided for control.dynamics Bug Fixes --------- - recompilation of pyx files on first import removed - tau array in control.pulseoptim funcs now works QuTiP 3.2.0 =========== (Never officially released) New Features ------------ *Core libraries* - **MAJOR FEATURE**: Non-Markovian solvers: Hierarchy (**Added by Neill Lambert**), Memory-Cascade, and Transfer-Tensor methods. - **MAJOR FEATURE**: Default steady state solver now up to 100x faster using the Intel Pardiso library under the Anaconda and Intel Python distributions. - The default Wigner function now uses a Clenshaw summation algorithm to evaluate a polynomial series that is applicable for any number of exciations (previous limitation was ~50 quanta), and is ~3x faster than before. (**Added by Denis Vasilyev**) - Can now define a given eigen spectrum for random Hermitian and density operators. - The Qobj ``expm`` method now uses the equivilent SciPy routine, and performs a much faster ``exp`` operation if the matrix is diagonal. - One can now build zero operators using the ``qzero`` function. *Control modules* - **MAJOR FEATURE**: CRAB algorithm added This is an alternative to the GRAPE algorithm, which allows for analytical control functions, which means that experimental constraints can more easily be added into optimisation. See tutorial notebook for full information. Improvements ------------ *Core libraries* - Two-time correlation functions can now be calculated for fully time-dependent Hamiltonians and collapse operators. (**Added by Kevin Fischer**) - The code for the inverse-power method for the steady state solver has been simplified. - Bloch-Redfield tensor creation is now up to an order of magnitude faster. (**Added by Johannes Feist**) - Q.transform now works properly for arrays directly from sp_eigs (or eig). - Q.groundstate now checks for degeneracy. - Added ``sinm`` and ``cosm`` methods to the Qobj class. - Added ``charge`` and ``tunneling`` operators. - Time-dependent Cython code is now easier to read and debug. *Control modules* - The internal state / quantum operator data type can now be either Qobj or ndarray Previous only ndarray was possible. This now opens up possibility of using Qobj methods in fidelity calculations The attributes and functions that return these operators are now preceded by an underscore, to indicate that the data type could change depending on the configuration options. In most cases these functions were for internal processing only anyway, and should have been 'private'. Accessors to the properties that could be useful outside of the library have been added. These always return Qobj. If the internal operator data type is not Qobj, then there could be signicant overhead in the conversion, and so this should be avoided during pulse optimisation. If custom sub-classes are developed that use Qobj properties and methods (e.g. partial trace), then it is very likely that it will be more efficient to set the internal data type to Qobj. The internal operator data will be chosen automatically based on the size and sparsity of the dynamics generator. It can be forced by setting ``dynamics.oper_dtype = `` Note this can be done by passing ``dyn_params={'oper_dtype':}`` in any of the pulseoptim functions. Some other properties and methods were renamed at the same time. A full list is given here. - All modules - function: ``set_log_level`` -> property: ``log_level`` - dynamics functions - ``_init_lists`` now ``_init_evo`` - ``get_num_ctrls`` now property: ``num_ctrls`` - ``get_owd_evo_target`` now property: ``onto_evo_target`` - ``combine_dyn_gen`` now ``_combine_dyn_gen`` (no longer returns a value) - ``get_dyn_gen`` now ``_get_phased_dyn_gen`` - ``get_ctrl_den_gen`` now ``_get_phased_ctrl_dyn_gen`` - ``ensure_decomp_curr`` now ``_ensure_decomp_curr`` - ``spectral_decomp`` now ``_spectral_decomp`` - dynamics properties - ``evo_init2t`` now ``_fwd_evo`` (``fwd_evo`` as Qobj) - ``evo_t2end`` now ``_onwd_evo`` (``onwd_evo`` as Qobj) - ``evo_t2targ`` now ``_onto_evo`` (``onto_evo`` as Qobj) - fidcomp properties - ``uses_evo_t2end`` now ``uses_onwd_evo`` - ``uses_evo_t2targ`` now ``uses_onto_evo`` - ``set_phase_option`` function now property ``phase_option`` - propcomp properties - ``grad_exact`` (now read only) - propcomp functions - ``compute_propagator`` now ``_compute_propagator`` - ``compute_diff_prop`` now ``_compute_diff_prop`` - ``compute_prop_grad`` now ``_compute_prop_grad`` - tslotcomp functions - ``get_timeslot_for_fidelity_calc`` now ``_get_timeslot_for_fidelity_calc`` *Miscellaneous* - QuTiP Travis CI tests now use the Anaconda distribution. - The ``about`` box and ipynb ``version_table`` now display addition system information. - Updated Cython cleanup to remove depreciation warning in sysconfig. - Updated ipynb_parallel to look for ``ipyparallel`` module in V4 of the notebooks. Bug Fixes --------- - Fixes for countstat and psuedo-inverse functions - Fixed Qobj division tests on 32-bit systems. - Removed extra call to Python in time-dependent Cython code. - Fixed issue with repeated Bloch sphere saving. - Fixed T_0 triplet state not normalized properly. (**Fixed by Eric Hontz**) - Simplified compiler flags (support for ARM systems). - Fixed a decoding error in ``qload``. - Fixed issue using complex.h math and np.kind_t variables. - Corrected output states mismatch for ``ntraj=1`` in the mcf90 solver. - Qobj data is now copied by default to avoid a bug in multiplication. (**Fixed by Richard Brierley**) - Fixed bug overwriting ``hardware_info`` in ``__init__``. (**Fixed by Johannes Feist**) - Restored ability to explicity set Q.isherm, Q.type, and Q.superrep. - Fixed integer depreciation warnings from NumPy. - Qobj * (dense vec) would result in a recursive loop. - Fixed args=None -> args={} in correlation functions to be compatible with mesolve. - Fixed depreciation warnings in mcsolve. - Fixed neagtive only real parts in ``rand_ket``. - Fixed a complicated list-cast-map-list antipattern in super operator reps. (**Fixed by Stefan Krastanov**) - Fixed incorrect ``isherm`` for ``sigmam`` spin operator. - Fixed the dims when using ``final_state_output`` in ``mesolve`` and ``sesolve``. QuTiP 3.1.0 (2015-01-01) ======================== New Features ------------ - **MAJOR FEATURE**: New module for quantum control (qutip.control). - **NAMESPACE CHANGE**: QuTiP no longer exports symbols from NumPy and matplotlib, so those modules must now be explicitly imported when required. - New module for counting statistics. - Stochastic solvers now run trajectories in parallel. - New superoperator and tensor manipulation functions (super_tensor, composite, tensor_contract). - New logging module for debugging (qutip.logging). - New user-available API for parallelization (parallel_map). - New enhanced (optional) text-based progressbar (qutip.ui.EnhancedTextProgressBar) - Faster Python based monte carlo solver (mcsolve). - Support for progress bars in propagator function. - Time-dependent Cython code now calls complex cmath functions. - Random numbers seeds can now be reused for successive calls to mcsolve. - The Bloch-Redfield master equation solver now supports optional Lindblad type collapse operators. - Improved handling of ODE integration errors in mesolve. - Improved correlation function module (for example, improved support for time-dependent problems). - Improved parallelization of mcsolve (can now be interrupted easily, support for IPython.parallel, etc.) - Many performance improvements, and much internal code restructuring. Bug Fixes --------- - Cython build files for time-dependent string format now removed automatically. - Fixed incorrect solution time from inverse-power method steady state solver. - mcsolve now supports `Options(store_states=True)` - Fixed bug in `hadamard` gate function. - Fixed compatibility issues with NumPy 1.9.0. - Progressbar in mcsolve can now be suppressed. - Fixed bug in `gate_expand_3toN`. - Fixed bug for time-dependent problem (list string format) with multiple terms in coefficient to an operator. QuTiP 3.0.1 (2014-08-05) ======================== Bug Fixes --------- - Fix bug in create(), which returned a Qobj with CSC data instead of CSR. - Fix several bugs in mcsolve: Incorrect storing of collapse times and collapse operator records. Incorrect averaging of expectation values for different trajectories when using only 1 CPU. - Fix bug in parsing of time-dependent Hamiltonian/collapse operator arguments that occurred when the args argument is not a dictionary. - Fix bug in internal _version2int function that cause a failure when parsingthe version number of the Cython package. QuTiP 3.0.0 (2014-07-17) ======================== New Features ------------ - New module `qutip.stochastic` with stochastic master equation and stochastic SchrĂśdinger equation solvers. - Expanded steady state solvers. The function ``steady`` has been deprecated in favor of ``steadystate``. The steadystate solver no longer use umfpack by default. New pre-processing methods for reordering and balancing the linear equation system used in direct solution of the steady state. - New module `qutip.qip` with utilities for quantum information processing, including pre-defined quantum gates along with functions for expanding arbitrary 1, 2, and 3 qubit gates to N qubit registers, circuit representations, library of quantum algorithms, and basic physical models for some common QIP architectures. - New module `qutip.distributions` with unified API for working with distribution functions. - New format for defining time-dependent Hamiltonians and collapse operators, using a pre-calculated numpy array that specifies the values of the Qobj-coefficients for each time step. - New functions for working with different superoperator representations, including Kraus and Chi representation. - New functions for visualizing quantum states using Qubism and Schimdt plots: ``plot_qubism`` and ``plot_schmidt``. - Dynamics solver now support taking argument ``e_ops`` (expectation value operators) in dictionary form. - Public plotting functions from the ``qutip.visualization`` module are now prefixed with ``plot_`` (e.g., ``plot_fock_distribution``). The ``plot_wigner`` and ``plot_wigner_fock_distribution`` now supports 3D views in addition to contour views. - New API and new functions for working with spin operators and states, including for example ``spin_Jx``, ``spin_Jy``, ``spin_Jz`` and ``spin_state``, ``spin_coherent``. - The ``expect`` function now supports a list of operators, in addition to the previously supported list of states. - Simplified creation of qubit states using ``ket`` function. - The module ``qutip.cyQ`` has been renamed to ``qutip.cy`` and the sparse matrix-vector functions ``spmv`` and ``spmv1d`` has been combined into one function ``spmv``. New functions for operating directly on the underlaying sparse CSR data have been added (e.g., ``spmv_csr``). Performance improvements. New and improved Cython functions for calculating expectation values for state vectors, density matrices in matrix and vector form. - The ``concurrence`` function now supports both pure and mixed states. Added function for calculating the entangling power of a two-qubit gate. - Added function for generating (generalized) Lindblad dissipator superoperators. - New functions for generating Bell states, and singlet and triplet states. - QuTiP no longer contains the demos GUI. The examples are now available on the QuTiP web site. The ``qutip.gui`` module has been renamed to ``qutip.ui`` and does no longer contain graphical UI elements. New text-based and HTML-based progressbar classes. - Support for harmonic oscillator operators/states in a Fock state basis that does not start from zero (e.g., in the range [M,N+1]). Support for eliminating and extracting states from Qobj instances (e.g., removing one state from a two-qubit system to obtain a three-level system). - Support for time-dependent Hamiltonian and Liouvillian callback functions that depend on the instantaneous state, which for example can be used for solving master equations with mean field terms. Improvements ------------ - Restructured and optimized implementation of Qobj, which now has significantly lower memory footprint due to avoiding excessive copying of internal matrix data. - The classes ``OdeData``, ``Odeoptions``, ``Odeconfig`` are now called ``Result``, ``Options``, and ``Config``, respectively, and are available in the module `qutip.solver`. - The ``squeez`` function has been renamed to ``squeeze``. - Better support for sparse matrices when calculating propagators using the ``propagator`` function. - Improved Bloch sphere. - Restructured and improved the module ``qutip.sparse``, which now only operates directly on sparse matrices (not on Qobj instances). - Improved and simplified implement of the ``tensor`` function. - Improved performance, major code cleanup (including namespace changes), and numerous bug fixes. - Benchmark scripts improved and restructured. - QuTiP is now using continuous integration tests (TravisCI). QuTiP 2.2.0 (2013-03-01) ======================== New Features ------------ - **Added Support for Windows** - New Bloch3d class for plotting 3D Bloch spheres using Mayavi. - Bloch sphere vectors now look like arrows. - Partial transpose function. - Continuos variable functions for calculating correlation and covariance matrices, the Wigner covariance matrix and the logarithmic negativity for for multimode fields in Fock basis. - The master-equation solver (mesolve) now accepts pre-constructed Liouvillian terms, which makes it possible to solve master equations that are not on the standard Lindblad form. - Optional Fortran Monte Carlo solver (mcsolve_f90) by Arne Grimsmo. - A module of tools for using QuTiP in IPython notebooks. - Increased performance of the steady state solver. - New Wigner colormap for highlighting negative values. - More graph styles to the visualization module. Bug Fixes --------- - Function based time-dependent Hamiltonians now keep the correct phase. - mcsolve no longer prints to the command line if ntraj=1. QuTiP 2.1.0 (2012-10-05) ======================== New Features ------------ - New method for generating Wigner functions based on Laguerre polynomials. - coherent(), coherent_dm(), and thermal_dm() can now be expressed using analytic values. - Unittests now use nose and can be run after installation. - Added iswap and sqrt-iswap gates. - Functions for quantum process tomography. - Window icons are now set for Ubuntu application launcher. - The propagator function can now take a list of times as argument, and returns a list of corresponding propagators. Bug Fixes --------- - mesolver now correctly uses the user defined rhs_filename in Odeoptions(). - rhs_generate() now handles user defined filenames properly. - Density matrix returned by propagator_steadystate is now Hermitian. - eseries_value returns real list if all imag parts are zero. - mcsolver now gives correct results for strong damping rates. - Odeoptions now prints mc_avg correctly. - Do not check for PyObj in mcsolve when gui=False. - Eseries now correctly handles purely complex rates. - thermal_dm() function now uses truncated operator method. - Cython based time-dependence now Python 3 compatible. - Removed call to NSAutoPool on mac systems. - Progress bar now displays the correct number of CPU's used. - Qobj.diag() returns reals if operator is Hermitian. - Text for progress bar on Linux systems is no longer cutoff. QuTiP 2.0.0 (2012-06-01) ======================== The second version of QuTiP has seen many improvements in the performance of the original code base, as well as the addition of several new routines supporting a wide range of functionality. Some of the highlights of this release include: New Features ------------ - QuTiP now includes solvers for both Floquet and Bloch-Redfield master equations. - The Lindblad master equation and Monte Carlo solvers allow for time-dependent collapse operators. - It is possible to automatically compile time-dependent problems into c-code using Cython (if installed). - Python functions can be used to create arbitrary time-dependent Hamiltonians and collapse operators. - Solvers now return Odedata objects containing all simulation results and parameters, simplifying the saving of simulation results. .. important:: This breaks compatibility with QuTiP version 1.x. - mesolve and mcsolve can reuse Hamiltonian data when only the initial state, or time-dependent arguments, need to be changed. - QuTiP includes functions for creating random quantum states and operators. - The generation and manipulation of quantum objects is now more efficient. - Quantum objects have basis transformation and matrix element calculations as built-in methods. - The quantum object eigensolver can use sparse solvers. - The partial-trace (ptrace) function is up to 20x faster. - The Bloch sphere can now be used with the Matplotlib animation function, and embedded as a subplot in a figure. - QuTiP has built-in functions for saving quantum objects and data arrays. - The steady-state solver has been further optimized for sparse matrices, and can handle much larger system Hamiltonians. - The steady-state solver can use the iterative bi-conjugate gradient method instead of a direct solver. - There are three new entropy functions for concurrence, mutual information, and conditional entropy. - Correlation functions have been combined under a single function. - The operator norm can now be set to trace, Frobius, one, or max norm. - Global QuTiP settings can now be modified. - QuTiP includes a collection of unit tests for verifying the installation. - Demos window now lets you copy and paste code from each example. QuTiP 1.1.4 (2012-05-28) ======================== Bug Fixes --------- - Fixed bug pointed out by Brendan Abolins. - Qobj.tr() returns zero-dim ndarray instead of float or complex. - Updated factorial import for scipy version 0.10+ QuTiP 1.1.3 (2011-11-21) ======================== New Functions ------------- - Allow custom naming of Bloch sphere. Bug Fixes --------- - Fixed text alignment issues in AboutBox. - Added fix for SciPy V>0.10 where factorial was moved to scipy.misc module. - Added tidyup function to tensor function output. - Removed openmp flags from setup.py as new Mac Xcode compiler does not recognize them. - Qobj diag method now returns real array if all imaginary parts are zero. - Examples GUI now links to new documentation. - Fixed zero-dimensional array output from metrics module. QuTiP 1.1.2 (2011-10-27) ======================== Bug Fixes --------- - Fixed issue where Monte Carlo states were not output properly. QuTiP 1.1.1 (2011-10-25) ======================== **THIS POINT-RELEASE INCLUDES VASTLY IMPROVED TIME-INDEPENDENT MCSOLVE AND ODESOLVE PERFORMANCE** New Functions ------------- - Added linear entropy function. - Number of CPU's can now be changed. Bug Fixes --------- - Metrics no longer use dense matrices. - Fixed Bloch sphere grid issue with matplotlib 1.1. - Qobj trace operation uses only sparse matrices. - Fixed issue where GUI windows do not raise to front. QuTiP 1.1.0 (2011-10-04) ======================== **THIS RELEASE NOW REQUIRES THE GCC COMPILER TO BE INSTALLED** New Functions ------------- - tidyup function to remove small elements from a Qobj. - Added concurrence function. - Added simdiag for simultaneous diagonalization of operators. - Added eigenstates method returning eigenstates and eigenvalues to Qobj class. - Added fileio for saving and loading data sets and/or Qobj's. - Added hinton function for visualizing density matrices. Bug Fixes --------- - Switched Examples to new Signals method used in PySide 1.0.6+. - Switched ProgressBar to new Signals method. - Fixed memory issue in expm functions. - Fixed memory bug in isherm. - Made all Qobj data complex by default. - Reduced ODE tolerance levels in Odeoptions. - Fixed bug in ptrace where dense matrix was used instead of sparse. - Fixed issue where PyQt4 version would not be displayed in about box. - Fixed issue in Wigner where xvec was used twice (in place of yvec). QuTiP 1.0.0 (2011-07-29) ======================== - **Initial release.** qutip-5.1.1/doc/changes/000077500000000000000000000000001474175217300150505ustar00rootroot00000000000000qutip-5.1.1/doc/changes/.gitignore000066400000000000000000000001621474175217300170370ustar00rootroot00000000000000# This ensures that the folder persists after the removal of the files in it in a new version release. !.gitignorequtip-5.1.1/doc/conf.py000077500000000000000000000276151474175217300147550ustar00rootroot00000000000000#!/usr/bin/env python3 # -*- coding: utf-8 -*- # # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. # import os import pathlib import warnings # -- General configuration ------------------------------------------------ # If your documentation needs a minimal Sphinx version, state it here. # needs_sphinx = '1.8.3' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = ['sphinx.ext.mathjax', 'matplotlib.sphinxext.plot_directive', 'sphinx.ext.autodoc', 'sphinx.ext.todo', 'sphinx.ext.doctest', 'sphinx.ext.autosummary', 'numpydoc', 'sphinx.ext.extlinks', 'sphinx.ext.viewcode', 'sphinx.ext.ifconfig', 'sphinx.ext.napoleon', 'sphinxcontrib.bibtex'] # Add any paths that contain templates here, relative to this directory. templates_path = ['templates'] # This is needed for ipython @savefig # Otherwise it just puts the png in the root dir savefig_dir = '_images' # The suffix(es) of source filenames. # You can specify multiple suffix as a list of string: # # source_suffix = ['.rst', '.md'] source_suffix = '.rst' # The master toctree document. master_doc = 'index' # General information about the project. project = 'QuTiP: Quantum Toolbox in Python' author = ', '.join([ 'P.D. Nation', 'J.R. Johansson', 'A.J.G. Pitchford', 'C. Granade', 'A.L. Grimsmo', 'N. Shammah', 'S. Ahmed', 'N. Lambert', 'B. Li', 'J. Lishman', 'S. Cross', 'A. Galicia', 'P. Menczel', 'P. Hopf', 'and E. Giguère' ]) copyright = '2011 to 2024 inclusive, QuTiP developers and contributors' def _check_source_folder_and_imported_qutip_match(): """ Warn if the imported qutip and the source folder the documentation is being built from don't match. The generated documentation contains material from both the source folder (e.g. ``.rst`` files) and from the imported qutip (e.g. docstrings), so if the two don't match the generated documentation will be a chimera. """ import qutip qutip_folder = pathlib.Path(qutip.__file__).absolute().parent.parent source_folder = pathlib.Path(__file__).absolute().parent.parent if qutip_folder != source_folder: warnings.warn( "The documentation source and imported qutip package are" " not from the same source folder. This may result in the" " documentation containing text from different sources." " Documentation source: {!r}." " Qutip package source: {!r}.".format( str(source_folder), str(qutip_folder) ) ) _check_source_folder_and_imported_qutip_match() def qutip_version(): """ Retrieve the QuTiP version from ``../VERSION``. """ src_folder_root = pathlib.Path(__file__).absolute().parent.parent version = src_folder_root.joinpath( "VERSION" ).read_text().strip() return version # The version info for the project you're documenting, acts as replacement for # |version| and |release|, also used in various other places throughout the # built documents. # The full version, including alpha/beta/rc tags. release = qutip_version() # The short X.Y version. version = ".".join(release.split(".")[:2]) # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. language = "en" # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This patterns also effect to html_static_path and html_extra_path exclude_patterns = [ '_build', 'Thumbs.db', '.DS_Store', ] # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # If true, '()' will be appended to :func: etc. cross-reference text. add_function_parentheses = False # If true, the current module name will be prepended to all description # unit titles (such as .. function::). add_module_names = False # If true, sectionauthor and moduleauthor directives will be shown in the # output. They are ignored by default. show_authors = True # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # A list of ignored prefixes for module index sorting. #modindex_common_prefix = [] todo_include_todos = True numpydoc_show_class_members = False napoleon_numpy_docstring = True napoleon_use_admonition_for_notes = True # sphinxcontrib.bixtex options bibtex_bibfiles = [ "guide/heom/heom.bib", ] # -- Options for HTML output ---------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # html_theme = 'sphinx_rtd_theme' full_logo= True # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. html_theme_options = { } # Add any paths that contain custom themes here, relative to this directory. # The name for this set of Sphinx documents. If None, it defaults to # " v documentation". html_title = 'QuTiP {} Documentation'.format(version) # A shorter title for the navigation bar. Default is the same as html_title. html_short_title = 'QuTiP' # The name of an image file (within the static path) to use as favicon of the # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 # pixels large. html_favicon = 'figures/favicon.ico' # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['static'] # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, # using the given strftime format. html_last_updated_fmt = '%b %d, %Y' # If true, SmartyPants will be used to convert quotes and dashes to # typographically correct entities. #html_use_smartypants = True # Custom sidebar templates, maps document names to template names. html_sidebars = {'sidebar': ['localtoc.html', 'sourcelink.html', 'searchbox.html']} # Additional templates that should be rendered to pages, maps page names to # template names. #html_additional_pages = {} # If false, no module index is generated. #html_domain_indices = True # If false, no index is generated. #html_use_index = True # If true, the index is split into individual pages for each letter. #html_split_index = False # If true, links to the reST sources are added to the pages. html_show_sourcelink = False # If true, "Created using Sphinx" is shown in the HTML footer. Default is True. html_show_sphinx = True # If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. html_show_copyright = True # If true, an OpenSearch description file will be output, and all pages will # contain a tag referring to it. The value of this option must be the # base URL from which the finished HTML is served. #html_use_opensearch = '' # This is the file name suffix for HTML files (e.g. ".xhtml"). #html_file_suffix = None html_css_files = [ 'site.css', ] # -- Options for HTMLHelp output ------------------------------------------ # Output file base name for HTML help builder. htmlhelp_basename = 'QuTiPdoc' # -- Configure MathJax for maths output in HTML targets # Currently (2021-04-10) Sphinx 3.5.3 loads MathJax 2.7, which does not have # support for the 'physics' package. MathJax 3 does, so once Sphinx is using # that (should be in Sphinx 4), you will be able to swap to using that. In the # meantime, we just have to define all the functions we're going to use. # # See: # - https://docs.mathjax.org/en/v3.0-latest/input/tex/extensions/physics.html mathjax3_config = { 'TeX': { 'Macros': { 'bra': [r'\left\langle{#1}\right\rvert', 1], 'ket': [r'\left\lvert{#1}\right\rangle', 1], 'tr': r'\operatorname{tr}', }, }, } # -- Options for LaTeX output --------------------------------------------- latex_elements = { 'papersize': 'a4paper', 'pointsize': '10pt', 'classoptions': '', 'babel': '\\usepackage[english]{babel}', 'fncychap': '', 'figure_align': 'H', # This preamble is inserted into the build tools for the latex make targets # but not any others. Be sure to change mathjax_config too if you need to # define more commands. 'preamble': r"\usepackage{physics}", } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ ('index', 'qutip.tex', project, author, 'manual'), ] # The name of an image file (relative to this directory) to place at the top of # the title page. latex_logo = 'figures/logo.png' # Sometimes make might suggest setting this to False. # It screws a few things up if you do - don't be tempted. latex_keep_old_macro_names=True # For "manual" documents, if this is true, then toplevel headings are parts, # not chapters. #latex_use_parts = True # If true, show page references after internal links. #latex_show_pagerefs = False # If true, show URL addresses after external links. #latex_show_urls = False # Documents to append as an appendix to all manuals. #latex_appendices = [] # If false, no module index is generated. #latex_domain_indices = True # -- Options for manual page output --------------------------------------- # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ (master_doc, 'qutip', project, [author], 1) ] # -- Doctest Setup --------------------------------------- os_nt = False if os.name == "nt": os_nt = True doctest_global_setup = ''' import matplotlib.pyplot as plt import numpy as np import os import warnings warnings.filterwarnings("ignore") from qutip import * os_nt = {} '''.format(os_nt) # -- Options for plot directive --------------------------------------- plot_working_directory = "./" plot_pre_code = """ import numpy as np import matplotlib.pyplot as plt from qutip import * plt.close("all") """ plot_include_source = True plot_html_show_source_link = False plot_html_show_formats = False # -- Options for Texinfo output ------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ (master_doc, 'qutip', project, author, 'QuTiP', 'Quantum Toolbox in Python', 'Miscellaneous'), ] autodoc_member_order = 'alphabetical' # Type hint are already in the parameter section of the documentation in # (hopefully) user readable format. # "signature" : In the signature # "description" : Added to the description (doubled) # "none": Removed autodoc_typehints = "signature" python_maximum_signature_line_length = 80 # Makes the following types appear as their alias in the apidoc # instead of expanding the alias autodoc_type_aliases = { 'CoefficientLike': 'CoefficientLike', 'ElementType': 'ElementType', 'QobjEvoLike': 'QobjEvoLike', 'EopsLike': 'EopsLike', 'LayerType': 'LayerType', 'ArrayLike': 'ArrayLike', 'SpaceLike': 'SpaceLike', 'DimensionLike': 'DimensionLike', } ## EXTLINKS CONFIGURATION ###################################################### extlinks = { 'arxiv': ('https://arxiv.org/abs/%s', 'arXiv:%s'), 'doi': ('https://dx.doi.org/%s', 'doi:%s'), } ipython_strict_fail = False qutip-5.1.1/doc/contributors.rst000066400000000000000000000146641474175217300167420ustar00rootroot00000000000000.. _developers: ************ Developers ************ .. plot:: :context: close-figs :include-source: False import json import urllib.request import numpy as np import matplotlib.pyplot as plt from matplotlib.path import Path from matplotlib.patches import PathPatch from matplotlib.textpath import TextPath from matplotlib.collections import PolyCollection from matplotlib.font_manager import FontProperties import PIL LINK_CONTRIBUTORS = "https://api.github.com/repos/qutip/qutip/contributors" LINK_LOGO = "https://qutip.org/images/logo.png" # font properties FONT_SIZE = 6 FONT_FAMILY = "DejaVu Sans" # figures properties FIGURE_SIZE = 8 AXIS_SIZE = 50 FONT_COLOR = "black" LOGO_SIZE = 40 LOGO_TRANSPARENCY = 0.5 # load the list of contributors from qutip/qutip repo url_object = urllib.request.urlopen(LINK_CONTRIBUTORS) list_contributors = json.loads(url_object.read()) qutip_contributors = [element["login"] for element in list_contributors] qutip_contributors = [s.lower() for s in qutip_contributors] text = " ".join(qutip_contributors) # load the QuTiP logo img = PIL.Image.open(urllib.request.urlopen(LINK_LOGO)) # code below was inspired in the following link: # https://github.com/dynamicwebpaige/nanowrimo-2021/blob/main/15_VS_Code_contributors.ipynb n = 100 A = np.linspace(np.pi, n * 2 * np.pi, 10_000) R = 5 + np.linspace(np.pi, n * 2 * np.pi, 10_000) T = np.stack([R * np.cos(A), R * np.sin(A)], axis=1) dx = np.cos(A) - R * np.sin(A) dy = np.sin(A) + R * np.cos(A) O = np.stack([-dy, dx], axis=1) O = O / (np.linalg.norm(O, axis=1)).reshape(len(O), 1) L = np.zeros(len(T)) np.cumsum(np.sqrt(((T[1:] - T[:-1]) ** 2).sum(axis=1)), out=L[1:]) path = TextPath( (0, 0), text, size=FONT_SIZE, prop=FontProperties(family=FONT_FAMILY), ) vertices = path.vertices codes = path.codes Vx, Vy = vertices[:, 0], vertices[:, 1] X = np.interp(Vx, L, T[:, 0]) + Vy * np.interp(Vx, L, O[:, 0]) Y = np.interp(Vx, L, T[:, 1]) + Vy * np.interp(Vx, L, O[:, 1]) vertices = np.stack([X, Y], axis=-1) path = Path(vertices, codes, closed=False) # creating figure fig, ax = plt.subplots(figsize=(FIGURE_SIZE, FIGURE_SIZE)) patch = PathPatch(path, facecolor=FONT_COLOR, linewidth=0) ax.add_artist(patch) ax.set_xlim(-AXIS_SIZE, AXIS_SIZE), ax.set_xticks([]) ax.set_ylim(-AXIS_SIZE, AXIS_SIZE), ax.set_yticks([]) # add qutip logo ax.imshow(img, alpha=LOGO_TRANSPARENCY, extent=[-LOGO_SIZE,LOGO_SIZE, -LOGO_SIZE, LOGO_SIZE]) .. _developers-lead: Lead Developers =============== - `Alex Pitchford `_ - `Nathan Shammah `_ - `Shahnawaz Ahmed `_ - `Neill Lambert `_ - `Eric Giguère `_ - `Boxi Li `_ - `Simon Cross `_ - `Asier Galicia `_ - `Paul Menczel `_ Past Lead Developers ==================== - `Robert Johansson `_ (RIKEN) - `Paul Nation `_ (Korea University) - `Chris Granade `_ - `Arne Grimsmo `_ - `Jake Lishman `_ .. _developers-contributors: Contributors ============ .. note:: Anyone is welcome to contribute to QuTiP. If you are interested in helping, please let us know! - Abhisek Upadhyaya - adria.labay - Adriaan - AGaliciaMartinez - alan-nala - Alberto Mercurio - alex - Alexander Pitchford - Alexios-xi - Amit - Andrey Nikitin - Andrey Rakhubovsky - Anna Naden - anonymousdouble - Anto Luketina - Antonio Andrea Gentile - Anubhav Vardhan - Anush Venkatakrishnan - Arie van Deursen - Arne Grimsmo - Arne Hamann - Aryaman Kolhe - Ashish Panigrahi - Asier Galicia Martinez - awkwardPotato812 - Ben Bartlett - Ben Criger - Ben Jones - Bo Yang - Bogdan Reznychenko - Boxi Li - CamilleLCal - Canoming - christian512 - christian512 - Christoph Gohlke - Christopher Granade - Craig Gidney - Daniel Weiss - Danny - davidschlegel - Denis Vasilyev - dependabot[bot] - dev-aditya - DnMGalan - Dominic Meiser - Drew Parsons - drodper - dweigand - Edward Thomas - Élie Gouzien - eliegenois - Emi - EmilianoG-byte - Eric Giguère - Eric Hontz - essence-of-waqf - Felipe Bivort Haiek - fhenneke - fhopfmueller - Florestan Ziem - Florian Hopfmueller - gadhvirushiraj - Gaurav Saxena - gecrooks - Gerardo Jose Suarez - Gilbert Shih - Harry Adams - Harsh Khilawala - HGSilveri - Hristo Georgiev - Ivan Carvalho - Jake Lishman - jakobjakobson13 - Javad Noorbakhsh - Jevon Longdell - Johannes Feist - Jon Crall - Jonas Hoersch - Jonas Neergaard-Nielsen - Jonathan A. Gross - Joseph Fox-Rabinovitz - Julian Iacoponi - Kevin Fischer - Kosuke Mizuno - kwyip - L K Livingstone - Lajos Palanki - Laurence Stant - Laurent AJDNIK - Leo_am - Leonardo Assis - Louis Tessler - Lucas Verney - Maggie - Mahdi Aslani - maij - Marco David - Marek - marekyggdrasil - Mark Johnson - Markus Baden - MartĂ­n Sande - Mateo Laguna - Matt - Matthew O'Brien - Matthew Treinish - mcditooss - Mehdi Aslani - Michael Goerz - Michael V. DePalatis - Moritz Oberhauser - MrRobot2211 - Nathan Shammah - Neill Lambert - Nicolas Quesada - Nikhil Harle - Nikolas Tezak - Nithin Ramu - obliviateandsurrender - owenagnel - Paul - Paul Menczel - Paul Nation - Peter Kirton - Philipp Schindler - PierreGuilmin - Pieter Eendebak - Piotr Migdal - PositroniumJS - Purva Thakre - quantshah - Rajath Shetty - Rajiv-B - Ray Ganardi - Reinier Heeres - Richard Brierley - Rita Abani - Robert Johansson - Rochisha Agarwal - rochisha0 - ruffa - Rushiraj Gadhvi - Sam Griffiths - Sam Wolski - Samesh Lakhotia - Sampreet Kalita - sbisw002 - Sebastian Krämer - Shahnawaz Ahmed - Sidhant Saraogi - Simon Cross - Simon Humpohl - Simon Whalen - SJUW - Srinidhi P V - Stefan Krastanov - tamakoshi - tamakoshi2001 - Tanya Garg - Tarun Raheja - Thomas Walker - Tobias Schmale - trentfridey - valanm22 - Viacheslav Ostroukh - Victory Omole - vikas-chaudhary-2802 - Vlad Negnevitsky - Vladimir Vargas-CalderĂłn - Wikstahl - WingCode - Wojciech Rzadkowski - Xavier Spronken - Xiaodong Qi - Xiaoliang Wu - xspronken - Yariv Yanay - Yash-10 - YouWei Zhao - Yuji TAMAKOSHI - yulanl22 - yuri@FreeBSD qutip-5.1.1/doc/copyright.rst000066400000000000000000000016721474175217300162100ustar00rootroot00000000000000.. _copyright: *********************** Copyright and Licensing *********************** The text of this documentation is licensed under the `Creative Commons Attribution 3.0 Unported License `_. Unless specifically indicated otherwise, all code samples, the source code of QuTiP, and its reproductions in this documentation, are licensed under the terms of the 3-clause BSD license, reproduced below. License Terms for Documentation Text ==================================== The canonical form of this license is available at `https://creativecommons.org/licenses/by/3.0/ `_, which should be considered the binding version of this license. It is reproduced here for convenience. .. include:: LICENSE_cc-by-3.0.txt License Terms for Source Code of QuTiP and Code Samples ======================================================= .. include:: ../LICENSE.txt qutip-5.1.1/doc/development/000077500000000000000000000000001474175217300157625ustar00rootroot00000000000000qutip-5.1.1/doc/development/contributing.rst000066400000000000000000000371661474175217300212400ustar00rootroot00000000000000.. _development-contributing: ********************************* Contributing to QuTiP Development ********************************* Quick Start =========== QuTiP is developed through wide collaboration using the ``git`` version-control system, with the main repositories hosted in the `qutip organisation on GitHub `_. You will need to be familiar with ``git`` as a tool, and the `GitHub Flow `_ workflow for branching and making pull requests. The exact details of environment set-up, build process and testing vary by repository and are discussed below, however in overview, the steps to contribute are: #. Consider creating an issue on the GitHub page of the relevant repository, describing the change you think should be made and why, so we can discuss details with you and make sure it is appropriate. #. (If this is your first contribution.) Make a fork of the relevant repository on GitHub and clone it to your local computer. Also add our copy as a remote (``git remote add qutip https://github.com/qutip/``) #. Begin on the ``master`` branch (``git checkout master``), and pull in changes from the main QuTiP repository to make sure you have an up-to-date copy (``git pull qutip master``). #. Switch to a new ``git`` branch (``git checkout -b ``). #. Make the changes you want to make, then create some commits with short, descriptive names (``git add `` then ``git commit``). #. Follow the build process for this repository to build the final result so you can check your changes work sensibly. #. Run the tests for the repository (if it has them). #. Push the changes to your fork (``git push -u origin ``). You won't be able to push to the main QuTiP repositories directly. #. Go to the GitHub website for the repository you are contributing to, click on the "Pull Requests" tab, click the "New Pull Request" button, and follow the instructions there. Once the pull request is created, some members of the QuTiP admin team will review the code to make sure it is suitable for inclusion in the library, to check the programming, and to ensure everything meets our standards. For some repositories, several automated tests will run whenever you create or modify a pull request; in general these will be the same tests you can run locally, and all tests are required to pass online before your changes are merged. There may be some feedback and possibly some requested changes. You can add more commits to address these, and push them to the relevant branch of your fork to update the pull request. The rest of this document covers programming standards, and particular considerations for some of the more complicated repositories. .. _contributing-qutip: Core Library: qutip/qutip ========================= The core library is in the `qutip/qutip repository on GitHub `_. Building -------- Building the core library from source is typically a bit more difficult than simply installing the package for regular use. You will most likely want to do this in a clean Python environment so that you do not compromise a working installation of a release version, for example by starting from :: conda create -n qutip-dev python :ref:`Complete instructions for the build ` are elsewhere in this guide, however beware that you will need to follow the :ref:`installation from source using setuptools section `, not the general installation. You will need all the *build* and *tests* "optional" requirements for the package. The build requirements can be found in the |pyproject.toml file|_, and the testing requirements are in the ``tests`` key of the ``options.extras_require`` section of |setup.cfg|_. You will also need the requirements for any optional features you want to test as well. .. |pyproject.toml file| replace:: ``pyproject.toml`` file .. _pyproject.toml file: https://github.com/qutip/qutip/blob/master/pyproject.toml .. |setup.cfg| replace:: ``setup.cfg`` .. _setup.cfg: https://github.com/qutip/qutip/blob/master/setup.cfg Refer to the main instructions for the most up-to-date version, however as of version 4.6 the requirements can be installed into a conda environment with :: conda install setuptools wheel numpy scipy cython packaging pytest pytest-rerunfailures Note that ``qutip`` should *not* be installed with ``conda install``. .. note:: If you prefer, you can also use ``pip`` to install all the dependencies. We typically recommend ``conda`` when doing main-library development because it is easier to switch low-level packages around like BLAS implementations, but if this doesn't mean anything to you, feel free to use ``pip``. You will need to make sure you have a functioning C++ compiler to build QuTiP. If you are on Linux or Mac, this is likely already done for you, however if you are on Windows, refer to the :ref:`Windows installation ` section of the installation guide. The command to build QuTiP in editable mode is :: python setup.py develop from the repository directory. If you now load up a Python interpreter, you should be able to ``import qutip`` from anywhere as long as the correct Python environment is active. Any changes you make to the Python files in the git repository should be immediately present if you restart your Python interpreter and re-import ``qutip``. On the first run, the setup command will compile many C++ extension modules built from Cython sources (files ending ``.pxd`` and ``.pyx``). Generally the low-level linear algebra routines that QuTiP uses are written in these files, not in pure Python. Unlike Python files, changes you make to Cython files will not appear until you run ``python setup.py develop`` again; you will only need to re-run this if you are changing Cython files. Cython will detect and compile only the files that have been changed, so this command will be faster on subsequent runs. .. note:: When undertaking Cython development, the reason we use ``python setup.py develop`` instead of ``pip install -e .`` is because Cython's changed-file detection does not reliably work in the latter. ``pip`` tends to build in temporary virtual environments, which often makes Cython think its core library files have been updated, triggering a complete, slow rebuild of everything. .. note:: QuTiP follows `NEP29`_ when selecting the supported version of its dependencies. To see which versions are planned to be supported in the next release, please refer to the :ref:`release roadmap`. These coincide with the versions employed for testing in continuous integration. In the event of a feature requiring a version upgrade of python or a dependency, it will be considered appropriately in the pull request. In any case, python and dependency upgrades will only happen in mayor or minor versions of QuTiP, not in a patch. .. _NEP29: https://numpy.org/neps/nep-0029-deprecation_policy.html Code Style ---------- The biggest concern you should always have is to make it easy for your code to be read and understood by the person who comes next. All new contributions must follow `PEP 8 style `_; all pull requests will be passed through a linter that will complain if you violate it. You should use the ``pycodestyle`` package locally (available on ``pip``) to test you satisfy the requirements before you push your commits, since this is rather faster than pushing 10 different commits trying to fix minor niggles. Keep in mind that there is quite a lot of freedom in this style, especially when it comes to line breaks. If a line is too long, consider the *best* way to split it up with the aim of making the code readable, not just the first thing that doesn't generate a warning. Try to stay consistent with the style of the surrounding code. This includes using the same variable names, especially if they are function arguments, even if these "break" PEP 8 guidelines. *Do not* change existing parameter, attribute or method names to "match" PEP 8; these are breaking user-facing changes, and cannot be made except in a new major release of QuTiP. Other than this, general "good-practice" Python standards apply: try not to duplicate code; try to keep functions short, descriptively-named and side-effect free; provide a docstring for every new function; and so on. Type Hints ---------- Adding type hints to users facing functions is recommended. QuTiP's approach is such: - Type hints are *hints* for the users. - Type hints can show the preferred usage over real implementation, for example: - ``Qobj.__mul__`` is typed to support product with scalar, not other ``Qobj``, for which ``__matmul__`` should is preferred. - ``solver.options`` claims it return a dict not ``_SolverOptions`` (which is a subclass of dict). - Type alias are added to ``qutip.typing``. - `Any` can be used for input which type can be extended by plugin modules, (``qutip-cupy``, ``qutip-jax``, etc.) Documenting ----------- When you make changes in the core library, you should update the relevant documentation if needed. If you are making a bug fix, or other relatively minor changes, you will probably only need to make sure that the docstrings of the modified functions and classes are up-to-date; changes here will propagate through to the documentation the next time it is built. Be sure to follow the |numpydoc|_ when writing docstrings. All docstrings will be parsed as reStructuredText, and will form the API documentation section of the documentation. .. |numpydoc| replace:: Numpy documentation standards (``numpydoc``) .. _numpydoc: https://numpydoc.readthedocs.io/en/latest/format.html Testing ------- We use ``pytest`` as our test runner. The base way to run every test is :: pytest /path/to/repo/qutip/tests This will take around 10 to 30 minutes, depending on your computer and how many of the optional requirements you have installed. It is normal for some tests to be marked as "skip" or "xfail" in yellow; these are not problems. True failures will appear in red and be called "fail" or "error". While prototyping and making changes, you might want to use some of the filtering features of ``pytest``. Instead of passing the whole ``tests`` directory to the ``pytest`` command, you can also pass a list of files. You can also use the ``-k`` selector to only run tests whose names include a particular pattern, for example :: pytest qutip/tests/test_qobj.py -k "expm" to run the tests of :meth:`Qobj.expm`. Changelog Generation -------------------- We use ``towncrier`` for tracking changes and generating a changelog. When making a pull request, we require that you add a towncrier entry along with the code changes. You should create a file named ``.`` in the ``doc/changes`` directory, where the PR number should be substituted for ````, and ```` is either ``feature``, ``bugfix``, ``doc``, ``removal``, ``misc``, or ``deprecation``, depending on the type of change included in the PR. You can also create this file by installing ``towncrier`` and running towncrier create . Running this will create a file in the ``doc/changes`` directory with a filename corresponding to the argument you passed to ``towncrier create``. In this file, you should add a short description of the changes that the PR introduces. .. _contributing-docs: Documentation: qutip/qutip (doc directory) ========================================== The core library is in the `qutip/qutip repository on GitHub, inside the doc directory `_. Building -------- The documentation is built using ``sphinx``, ``matplotlib`` and ``numpydoc``, with several additional extensions including ``sphinx-gallery`` and ``sphinx-rtd-theme``. The most up-to-date instructions and dependencies will be in the ``README.md`` file of the documentation directory. You can see the rendered version of this file simply by going to the `documentation GitHub page `_ and scrolling down. Building the documentation can be a little finnicky on occasion. You likely will want to keep a separate Python environment to build the documentation in, because some of the dependencies can have tight requirements that may conflict with your favourite tools for Python development. We recommend creating an empty ``conda`` environment containing only Python with :: conda create -n qutip-doc python=3.8 and install all further dependencies with ``pip``. There is a ``requirements.txt`` file in the repository root that fixes all package versions exactly into a known-good configuration for a completely empty environment, using :: pip install -r requirements.txt This known-good configuration was intended for Python 3.8, though in principle it is possible that other Python versions will work. .. note:: We recommend you use ``pip`` to install dependencies for the documentation rather than ``conda`` because several necessary packages can be slower to update their ``conda`` recipes, so suitable versions may not be available. The documentation build includes running many components of the main QuTiP library to generate figures and to test the output, and to generate all the API documentation. You therefore need to have a version of QuTiP available in the same Python environment. If you are only interested in updating the users' guide, you can use a release version of QuTiP, for example by running ``pip install qutip``. If you are also modifying the main library, you need to make your development version accessible in this environment. See the `above section on building QuTiP `_ for more details, though the ``requirements.txt`` file will have already installed all the build requirements, so you should be able to simply run :: python setup.py develop in the main library repository. The documentation is built by running the ``make`` command. There are several targets to build, but the most useful will be ``html`` to build the webpage documentation, ``latexpdf`` to build the PDF documentation (you will also need a full ``pdflatex`` installation), and ``clean`` to remove all built files. The most important command you will want to run is :: make html You should re-run this any time you make changes, and it should only update files that have been changed. .. important:: The documentation build includes running almost all the optional features of QuTiP. If you get failure messages in red, make sure you have installed all of the optional dependencies for the main library. The HTML files will be placed in the ``_build/html`` directory. You can open the file ``_build/html/index.html`` in your web browser to check the output. Code Style ---------- All user guide pages and docstrings are parsed by Sphinx using reStructuredText. There is a general `Sphinx usage guide `_, which has a lot of information that can sometimes be a little tricky to follow. It may be easier just to look at other ``.rst`` files already in the documentation to copy the different styles. .. note:: reStructuredText is a very different language to the Markdown that you might be familiar with. It's always worth checking your work in a web browser to make sure it's appeared the way you intended. Testing ------- There are unfortunately no automated tests for the documentation. You should ensure that no errors appeared in red when you ran ``make html``. Try not to introduce any new warnings during the build process. The main test is to open the HTML pages you have built (open ``_build/html/index.html`` in your web browser), and click through to the relevant pages to make sure everything has rendered the way you expected it to. qutip-5.1.1/doc/development/development.rst000066400000000000000000000005471474175217300210440ustar00rootroot00000000000000.. _development: ************************* Development Documentation ************************* This chapter covers the development of QuTiP and its subpackages, including a roadmap for upcoming releases and ideas for future improvements. .. toctree:: :maxdepth: 3 contributing.rst roadmap.rst ideas.rst docs.rst release_distribution.rst qutip-5.1.1/doc/development/docs.rst000066400000000000000000000143101474175217300174430ustar00rootroot00000000000000.. _user_guide.rst: ************************************ Working with the QuTiP Documentation ************************************ The user guide provides an overview of QuTiP's functionality. The guide is composed of individual reStructuredText (``.rst``) files which each get rendered as a webpage. Each page typically tackles one area of functionality. To learn more about how to write ``.rst`` files, it is useful to follow the `sphinx guide `_. The documentation build also utilizes a number of `Sphinx Extensions `_ including but not limited to `doctest `_, `autodoc `_, `sphinx gallery `_ and `plot `_. Additional extensions can be configured in the `conf.py `_ file. .. _directives.rst: Directives ========== There are two Sphinx directives that can be used to write code examples in the user guide: - `Doctest `_ - `Plot `_ For a more comprehensive account of the usage of each directive, please refer to their individual pages. Here we outline some general guidelines on how to these directives while making a user guide. Doctest ------- The doctest directive enables tests on interactive code examples. The simplest way to do this is by specifying a prompt along with its respective output: :: .. doctest:: >>> a = 2 >>> a 2 This is rendered in the documentation as follows: .. doctest:: >>> a = 2 >>> a 2 While specifying code examples under the ``.. doctest::`` directive, either all statements must be specified by the ``>>>`` prompt or without it. For every prompt, any potential corresponding output must be specified immediately after it. This directive is ideally used when there are a number of examples that need to be checked in quick succession. A different way to specify code examples (and test them) is using the associated ``.. testcode::`` directive which is effectively a code block: :: .. testcode:: a = 2 print(a) followed by its results. The result can be specified with the ``.. testoutput::`` block: :: .. testoutput:: 2 The advantage of the ``testcode`` directive is that it is a lot simpler to specify and amenable to copying the code to clipboard. Usually, tests are more easily specified with this directive as the input and output are specified in different blocks. The rendering is neater too. .. note:: The ``doctest`` and ``testcode`` directives should not be assumed to have the same namespace. **Output:** .. testcode:: a = 2 print(a) .. testoutput:: 2 A few notes on using the doctest extension: - By default, each ``testcode`` and ``doctest`` block is run in a fresh namespace. To share a common namespace, we can specify a common group across the blocks (within a single ``.rst`` file). For example, :: .. doctest:: [group_name] >>> a = 2 can be followed by some explanation followed by another code block sharing the same namespace :: .. doctest:: [group_name] >>> print(a) 2 - To only print the code blocks (or the output), use the option ``+SKIP`` to specify the block without the code being tested when running ``make doctest``. - To check the result of a ``Qobj`` output, it is useful to make sure that spacing irregularities between the expected and actual output are ignored. For that, we can use the option ``+NORMALIZE_WHITESPACE``. Plot ---- Since the doctest directive cannot render matplotlib figures, we use Matplotlib's `Plot `_ directive when rendering to LaTeX or HTML. The plot directive can also be used in the doctest format. In this case, when running doctests (which is enabled by specifying all statements with the ``>>>`` prompts), tests also include those specified under the plot directive. **Example:** :: First we specify some data: .. plot:: >>> import numpy as np >>> x = np.linspace(0, 2 * np.pi, 1000) >>> x[:10] # doctest: +NORMALIZE_WHITESPACE array([ 0. , 0.00628947, 0.01257895, 0.01886842, 0.0251579 , 0.03144737, 0.03773685, 0.04402632, 0.0503158 , 0.05660527]) .. plot:: :context: >>> import matplotlib.pyplot as plt >>> plt.plot(x, np.sin(x)) [...] Note the use of the ``NORMALIZE_WHITESPACE`` option to ensure that the multiline output matches. **Render:** .. plot:: >>> import numpy as np >>> x = np.linspace(0, 2 * np.pi, 1000) >>> x[:10] # doctest: +SKIP array([ 0. , 0.00628947, 0.01257895, 0.01886842, 0.0251579 , 0.03144737, 0.03773685, 0.04402632, 0.0503158 , 0.05660527]) >>> import matplotlib.pyplot as plt >>> plt.plot(x, np.sin(x)) [...] A few notes on using the plot directive: - A useful argument to specify in plot blocks is that of ``context`` which ensures that the code is being run in the namespace of the previous plot block within the same file. - By default, each rendered figure in one plot block (when using ``:context:``) is carried over to the next block. - When the ``context`` argument is specified with the ``reset`` option as ``:context: reset``, the namespace is reset to a new one and all figures are erased. - When the ``context`` argument is specified with the ``close-figs`` option as ``:context: reset``, the namespace is reset to a new one and all figures are erased. The Plot directive cannot be used in conjunction with Doctest because they do not share the same namespace when used in the same file. Since Plot can also be used in doctest mode, in the case where code examples require both testing and rendering figures, it is easier to use the Plot directive. To learn more about each directive, it is useful to refer to their individual pages. qutip-5.1.1/doc/development/ideas.rst000066400000000000000000000020401474175217300175750ustar00rootroot00000000000000.. _development_ideas: ********************************** Ideas for future QuTiP development ********************************** Ideas for significant new features are listed here. For the general roadmap, see :doc:`roadmap`. .. toctree:: :maxdepth: 1 ideas/qutip-interactive.rst ideas/pulse-level-quantum-circuits.rst ideas/quantum-error-mitigation.rst ideas/heom-gpu.rst Google Summer of Code ===================== Many possible extensions and improvements to QuTiP have been documented as part of `Google Summer of Code `_: * `GSoC 2021 `_ * `GSoC 2022 `_ * `GSoC 2023 `_ * `GSoC 2024 `_ Completed Projects ================== These projects have been completed: .. toctree:: :maxdepth: 1 ideas/tensorflow-data-backend.rst qutip-5.1.1/doc/development/ideas/000077500000000000000000000000001474175217300170475ustar00rootroot00000000000000qutip-5.1.1/doc/development/ideas/README000066400000000000000000000002311474175217300177230ustar00rootroot00000000000000This folder contains ideas for future QuTiP development. Please put each project or idea in a separate file and link to them from development/ideas.rst. qutip-5.1.1/doc/development/ideas/heom-gpu.rst000066400000000000000000000025601474175217300213250ustar00rootroot00000000000000********************************************************** GPU implementation of the Hierarchical Equations of Motion ********************************************************** .. contents:: Contents :local: :depth: 3 The Hierarchical Equations of Motion (HEOM) method is a non-perturbative approach to simulate the evolution of the density matrix of dissipative quantum systems. The underlying equations are a system of coupled ODEs which can be run on a GPU. This will allow the study of larger systems as discussed in [1]_. The goal of this project would be to extend QuTiP's HEOM method [2]_ and implement it on a GPU. Since the method is related to simulating large, coupled ODEs, it can also be quite general and extended to other solvers. Expected outcomes ================= * A version of HEOM which runs on a GPU. * Performance comparison with the CPU version. * Implement dynamic scaling. Skills ====== * Git, python and familiarity with the Python scientific computing stack * CUDA and OpenCL knowledge Difficulty ========== * Hard Mentors ======= * Neill Lambert (nwlambert@gmail.com) * Alex Pitchford (alex.pitchford@gmail.com) * Shahnawaz Ahmed (shahnawaz.ahmed95@gmail.com) * Simon Cross (hodgestar@gmail.com) References ========== .. [1] https://pubs.acs.org/doi/abs/10.1021/ct200126d?src=recsys&journalCode=jctcce .. [2] https://arxiv.org/abs/2010.10806 qutip-5.1.1/doc/development/ideas/pulse-level-quantum-circuits.rst000066400000000000000000000056231474175217300253570ustar00rootroot00000000000000******************************************* Pulse level description of quantum circuits ******************************************* .. contents:: Contents :local: :depth: 3 The aim of this proposal is to enhance QuTiP quantum-circuit compilation features with regard to quantum information processing. While QuTiP core modules deal with dynamics simulation, there is also a module for quantum circuits simulation. The two subsequent Google Summer of Code projects, in 2019 and 2020, enhanced them in capabilities and features, allowing the simulation both at the level of gates and at the level of time evolution. To connect them, a compiler is implemented to compile quantum gates into the Hamiltonian model. We would like to further enhance this feature in QuTiP and the connection with other libraries. Expected outcomes ================= * APIs to import and export pulses to other libraries. Quantum compiler is a current research topic in quantum engineering. Although QuTiP has a simple compiler, many may want to try their own compiler which is more compatible with their quantum device. Allowing importation and exportation of control pulses will make this much easier. This will include a study of existing libraries, such as `qiskit.pulse` and `OpenPulse` [1]_, comparing them with `qutip.qip.pulse` module and building a more general and comprehensive description of the pulse. * More examples of quantum system in the `qutip.qip.device` module. The circuit simulation and compilation depend strongly on the physical system. At the moment, we have two models: spin chain and cavity QED. We would like to include some other commonly used planform such as Superconducting system [2]_, Ion trap system [3]_ or silicon system. Each model will need a new set of control Hamiltonian and a compiler that finds the control pulse of a quantum gate. More involved noise models can also be added based on the physical system. This part is going to involve some physics and study of commonly used hardware platforms. The related code can be found in `qutip.qip.device` and `qutip.qip.compiler`. Skills ====== * Git, Python and familiarity with the Python scientific computing stack * quantum information processing and quantum computing (quantum circuit formalism) Difficulty ========== * Medium Mentors ======= * Boxi Li (etamin1201@gmail.com) [QuTiP GSoC 2019 graduate] * Nathan Shammah (nathan.shammah@gmail.com) * Alex Pitchford (alex.pitchford@gmail.com) References ========== .. [1] McKay D C, Alexander T, Bello L, et al. Qiskit backend specifications for openqasm and openpulse experiments[J]. arXiv preprint arXiv:1809.03452, 2018. .. [2] Häffner H, Roos C F, Blatt R, **Quantum computing with trapped ions**, Physics reports, 2008, 469(4): 155-203. .. [3] Krantz P, Kjaergaard M, Yan F, et al. **A quantum engineer's guide to superconducting qubits**, Applied Physics Reviews, 2019, 6(2): 021318. qutip-5.1.1/doc/development/ideas/quantum-error-mitigation.rst000066400000000000000000000061121474175217300245640ustar00rootroot00000000000000************************ Quantum Error Mitigation ************************ .. contents:: Contents :local: :depth: 3 From the QuTiP 4.5 release, the qutip.qip module now contains the noisy quantum circuit simulator (which was a GSoC project) providing enhanced features for a pulse-level description of quantum circuits and noise models. A new class `Processor` and several subclasses are added to represent different platforms for quantum computing. They can transfer a quantum circuit into the corresponding control sequence and simulate the dynamics with QuTiP solvers. Different noise models can be added to `qutip.qip.noise` to simulate noise in a quantum device. This module is still young and many features can be improved, including new device models, new noise models and integration with the existing general framework for quantum circuits (`qutip.qip.circuit`). There are also possible applications such as error mitigation techniques ([1]_, [2]_, [3]_). The tutorial notebooks can be found in the Quantum information processing section of https://qutip.org/qutip-tutorials/index-v5.html. A recent presentation on the FOSDEM conference may help you get an overview (https://fosdem.org/2020/schedule/event/quantum_qutip/). See also the Github Project page for a collection of related issues and ongoing Pull Requests. Expected outcomes ================= - Make an overview of existing libraries and features in error mitigation, similarly to a literature survey for a research article, but for a code project (starting from Refs. [4]_, [5]_). This is done in order to best integrate the features in QuTiP with existing libraries and avoid reinventing the wheel. - Features to perform error mitigation techniques in QuTiP, such as zero-noise extrapolation by pulse stretching. - Tutorials implementing basic quantum error mitigation protocols - Possible integration with Mitiq [6]_ Skills ====== * Background in quantum physics and quantum circuits. * Git, python and familiarity with the Python scientific computing stack Difficulty ========== * Medium Mentors ======= * Nathan Shammah (nathan.shammah@gmail.com) * Alex Pitchford (alex.pitchford@gmail.com) * Eric Giguère (eric.giguere@usherbrooke.ca) * Neill Lambert (nwlambert@gmail.com) * Boxi Li (etamin1201@gmail.com) [QuTiP GSoC 2019 graduate] References ========== .. [1] Kristan Temme, Sergey Bravyi, Jay M. Gambetta, **Error mitigation for short-depth quantum circuits**, Phys. Rev. Lett. 119, 180509 (2017) .. [2] Abhinav Kandala, Kristan Temme, Antonio D. Corcoles, Antonio Mezzacapo, Jerry M. Chow, Jay M. Gambetta, **Extending the computational reach of a noisy superconducting quantum processor**, Nature *567*, 491 (2019) .. [3] S. Endo, S.C. Benjamin, Y. Li, **Practical quantum error mitigation for near-future applications**, Physical Review X *8*, 031027 (2018) .. [4] Boxi Li's blog on the GSoC 2019 project on pulse-level control, https://gsoc2019-boxili.blogspot.com/ .. [5] Video of a recent talk on the GSoC 2019 project, https://fosdem.org/2020/schedule/event/quantum_qutip/ .. [6] `Mitiq `_ qutip-5.1.1/doc/development/ideas/qutip-interactive.rst000066400000000000000000000037751474175217300232720ustar00rootroot00000000000000***************** QuTiP Interactive ***************** .. contents:: Contents :local: :depth: 3 QuTiP is pretty simple to use at an entry level for anyone with basic Python skills. However, *some* Python skills are necessary. A graphical user interface (GUI) for some parts of qutip could help make qutip more accessible. This could be particularly helpful in education, for teachers and learners. Ideally, interactive components could be embedded in web pages. Including, but not limited to, Jupyter notebooks. The scope for this is broad and flexible. Ideas including, but not limited to: Interactive Bloch sphere ------------------------ QuTiP has a Bloch sphere virtualisation for qubit states. This could be made interactive through sliders, radio buttons, cmd buttons etc. An interactive Bloch sphere could have sliders for qubit state angles. Buttons to add states, toggle state evolution path. Potential for recording animations. Matplotlib has some interactive features (sliders, radio buttons, cmd buttons) that can be used to control parameters. that could potentially be used. Interactive solvers ------------------- Options to configure dynamics generators (Lindbladian / Hamiltonian args etc) and expectation operators. Then run solver and view state evolution. Animated circuits ----------------- QIP circuits could be animated. Status lights showing evolution of states during the processing. Animated Bloch spheres for qubits. Expected outcomes ================= * Interactive graphical components for demonstrating quantum dynamics * Web pages for qutip.org or Jupyter notebooks introducing quantum dynamics using the new components Skills ====== * Git, Python and familiarity with the Python scientific computing stack * elementary understanding of quantum dynamics Difficulty ========== * Variable Mentors ======= * Nathan Shammah (nathan.shammah@gmail.com) * Alex Pitchford (alex.pitchford@gmail.com) * Simon Cross (hodgestar@gmail.com) * Boxi Li (etamin1201@gmail.com) [QuTiP GSoC 2019 graduate] qutip-5.1.1/doc/development/ideas/tensorflow-data-backend.rst000066400000000000000000000052271474175217300243050ustar00rootroot00000000000000*********************** TensorFlow Data Backend *********************** .. contents:: Contents :local: :depth: 3 .. note:: This project was completed as part of GSoC 2021 [3]_. QuTiP's data layer provides the mathematical operations needed to work with quantum states and operators, i.e. ``Qobj``, inside QuTiP. As part of Google Summer of Code 2020, the data layer was rewritten to allow new backends to be added more easily and for different backends to interoperate with each other. Backends using in-memory spares and dense matrices already exist, and we would like to add a backend that implements the necessary operations using TensorFlow [1]_. Why a TensorFlow backend? ------------------------- TensorFlow supports distributing matrix operations across multiple GPUs and multiple machines, and abstracts away some of the complexities of doing so efficiently. We hope that by using TensorFlow we might enable QuTiP to scale to bigger quantum systems (e.g. more qubits) and decrease the time taken to simulate them. There is particular interest in trying the new backend with the BoFiN HEOM (Hierarchical Equations of Motion) solver [2]_. Challenges ---------- TensorFlow is a very different kind of computational framework to the existing dense and sparse matrix backends. It uses flow graphs to describe operations, and to work efficiently. Ideally large graphs of operations need to be executed together in order to efficiently compute results. The QuTiP data layer might need to be adjusted to accommodate these differences, and it is possible that this will prove challenging or even that we will not find a reasonable way to achieve the desired performance. Expected outcomes ================= * Add a ``qutip.core.data.tensorflow`` data type. * Implement specialisations for some important operations (e.g. ``add``, ``mul``, ``matmul``, ``eigen``, etc). * Write a small benchmark to show how ``Qobj`` operations scale on the new backend in comparison to the existing backends. Run the benchmark both with and without using a GPU. * Implement enough for a solver to run on top of the new TensorFlow data backend and benchmark that (stretch goal). Skills ====== * Git, Python and familiarity with the Python scientific computing stack * Familiarity with TensorFlow (beneficial, but not required) * Familiarity with Cython (beneficial, but not required) Difficulty ========== * Medium Mentors ======= * Simon Cross (hodgestar@gmail.com) * Jake Lishman (jake@binhbar.com) * Alex Pitchford (alex.pitchford@gmail.com) References ========== .. [1] https://www.tensorflow.org/ .. [2] https://github.com/tehruhn/bofin .. [3] https://github.com/qutip/qutip-tensorflow/ qutip-5.1.1/doc/development/release_distribution.rst000066400000000000000000000466251474175217300227500ustar00rootroot00000000000000.. This file was created using retext 6.1 https://github.com/retext-project/retext .. _release_distribution: ************************ Release and Distribution ************************ Preamble ++++++++ This document covers the process for managing updates to the current minor release and making new releases. Within this document, the git remote ``upstream`` refers to the main QuTiP organsiation repository, and ``origin`` refers to your personal fork. In short, the steps you need to take are: 1. Prepare the release branch (see git_). 2. Run the "Build wheels, optionally deploy to PyPI" GitHub action to build binary and source packages and upload them to PyPI (see deploy_). 3. Create a GitHub release and uploaded the built files to it (see github_). 4. Update `qutip.org `_ with the new links and documentation (web_). 5. Update the conda feedstock, deploying the package to ``conda`` (cforge_). .. _git: Setting Up The Release Branch +++++++++++++++++++++++++++++ In this step you will prepare a git branch on the main QuTiP repository that has the state of the code that is going to be released. This procedure is quite different if you are releasing a new minor or major version compared to if you are making a bugfix patch release. For a new minor or major version, do update-changelog_ and then jump to release_. For a bug fix to an existing release, do update-changelog_ and then jump to bugfix_. Changes that are not backwards-compatible may only be made in a major release. New features that do not affect backwards-compatibility can be made in a minor release. Bug fix releases should be small, only fix bugs, and not introduce any new features. There are a few steps that *should* have been kept up-to-date during day-to-day development, but might not be quite accurate. For every change that is going to be part of your release, make sure that: - The user guide in the documentation is updated with any new features, or changes to existing features. - Any new API classes or functions have entries in a suitable RST file in ``doc/apidoc``. - Any new or changed docstrings are up-to-date and render correctly in the API documentation. Please make a normal PR to ``master`` correcting anything missing from these points and have it merged before you begin the release, if necessary. .. _update-requirement: Updating the Requirements ------------------------- Ensure that QuTiP's tests pass on the oldest version supported in the requirements. On major and minor version, requirements can be adjusted upwards, but patch release must not change minimum requirements. We follow `NEP29`_ for minimum supported versions :: - All minor versions of Python released 42 months prior to the project, and at minimum the two latest minor versions. - All minor versions of numpy and scipy released in the 24 months prior to the project, and at minimum the last three minor versions. If dependency versions need to be updated, update them in the master branch. The following files may need to be updated: `.github/workflows/tests.yml`, `setup.cfg` and `roadmap.rst`. Finally, ensure that PyPI wheels and conda builds cover at least these versions. .. _NEP29: https://numpy.org/neps/nep-0029-deprecation_policy.html .. _update-changelog: Updating the Changelog ---------------------- This needs to be done no matter what type of release is being made. #. Create a new branch to use to make a pull request. #. Update the changelog using ``towncrier``: towncrier build --version= Where ```` is the expected version number of the release #. Make a pull request on the main ``qutip/qutip`` repository with this changelog, and get other members of the admin team to approve it. #. Merge this into ``master``. Now jump to release_ if you are making a major or minor release, or bugfix_ if you are only fixing bugs in a previous release. .. _release: Create a New Minor or Major Release ----------------------------------- This involves making a new branch to hold the release and adding some commits to set the code into "release" mode. This release should be done by branching directly off the ``master`` branch at its current head. #. On your machine, make sure your copy of ``master`` is up-to-date (``git checkout master; git pull upstream master``). This should at least involve fetching the changelog PR that you just made. Now create a new branch off a commit in ``master`` that has the state of the code you want to release. The command is ``git checkout -b qutip-..X``, for example ``qutip-4.7.X``. This branch name will be public, and must follow this format. #. Push the new branch (with no commits in it relative to ``master``) to the main ``qutip/qutip`` repository (``git push upstream qutip-4.7.X``). Creating a branch is one of the only situations in which it is ok to push to ``qutip/qutip`` without making a pull request. #. Create a second new branch, which will be pushed to your fork and used to make a pull request against the ``qutip-..X`` branch on ``qutip/qutip`` you just created. You can call this branch whatever you like because it is not going to the main repository, for example ``git checkout -b prepare-qutip-4.7.0``. #. - Change the ``VERSION`` file to contain the new version number exactly, removing the ``.dev`` suffix. For example, if you are releasing the first release of the minor 4.7 track, set ``VERSION`` to contain the string ``4.7.0``. (*Special circumstances*: if you are making an alpha, beta or release candidate release, append a ``.a``, ``.b`` or ``.rc`` to the version string, where ```` is an integer starting from 0 that counts how many of that pre-release track there have been.) - Edit ``setup.cfg`` by changing the "Development Status" line in the ``classifiers`` section to :: Development Status :: 5 - Production/Stable Commit both changes (``git add VERSION setup.cfg; git commit -m "Set release mode for 4.7.0"``), and then push them to your fork (``git push -u origin prepare-qutip-4.7.0``) #. Using GitHub, make a pull request to the release branch (e.g. ``qutip-4.7.X``) using this branch that you just created. You will need to change the "base branch" in the pull request, because GitHub will always try to make the PR against ``master`` at first. When the tests have passed, merge this in. #. Finally, back on ``master``, make a new pull request that changes the ``VERSION`` file to be ``.dev``, for example ``4.8.0.dev``. The "Development Status" in ``setup.cfg`` on ``master`` should not have changed, and should be :: Development Status :: 2 - Pre-Alpha because ``master`` is never directly released. You should now have a branch that you can see on the GitHub website that is called ``qutip-4.7.X`` (or whatever minor version), and the state of the code in it should be exactly what you want to release as the new minor release. If you notice you have made a mistake, you can make additional pull requests to the release branch to fix it. ``master`` should look pretty similar, except the ``VERSION`` will be higher and have a ``.dev`` suffix, and the "Development Status" in ``setup.cfg`` will be different. * Activate the readthedocs build for the newly created version branch and set it as the latest. You are now ready to actually perform the release. Go to deploy_. .. _bugfix: Create a Bug Fix Release ------------------------ In this you will modify an already-released branch by "cherry-picking" one or more pull requests that have been merged to ``master`` (including your new changelog), and bump the "patch" part of the version number. #. On your machine, make sure your copy of ``master`` is up-to-date (``git checkout master; git pull upstream master``). In particular, make sure the changelog you wrote in the first step is visible. #. Find the branch of the release that you will be modifying. This should already exist on the ``qutip/qutip`` repository, and be called ``qutip-..X`` (e.g. ``qutip-4.6.X``). If you cannot see it, run ``git fetch upstream`` to update all the branch references from the main repository. Checkout a new private branch, starting from the head of the release branch (``git checkout -b prepare-qutip-4.6.1 upstream/qutip-4.6.X``). You can call this branch whatever you like (in the example it is ``prepare-qutip-4.6.1``), because it will only be used to make a pull request. #. Cherry-pick all the commits that will be added to this release in order, including your PR that wrote the new changelog entries (this will be the last one you cherry-pick). You will want to use ``git log`` to find the relevant commits, going from **oldest to newest** (their "age" is when they were merged into ``master``, not when the PR was first opened). The command is slightly different depending on which merge strategy was used for a particular PR: - "merge": you only need to find one commit though the log will have included several; there will be an entry in ``git log`` with a title such as "Merge pull request #1000 from <...>". Note the first 7 characters of its hash. Cherry-pick this by ``git cherry-pick --mainline 1 ``. - "squash and merge": there will only be a single commit for the entire PR. Its name will be " (#1000)". Note the first 7 characters of its hash. Cherry-pick this by ``git cherry-pick ``. - "rebase and merge": this is the most difficult, because there will be many commits that you will have to find manually, and cherry-pick all of them. Go to the GitHub page for this PR, and go to the "Commits" tab. Using your local ``git log`` (you may find ``git log --oneline`` useful), find the hash for every single commit that is listed on the GitHub page, in order from **oldest to newest** (top-to-bottom in the GitHub view, which is bottom-to-top in ``git log``). You will need to use the commit message to do this; the hashes that GitHub reports will probably not be the same as how they appear locally. Find the first 7 characters of each of the hashes. Cherry-pick these all in one go by ``git cherry-pick ... ``, where ```` is the oldest. If any of the cherry-picks have merge conflicts, first verify that you are cherry-picking in order from oldest to newest. If you still have merge conflicts, you will either need to manually fix them (if it is a *very* simple fix), or else you will need to find which additional PR this patch depends on, and restart the bug fix process including this additional patch. This generally should not happen if you are sticking to very small bug fixes; if the fixes had far-reaching changes, a new minor release may be more appropriate. #. Change the ``VERSION`` file by bumping the last number up by one (double-digit numbers are fine, so ``4.6.10`` comes after ``4.6.9``), and commit the change. #. Push this branch to your fork, and make a pull request against the release branch. On GitHub in the PR screen, you will need to change the "Base" branch to ``qutip-4.6.X`` (or whatever version), because GitHub will default to making it against ``master``. It should be quite clear if you have forgotten to do this, because there will probably be many merge conflicts. Once the tests have passed and you have another admin's approval, merge the PR. You should now see that the ``qutip-4.6.X`` (or whatever) branch on GitHub has been updated, and now includes all the changes you have just made. If you have made a mistake, feel free to make additonal PRs to rectify the situation. You are now ready to actually perform the release. Go to deploy_. .. _deploy: Build Release Distribution and Deploy +++++++++++++++++++++++++++++++++++++ This step builds the source (sdist) and binary (wheel) distributions, and uploads them to PyPI (pip). You will also be able to download the built files yourself in order to upload them to the QuTiP website. Build and Deploy ---------------- This is handled entirely by a GitHub Action. Go to the `"Actions" tab at the top of the QuTiP code repository `_. Click on the "Build wheels, optionally deploy to PyPI" action in the left-hand sidebar. Click the "Run workflow" dropdown in the header notification; it should look like the image below. .. image:: ../figures/release_guide_run_build_workflow.png - Use the drop-down menu to choose the branch or tag you want to release from. This should be called ``qutip-4.5.X`` or similar, depending on what you made earlier. This must *never* be ``master``. - To make the release to PyPI, type the branch name (e.g. ``qutip-4.5.X``) into the "Confirm chosen branch name [...]" field. You *may* leave this field blank to skip the deployment and only build the package. - (Special circumstances) If for some reason you need to override the version number (for example if the previous deployment to PyPI only partially succeeded), you can type a valid Python version identifier into the "Override version number" field. You probably do not need to do this. The mechanism is designed to make alpha-testing major upgrades with nightly releases easier. For even a bugfix release, you should commit the change to the ``VERSION`` file. - Click the lower "Run workflow" to perform the build and deployment. At this point, the deployment will take care of itself. It should take between 30 minutes and an hour, after which the new version will be available for install by ``pip install qutip``. You should see the new version appear on `QuTiP's PyPI page `_. Download Built Files -------------------- When the build is complete, click into its summary screen. This is the main screen used to both monitor the build and see its output, and should look like the below image on a success. .. image:: ../figures/release_guide_after_workflow.png The built binary wheels and the source distribution are the "build artifacts" at the bottom. You need to download both the wheels and the source distribution. Save them on your computer, and unzip both files; you should have many wheel ``qutip-*.whl`` files, and two sdist files: ``qutip-*.tar.gz`` and ``qutip-*.zip``. These are the same files that have just been uploaded to PyPI. Monitoring Progress (optional) ------------------------------ While the build is in progress, you can monitor its progress by clicking on its entry in the list below the "Run workflow" button. You should see several subjobs, like the completed screen, except they might not yet be completed. The "Verify PyPI deployment confirmation" should get ticked, no matter what. If it fails, you have forgotten to choose the correct branch in the drop-down menu or you made a typo when confirming the correct branch, and you will need to restart this step. You can check that the deployment instruction has been understood by clicking the "Verify PyPI deployment confirmation" job, and opening the "Compare confirmation to current reference" subjob. You will see a message saying "Built wheels will be deployed" if you typed in the confirmation, or "Only building wheels" if you did not. If you see "Only building wheels" but you meant to deploy the release to PyPI, you can cancel the workflow and re-run it after typing the confirmation. .. _github: Making a Release on GitHub ++++++++++++++++++++++++++ This is all done through `the "Releases" section `_ of the ``qutip/qutip`` repository on GitHub. - Click the "Draft a new release" button. - Choose the correct branch for your release (e.g. ``qutip-4.5.X``) in the drop-down. - For the tag name, use ``v``, where the version matches the contents of the ``VERSION`` file. In other words, if you are releasing a micro version 4.5.3, use ``v4.5.3`` as the tag, or if you are releasing major version 5.0.0, use ``v5.0.0``. - The title is "QuTiP ", e.g. "QuTiP 4.6.0". - For the description, write a short (~two-line for a patch release) summary of the reason for this release, and note down any particular user-facing changes that need special attention. Underneath, put the changelog you wrote when you did the documentation release. Note that there may be some syntax differences between the ``.rst`` file of the changelog and the Markdown of this description field (for example, GitHub's markdown typically maintains hard-wrap linebreaks, which is probably not what you wanted). - Drag-and-drop all the ``qutip-*.whl``, ``qutip-*.tar.gz`` and ``qutip-*.zip`` files you got after the build step into the assets box. You may need to unzip the files ``wheels.zip`` and ``sdist.zip`` to find them if you haven't already; **don't** upload those two zip files. Click on the "Publish release" button to finalise. .. _web: Website +++++++ This assumes that qutip.github.io has already been forked and familiarity with the website updating workflow. The documentation need not be updated for every patch release. HTML File Updates ----------------- - Edit ``download.html`` * The 'Latest release' version and date should be updated. * The tar.gz and zip links need to have their micro release numbers updated in their filenames, labels and trackEvent javascript. These links should point to the "Source code" links that appeared when you made in the GitHub Releases section. They should look something like ``https://github.com/qutip/qutip/archive/refs/tags/v4.6.0.tar.gz``. * For a minor or major release links to the last micro release of the previous version will need to be moved (copied) to the 'Previous releases' section. - Edit ``_includes/sidebar.html`` * Add the new version and release date. Only actively developed version should be listed. Micro replace the previous entry but the last major can be kept. * Link to the installation instruction, documentation, source code and changelog should be updated. - Edit ``documentation.html`` * For major and minor release, the previous release tags should be moved (copied) to the 'Previous releases' section and the links to the readthedocs of the new version added the to 'Latest releases' section. .. _cforge: Conda Forge +++++++++++ If not done previously then fork the `qutip-feedstock `_. Checkout a new branch on your fork, e.g. :: $ git checkout -b version-4.0.2 Find the sha256 checksum for the tarball that the GitHub web interface generated when you produced the release called "Source code". This is *not* the sdist that you downloaded earlier, it's a new file that GitHub labels "Source code". When you download it, though, it will have a name that *looks* like it's the sdist :: $ openssl sha256 qutip-4.0.2.tar.gz Edit the ``recipe/meta.yaml`` file. Change the version at the top of the file, and update the sha256 checksum. Check that the recipe package version requirements at least match those in ``setup.cfg``, and that any changes to the build process are reflected in ``meta.yml``. Also ensure that the build number is reset :: build: number: 0 Push changes to your fork, e.g. :: $ git push --set-upstream origin version-4.0.2 Make a Pull Request. This will trigger tests of the package build process. If (when) the tests pass, the PR can be merged, which will trigger the upload of the packages to the conda-forge channel. To test the packages, add the conda-forge channel with lowest priority :: $ conda config --append channels conda-forge This should mean that the prerequistes come from the default channel, but the qutip packages are found in conda-forge. qutip-5.1.1/doc/development/roadmap.rst000066400000000000000000000405001474175217300201360ustar00rootroot00000000000000.. _development_roadmap: ************************* QuTiP Development Roadmap ************************* Preamble ======== This document outlines plan and ideas for the current and future development of QuTiP. The document is maintained by the QuTiP Admim team. Contributuions from the QuTiP Community are very welcome. In particular this document outlines plans for the next major release of qutip, which will be version 5. And also plans and dreams beyond the next major version. There is lots of development going on in QuTiP that is not recorded in here. This a just an attempt at coordinated stragetgy and ideas for the future. .. _what-is-qutip: What is QuTiP? -------------- The name QuTiP refers to a few things. Most famously, qutip is a Python library for simulating quantum dynamics. To support this, the library also contains various software tools (functions and classes) that have more generic applications, such as linear algebra components and visualisation utilities, and also tools that are specifically quantum related, but have applications beyond just solving dynamics (for instance partial trace computation). QuTiP is also an organisation, in the Github sense, and in the sense of a group of people working collaboratively towards common objectives, and also a web presence `qutip.org `_. The QuTiP Community includes all the people who have supported the project since in conception in 2010, including manager, funders, developers, maintainers and users. These related, and overlapping, uses of the QuTiP name are of little consequence until one starts to consider how to organise all the software packages that are somehow related to QuTiP, and specifically those that are maintained by the QuTiP Admim Team. Herin QuTiP will refer to the project / organisation and qutip to the library for simulating quantum dyanmics. Should we be starting again from scratch, then we would probably chose another name for the main qutip library, such as qutip-quantdyn. However, qutip is famous, and the name will stay. Library package structure ========================= With a name as general as Quantum Toolkit in Python, the scope for new code modules to be added to qutip is very wide. The library was becoming increasingly difficult to maintain, and in c. 2020 the QuTiP Admim Team decided to limit the scope of the 'main' (for want of a better name) qutip package. This scope is restricted to components for the simulation (solving) of the dynamics of quantum systems. The scope includes utilities to support this, including analysis and visualisation of output. At the same time, again with the intention of easing maintence, a decision to limit dependences was agreed upon. Main qutip runtime code components should depend only upon Numpy and Scipy. Installation (from source) requires Cython, and some optional components also require Cython at runtime. Unit testing requires Pytest. Visualisation (optional) components require Matplotlib. Due to the all encompassing nature of the plan to abstract the linear algebra data layer, this enhancement (developed as part of a GSoC project) was allowed the freedom (potential for non-backward compatibility) of requiring a major release. The timing of such allows for a restructuring of the qutip compoments, such that some that could be deemed out of scope could be packaged in a different way -- that is, not installed as part of the main qutip package. Hence the proposal for different types of package described next. With reference to the :ref:`discussion above ` on the name QuTiP/qutip, the planned restructuring suffers from confusing naming, which seems unavoidable without remaining either the organisation or the main package (neither of which are desirable). QuTiP family packages The main qutip package already has sub-packages, which are maintained in the main qutip repo. Any packages maitained by the QuTiP organisation will be called QuTiP 'family' packages. Sub-packages within qutip main will be called 'integrated' sub-packages. Some packages will be maintained in their own repos and installed separately within the main qutip folder structure to provide backwards compatibility, these are (will be) called qutip optional sub-packages. Others will be installed in their own folders, but (most likely) have qutip as a dependency -- these will just be called 'family' packages. QuTiP affilliated packages Other packages have been developed by others outside of the QuTiP organisation that work with, and are complementary to, qutip. The plan is to give some recognition to those that we deem worthy of such [this needs clarification]. These packages will not be maintained by the QuTiP Team. Family packages --------------- .. _qmain: qutip main ^^^^^^^^^^ * **current package status**: family package `qutip` * **planned package status**: family package `qutip` The in-scope components of the main qutip package all currently reside in the base folder. The plan is to move some components into integrated subpackages as follows: - `core` quantum objects and operations - `solver` quantum dynamics solvers What will remain in the base folder will be miscellaneous modules. There may be some opportunity for grouping some into a `visualisation` subpackage. There is also some potential for renaming, as some module names have underscores, which is unconventional. Qtrl ^^^^ * **current package status**: integrated sub-package `qutip.control` * **planned package status**: family package `qtrl` There are many OSS Python packages for quantum control optimisation. There are also many different algorithms. The current `control` integrated subpackage provides the GRAPE and CRAB algorithms. It is too ambitious for QuTiP to attempt (or want) to provide for all options. Control optimisation has been deemed out of scope and hence these components will be separated out into a family package called Qtrl. Potentially Qtrl may be replaced by separate packages for GRAPE and CRAB, based on the QuTiP Control Framework. QIP ^^^ * **current package status**: integrated sub-package `qutip.qip` * **planned package status**: family package `qutip-qip` The QIP subpackage has been deemed out of scope (feature-wise). It also depends on `qutip.control` and hence would be out of scope for dependency reasons. A separate repository has already been made for qutip-qip. qutip-symbolic ^^^^^^^^^^^^^^ * **current package status**: independent package `sympsi` * **planned package status**: family package `qutip-symbolic` Long ago Robert Johansson and Eunjong Kim developed Sympsi. It is a fairly coomplete library for quantum computer algebra (symbolic computation). It is primarily a quantum wrapper for `Sympy `_. It has fallen into unmaintained status. The latest version on the `sympsi repo `_ does not work with recent versions of Sympy. Alex Pitchford has a `fork `_ that does 'work' with recent Sympy versions -- unit tests pass, and most examples work. However, some (important) examples fail, due to lack of respect for non-commuting operators in Sympy simplifcation functions (note this was true as of Nov 2019, may be fixed now). There is a [not discussed with RJ & EK] plan to move this into the QuTiP family to allow the Admin Team to maintain, develop and promote it. The 'Sympsi' name is cute, but a little abstract, and qutip-symbolic is proposed as an alternative, as it is plainer and more distinct from Sympy. Affilliated packages -------------------- qucontrol-krotov ^^^^^^^^^^^^^^^^ * **code repository**: https://github.com/qucontrol/krotov A package for quantum control optimisation using Krotov, developed mainly by Michael Goerz. Generally accepted by the Admin Team as well developed and maintained. A solid candiate for affilliation. Development Projects ==================== .. _solve-dl: Solver data layer integration ----------------------------- :tag: solve-dl :status: development ongoing :admin lead: `Eric `_ :main dev: `Eric `_ The new data layer gives opportunity for significantly improving performance of the qutip solvers. Eric has been revamping the solvers by deploying `QobjEvo` (the time-dependent quantum object) that he developed. `QobjEvo` will exploit the data layer, and the solvers in turn exploit `QobjEvo`. .. _qtrl-mig: Qtrl migration -------------- :tag: qtrl-mig :status: conceptualised :admin lead: `Alex `_ :main dev: TBA The components currently packaged as an integrated subpackage of qutip main will be moved to separate package called Qtrl. This is the original codename of the package before it was integrated into qutip. Also changes to exploit the new data layer will be implemented. .. _ctrl-fw: QuTiP control framework ----------------------- :tag: ctrl-fw :status: conceptualised :admin lead: `Alex `_ :main dev: TBA Create new package qutip-ctrlfw "QuTiP Control Framework". The aim is provide a common framework that can be adopted by control optimisation packages, such that different packages (algorithms) can be applied to the same problem. Classes for defining a controlled system: - named control parameters. Scalar and n-dim. Continuous and discrete variables - mapping of control parameters to dynamics generator args - masking for control parameters to be optimised Classes for time-dependent variable parameterisation - piecewise constant - piecewise linear - Fourier basis - more Classes for defining an optimisation problem: - single and multiple objectives .. _qutip-optim: QuTiP optimisation ------------------ :tag: qutip-optim :status: conceptualised :admin lead: `Alex `_ :main dev: TBA A wrapper for multi-variable optimisation functions. For instance those in `scipy.optimize` (Nelder-Mead, BFGS), but also others, such as Bayesian optimisation and other machine learning based approaches. Initially just providing a common interface for quantum control optimisation, but applicable more generally. .. _sympsi-mig: Sympsi migration ---------------- :tag: sympsi-mig :status: conceptualised :admin lead: `Alex `_ :main dev: TBA Create a new family package qutip-symbolic from ajgpitch fork of Sympy. Must gain permission from Robert Johansson and Eunjong Kim. Extended Sympy simplify to respect non-commuting operators. Produce user documentation. .. _status-mig: Status messaging and recording ------------------------------ :tag: status-msg :status: conceptualised :admin lead: `Alex `_ :main dev: TBA QuTiP has various ways of recording and reporting status and progress. - `ProgressBar` used by some solvers - Python logging used in qutip.control - `Dump` used in qutip.control - heom records `solver.Stats` Some consolidation of these would be good. Some processes (some solvers, correlation, control optimisation) have many stages and many layers. `Dump` was initially developed to help with debugging, but it is also useful for recording data for analysis. qutip.logging_utils has been criticised for the way it uses Python logging. The output goes to stderr and hence the output looks like errors in Jupyter notebooks. Clearly, storing process stage data is costly in terms of memory and cpu time, so any implementation must be able to be optionally switched on/off, and avoided completely in low-level processes (cythonized components). Required features: - optional recording (storing) of process stage data (states, operators etc) - optionally write subsets to stdout - maybe other graphical representations - option to save subsets to file - should ideally replace use of `ProgressBar`, Python logging, `control.Dump`, `solver.Stats` .. _qutip-gui: qutip Interactive ----------------- :status: conceptualised :tag: qutip-gui :admin lead: `Alex `_ :main dev: TBA QuTiP is pretty simple to use at an entry level for anyone with basic Python skills. However, *some* Python skills are necessary. A graphical user interface (GUI) for some parts of qutip could help make qutip more accessible. This could be particularly helpful in education, for teachers and learners. This would make an good GSoC project. It is independent and the scope is flexible. The scope for this is broad and flexible. Ideas including, but not limited to: Interactive Bloch sphere ^^^^^^^^^^^^^^^^^^^^^^^^ Matplotlib has some interactive features (sliders, radio buttons, cmd buttons) that can be used to control parameters. They are a bit clunky to use, but they are there. Could maybe avoid these and develop our own GUI. An interactive Bloch sphere could have sliders for qubit state angles. Buttons to add states, toggle state evolution path. Interactive solvers ^^^^^^^^^^^^^^^^^^^ Options to configure dynamics generators (Lindbladian / Hamiltonian args etc) and expectation operators. Then run solver and view state evolution. Animated circuits ^^^^^^^^^^^^^^^^^ QIP circuits could be animated. Status lights showing evolution of states during the processing. Animated Bloch spheres for qubits. Completed Development Projects ============================== .. _dl-abs: data layer abstraction ---------------------- :tag: dl-abs :status: completed :admin lead: `Eric `_ :main dev: `Jake Lishman `_ Development completed as a GSoC project. Fully implemented in the dev.major branch. Currently being used by some research groups. Abstraction of the linear algebra data from code qutip components, allowing for alternatives, such as sparse, dense etc. Difficult to summarize. Almost every file in qutip affected in some way. A major milestone for qutip. Significant performance improvements throughout qutip. Some developments tasks remain, including providing full control over how the data-layer dispatchers choose the most appropriate output type. .. _qmain-reorg: qutip main reorganization ------------------------- :tag: qmain-reorg :status: completed :admin lead: `Eric `_ :main dev: `Jake Lishman `_ Reorganise qutip main components to the structure :ref:`described above `. .. _qmain-docs: qutip user docs migration ------------------------- :tag: qmain-docs :status: completed :admin lead: `Jake Lishman `_ :main dev: `Jake Lishman `_ The qutip user documentation build files are to be moved to the qutip/qutip repo. This is more typical for an OSS package. As part of the move, the plan is to reconstruct the Sphinx structure from scratch. Historically, there have been many issues with building the docs. Sphinx has come a long way since qutip docs first developed. The main source (rst) files will remain [pretty much] as they are, although there is a lot of scope to improve them. The qutip-doc repo will afterwards just be used for documents, such as this one, pertaining to the QuTiP project. .. _qip-mig: QIP migration ------------- :tag: qip-mig :status: completed :admin lead: `Boxi `_ :main dev: `Sidhant Saraogi `_ A separate package for qutip-qip was created during Sidhant's GSoC project. There is some fine tuning required, especially after qutip.control is migrated. .. _heom-revamp: HEOM revamp ----------- :tag: heom-revamp :status: completed :admin lead: `Neill `_ :main dev: `Simon Cross `_, `Tarun Raheja `_ An overhaul of the HEOM solver, to incorporate the improvements pioneered in BoFiN. .. _release roadmap: QuTiP major release roadmap =========================== QuTiP v.5 --------- These Projects need to be completed for the qutip v.5 release. - :ref:`dl-abs` (completed) - :ref:`qmain-reorg` (completed) - :ref:`qmain-docs` (completed) - :ref:`solve-dl` (in-progress) - :ref:`qip-mig` (completed) - :ref:`qtrl-mig` - :ref:`heom-revamp` (completed) The planned timeline for the release is: - **alpha version, December 2022**. Core features packaged and available for experienced users to test. - **beta version, January 2023**. All required features and documentation complete, packaged and ready for community testing. - **full release, April 2023**. Full tested version released. 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Johansson and P.D. Nation and Franco Nori", keywords = "Open quantum systems", keywords = "Lindblad master equation", keywords = "Quantum Monte Carlo", keywords = "Python" } qutip-5.1.1/doc/figures/citing/qutip2.bib000066400000000000000000000011761474175217300202700ustar00rootroot00000000000000@article{Johansson20131234, title = "QuTiP 2: A Python framework for the dynamics of open quantum systems", journal = "Computer Physics Communications", volume = "184", number = "4", pages = "1234 - 1240", year = "2013", note = "", issn = "0010-4655", doi = "10.1016/j.cpc.2012.11.019", url = "https://www.sciencedirect.com/science/article/pii/S0010465512003955", author = "J.R. Johansson and P.D. 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`. Let us calculate the coefficients and exponents in Python: .. plot:: :context: :nofigs: # Convenience functions and parameters: def cot(x): return 1. / np.tan(x) beta = 1. / T # Number of expansion terms to calculate: Nk = 2 # C_real expansion terms: ck_real = [lam * gamma / np.tan(gamma / (2 * T))] ck_real.extend([ (8 * lam * gamma * T * np.pi * k * T / ((2 * np.pi * k * T)**2 - gamma**2)) for k in range(1, Nk + 1) ]) vk_real = [gamma] vk_real.extend([2 * np.pi * k * T for k in range(1, Nk + 1)]) # C_imag expansion terms (this is the full expansion): ck_imag = [lam * gamma * (-1.0)] vk_imag = [gamma] After all that, constructing the bath is very straight forward: .. plot:: :context: :nofigs: from qutip.solver.heom import BosonicBath bath = BosonicBath(Q, ck_real, vk_real, ck_imag, vk_imag) And we're done! .. admonition:: Environment API The analogue of the ``BosonicBath`` is the ``ExponentialBosonicEnvironment``. Its usage is very similar: .. code-block:: python from qutip.core.environment import ExponentialBosonicEnvironment env = ExponentialBosonicEnvironment(ck_real, vk_real, ck_imag, vk_imag) The :class:`~qutip.solver.heom.BosonicBath` and the :class:`.ExponentialBosonicEnvironment` can be used with the :class:`~qutip.solver.heom.HEOMSolver` in exactly the same way as the baths and environments that we constructed previously using the built-in Drude-Lorentz bath expansions. Multiple baths -------------- The :class:`~qutip.solver.heom.HEOMSolver` supports having a system interact with multiple reservoirs. All that is needed is to supply a list of baths or environments instead of a single bath or environment. In the example below we calculate the evolution of a small system where each basis state of the system interacts with a separate bath. Such an arrangement can model, for example, the Fenna–Matthews–Olson (FMO) pigment-protein complex which plays an important role in photosynthesis (for a full FMO example see the `HEOM example notebook 2 `_). For each bath expansion, we also include the terminator in the system Liouvillian. At the end, we plot the populations of the system states as a function of time, and show the long-time beating of quantum state coherence that occurs: .. plot:: :context: close-figs # The size of the system: N_sys = 3 def proj(i, j): """ A helper function for creating an interaction operator. """ return basis(N_sys, i) * basis(N_sys, j).dag() # Construct one bath for each system state: baths = [] for i in range(N_sys): Q = proj(i, i) baths.append(DrudeLorentzBath(Q, lam, gamma, T, Nk)) # Construct the system Liouvillian from the system Hamiltonian and # bath expansion terminators: H_sys = sum((i + 0.5) * eps * proj(i, i) for i in range(N_sys)) H_sys += sum( (i + j + 0.5) * Del * proj(i, j) for i in range(N_sys) for j in range(N_sys) if i != j ) HL = liouvillian(H_sys) + sum(bath.terminator()[1] for bath in baths) # Construct the solver (pass a list of baths): solver = HEOMSolver(HL, baths, max_depth=max_depth, options=options) # Run the solver: rho0 = basis(N_sys, 0) * basis(N_sys, 0).dag() tlist = np.linspace(0, 5, 200) e_ops = { f"P{i}": proj(i, i) for i in range(N_sys) } result = solver.run(rho0, tlist, e_ops=e_ops) # Plot populations: fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8)) for label, values in result.e_data.items(): axes.plot(result.times, np.real(values), label=label) axes.set_xlabel(r't', fontsize=16) axes.set_ylabel(r"Population", fontsize=16) axes.legend(loc=0, fontsize=16) .. admonition:: Environment API Instead of a list ``[bath1, bath2, ...]``, one can of course also pass multiple environments with different coupling operators like .. code-block:: python HEOMSolver(Hsys, [(env1, Q1), (env2, Q2), ...], ...) or even a mixed list of baths and environments. .. plot:: :context: reset :include-source: false :nofigs: # reset the context at the end qutip-5.1.1/doc/guide/heom/fermionic.rst000066400000000000000000000403141474175217300201740ustar00rootroot00000000000000###################### Fermionic Environments ###################### Here we model a single fermion coupled to two electronic leads or reservoirs (e.g., this can describe a single quantum dot, a molecular transistor, etc). The system hamiltonian, :math:`H_{sys}`, and bath spectral density, :math:`J_D`, are .. math:: H_{sys} &= c^{\dagger} c J_D(\omega) &= \frac{\Gamma W^2}{(w - \mu)^2 + W^2}, We will demonstrate how to describe the bath using two different expansions of the spectral density correlation function (Matsubara's expansion and a PadĂŠ expansion), how to evolve the system in time, and how to calculate the steady state. Since our fermion is coupled to two reservoirs, we will construct two baths -- one for each reservoir or lead -- and call them the left (L) and right (R) baths for convenience. Each bath will have a different chemical potential :math:`\mu` which we will label :math:`\mu_L` and :math:`\mu_R`. First we will do this using the built-in implementations of the bath expansions, :class:`~qutip.solver.heom.LorentzianBath` and :class:`~qutip.solver.heom.LorentzianPadeBath`. Afterwards, we will show how to calculate the bath expansion coefficients and to use those coefficients to construct your own bath description so that you can implement your own fermionic baths. .. admonition:: Environment API As for the bosonic case, we will include brief intermissions showing how to achieve the same results using the newer environment API. The "bath" classes are part of an older API that is less powerful, but often more convenient to use when one only uses the HEOM solver and does not need any of the new features. Our implementation of fermionic baths primarily follows the definitions used in the `dissertation of Christian Schinabeck `_ and related publications. A notebook containing a complete example similar to this one implemented in BoFiN can be found in `HEOM example notebook 5a `_. Describing the system and bath ------------------------------ First, let us construct the system Hamiltonian, :math:`H_{sys}`, and the initial system state, ``rho0``: .. plot:: :context: reset :nofigs: from qutip import basis, destroy # The system Hamiltonian: e1 = 1. # site energy H_sys = e1 * destroy(2).dag() * destroy(2) # Initial state of the system: rho0 = basis(2,0) * basis(2,0).dag() Now let us describe the bath properties: .. plot:: :context: :nofigs: # Shared bath properties: gamma = 0.01 # coupling strength W = 1.0 # cut-off T = 0.025851991 # temperature beta = 1. / T # Chemical potentials for the two baths: mu_L = 1. mu_R = -1. # System-bath coupling operator: Q = destroy(2) where :math:`\Gamma` (``gamma``), :math:`W` and the temperature :math:`T` are the parameters of an Lorentzian bath, :math:`\mu_L` (``mu_L``) and :math:`\mu_R` (``mu_R``) are the chemical potentials of the left and right baths, and ``Q`` is the coupling operator between the system and the baths. QuTiP assumes a number-conserving coupling term, as described in the :ref:`section on fermionic environments `. We may the pass these parameters to either ``LorentzianBath`` or ``LorentzianPadeBath`` to construct an expansion of the bath correlations: .. plot:: :context: :nofigs: from qutip.solver.heom import LorentzianBath from qutip.solver.heom import LorentzianPadeBath # Number of expansion terms to retain: Nk = 2 # Matsubara expansion: bath_L = LorentzianBath(Q, gamma, W, mu_L, T, Nk, tag="L") bath_R = LorentzianBath(Q, gamma, W, mu_R, T, Nk, tag="R") # PadĂŠ expansion: bath_L = LorentzianPadeBath(Q, gamma, W, mu_L, T, Nk, tag="L") bath_R = LorentzianPadeBath(Q, gamma, W, mu_R, T, Nk, tag="R") Here, ``Nk`` is the number of terms to retain within the expansion of the bath. Note that we haved labelled each bath with a tag (either "L" or "R") so that we can identify the exponents from individual baths later when calculating the currents between the system and the bath. .. admonition:: Environment API In analogy to the Drude-Lorentz environment in the previous section, we first create a :class:`.LorentzianEnvironment` that describes the bath abstractly and then invoke approximation methods: .. plot:: :context: :nofigs: from qutip.core.environment import LorentzianEnvironment env_L = LorentzianEnvironment(T, mu_L, gamma, W) env_R = LorentzianEnvironment(T, mu_R, gamma, W) # Matsubara expansion: approx_L = env_L.approx_by_matsubara(Nk, tag="L") approx_R = env_R.approx_by_matsubara(Nk, tag="R") # Pade expansion: approx_L = env_L.approx_by_pade(Nk, tag="L") approx_R = env_R.approx_by_pade(Nk, tag="R") System and bath dynamics ------------------------ Now we are ready to construct a solver: .. plot:: :context: :nofigs: from qutip.solver.heom import HEOMSolver max_depth = 5 # maximum hierarchy depth to retain options = {"nsteps": 15_000} baths = [bath_L, bath_R] solver = HEOMSolver(H_sys, baths, max_depth=max_depth, options=options) and to calculate the system evolution as a function of time: .. code-block:: python tlist = [0, 10, 20] # times to evaluate the system state at result = solver.run(rho0, tlist) As in the bosonic case, the ``max_depth`` parameter determines how many levels of the hierarchy to retain. Also here, we can specify ``e_ops`` in order to retrieve the expectation values of operators at each given time. See :ref:`the previous section ` for a fuller description of the returned ``result`` object. .. admonition:: Environment API When using the environment API, we again have to pass the coupling operator to the HEOM solver together with the approximated environment: .. plot:: :context: :nofigs: solver = HEOMSolver(H_sys, [(approx_L, Q), (approx_R, Q)], max_depth=max_depth, options=options) Below we run the solver again, but use ``e_ops`` to store the expectation values of the population of the system states: .. plot:: :context: # Define the operators that measure the populations of the two # system states: P11p = basis(2,0) * basis(2,0).dag() P22p = basis(2,1) * basis(2,1).dag() # Run the solver: tlist = np.linspace(0, 500, 101) result = solver.run(rho0, tlist, e_ops={"11": P11p, "22": P22p}) # Plot the results: fig, axes = plt.subplots(1, 1, sharex=True, figsize=(6, 6)) axes.plot(result.times, np.real(result.e_data["11"]), 'b', linewidth=2, label="P11") axes.plot(result.times, np.real(result.e_data["22"]), 'r', linewidth=2, label="P22") axes.set_xlabel(r't', fontsize=16) axes.legend(loc=0, fontsize=16) The plot above is not very exciting. What we would really like to see in this case are the currents between the system and the two baths. We will plot these in the next section using the auxiliary density operators (ADOs) returned by the solver. .. _heom-determining-currents: Determining currents -------------------- The currents between the system and a fermionic bath may be calculated from the first level auxiliary density operators (ADOs) associated with the exponents of that bath. The contribution to the current into a given bath from each exponent in that bath is: .. math:: \text{Contribution from Exponent} = \pm i \mathrm{Tr}(Q^\pm \cdot A) where the :math:`\pm` sign depends on whether the exponent corresponds to the :math:`C^+(t)` or the :math:`C^-(t)` correlation function (see the explanation in the guide on :ref:`fermionic environments guide`) and :math:`Q^\pm` is :math:`Q` for ``+`` exponents and :math:`Q^{\dagger}` for ``-`` exponents. The first-level exponents for the left bath are retrieved by calling ``.filter(tags=["L"])`` on ``ado_state`` which is an instance of :class:`~qutip.solver.heom.HierarchyADOsState` and also provides access to the methods of :class:`~qutip.solver.heom.HierarchyADOs` which describes the structure of the hierarchy for a given problem. Here the tag "L" matches the tag passed when constructing ``bath_L`` earlier in this example. Similarly, we may calculate the current to the right bath from the exponents tagged with "R". .. plot:: :context: :nofigs: def exp_current(aux, exp): """ Calculate the current for a single exponent. """ sign = 1 if exp.type == exp.types["+"] else -1 op = exp.Q if exp.type == exp.types["+"] else exp.Q.dag() return 1j * sign * (op * aux).tr() def heom_current(tag, ado_state): """ Calculate the current between the system and the given bath. """ level_1_ados = [ (ado_state.extract(label), ado_state.exps(label)[0]) for label in ado_state.filter(tags=[tag]) ] return np.real(sum(exp_current(aux, exp) for aux, exp in level_1_ados)) heom_left_current = lambda t, ado_state: heom_current("L", ado_state) heom_right_current = lambda t, ado_state: heom_current("R", ado_state) Once we have defined functions for retrieving the currents for the baths, we can pass them to ``e_ops`` and plot the results: .. plot:: :context: close-figs # Run the solver (returning ADO states): tlist = np.linspace(0, 100, 201) result = solver.run(rho0, tlist, e_ops={ "left_currents": heom_left_current, "right_currents": heom_right_current, }) # Plot the results: fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8)) axes.plot( result.times, result.e_data["left_currents"], 'b', linewidth=2, label=r"Bath L", ) axes.plot( result.times, result.e_data["right_currents"], 'r', linewidth=2, label="Bath R", ) axes.set_xlabel(r't', fontsize=16) axes.set_ylabel(r'Current', fontsize=16) axes.set_title(r'System to Bath Currents', fontsize=16) axes.legend(loc=0, fontsize=16) And now we have a more interesting plot that shows the currents to the left and right baths decaying towards their steady states! In the next section, we will calculate the steady state currents directly. Steady state currents --------------------- Using the same solver, we can also determine the steady state of the combined system and bath using: .. plot:: :context: :nofigs: steady_state, steady_ados = solver.steady_state() and calculate the steady state currents to the two baths from ``steady_ados`` using the same ``heom_current`` function we defined previously: .. plot:: :context: :nofigs: steady_state_current_left = heom_current("L", steady_ados) steady_state_current_right = heom_current("R", steady_ados) Now we can add the steady state currents to the previous plot: .. plot:: :context: close-figs # Plot the results and steady state currents: fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8)) axes.plot( result.times, result.e_data["left_currents"], 'b', linewidth=2, label=r"Bath L", ) axes.plot( result.times, [steady_state_current_left] * len(result.times), 'b:', linewidth=2, label=r"Bath L (steady state)", ) axes.plot( result.times, result.e_data["right_currents"], 'r', linewidth=2, label="Bath R", ) axes.plot( result.times, [steady_state_current_right] * len(result.times), 'r:', linewidth=2, label=r"Bath R (steady state)", ) axes.set_xlabel(r't', fontsize=28) axes.set_ylabel(r'Current', fontsize=20) axes.set_title(r'System to Bath Currents (with steady states)', fontsize=20) axes.legend(loc=0, fontsize=12) As you can see, there is still some way to go beyond ``t = 100`` before the steady state is reached! .. _heom-fermionic-pade-expansion-coefficients: PadĂŠ expansion coefficients --------------------------- As in the bosonic case, we can also use manually calculated correlation function coefficients of fermionic environments with the HEOM solver. In the section on fermionic environments, we :ref:`defined ` their correlation functions and :ref:`calculated ` the Matsubara and Pade expansions for Lorentzian environments. For the Lorentzian bath, the PadĂŠ expansion converges much more quickly, so we will calculate the PadĂŠ expansion coefficients here. In Python code, the calculation can be done as follows: .. plot:: :context: :nofigs: # Imports from numpy.linalg import eigvalsh # Convenience functions and parameters: def deltafun(j, k): """ Kronecker delta function. """ return 1.0 if j == k else 0. def f_approx(x, Nk): """ PadĂŠ approxmation to Fermi distribution. """ f = 0.5 for ll in range(1, Nk + 1): # kappa and epsilon are calculated further down f = f - 2 * kappa[ll] * x / (x**2 + epsilon[ll]**2) return f def kappa_epsilon(Nk): """ Calculate kappa and epsilon coefficients. """ alpha = np.zeros((2 * Nk, 2 * Nk)) for j in range(2 * Nk): for k in range(2 * Nk): alpha[j][k] = ( (deltafun(j, k + 1) + deltafun(j, k - 1)) / np.sqrt((2 * (j + 1) - 1) * (2 * (k + 1) - 1)) ) eps = [-2. / val for val in eigvalsh(alpha)[:Nk]] alpha_p = np.zeros((2 * Nk - 1, 2 * Nk - 1)) for j in range(2 * Nk - 1): for k in range(2 * Nk - 1): alpha_p[j][k] = ( (deltafun(j, k + 1) + deltafun(j, k - 1)) / np.sqrt((2 * (j + 1) + 1) * (2 * (k + 1) + 1)) ) chi = [-2. / val for val in eigvalsh(alpha_p)[:Nk - 1]] eta_list = [ 0.5 * Nk * (2 * (Nk + 1) - 1) * ( np.prod([chi[k]**2 - eps[j]**2 for k in range(Nk - 1)]) / np.prod([ eps[k]**2 - eps[j]**2 + deltafun(j, k) for k in range(Nk) ]) ) for j in range(Nk) ] kappa = [0] + eta_list epsilon = [0] + eps return kappa, epsilon kappa, epsilon = kappa_epsilon(Nk) # Phew, we made it to function that calculates the coefficients for the # correlation function expansions: def C(sigma, mu, Nk): r""" Calculate the expansion coefficients for C_\sigma. """ beta = 1. / T ck = [0.5 * gamma * W * f_approx(1.0j * beta * W, Nk)] vk = [W - sigma * 1.0j * mu] for ll in range(1, Nk + 1): ck.append( -1.0j * (kappa[ll] / beta) * gamma * W**2 / (-(epsilon[ll]**2 / beta**2) + W**2) ) vk.append(epsilon[ll] / beta - sigma * 1.0j * mu) return ck, vk ck_plus_L, vk_plus_L = C(1.0, mu_L, Nk) # C_+, left bath ck_minus_L, vk_minus_L = C(-1.0, mu_L, Nk) # C_-, left bath ck_plus_R, vk_plus_R = C(1.0, mu_R, Nk) # C_+, right bath ck_minus_R, vk_minus_R = C(-1.0, mu_R, Nk) # C_-, right bath Finally we are ready to construct the :class:`~qutip.solver.heom.FermionicBath`: .. plot:: :context: :nofigs: from qutip.solver.heom import FermionicBath # PadĂŠ expansion: bath_L = FermionicBath(Q, ck_plus_L, vk_plus_L, ck_minus_L, vk_minus_L) bath_R = FermionicBath(Q, ck_plus_R, vk_plus_R, ck_minus_R, vk_minus_R) And we're done! The :class:`~qutip.solver.heom.FermionicBath` can be used with the :class:`~qutip.solver.heom.HEOMSolver` in exactly the same way as the baths we constructed previously using the built-in Lorentzian bath expansions. .. admonition:: Environment API The analogue of the ``FermionicBath`` is the ``ExponentialFermionicEnvironment``. Its usage is very similar: .. code-block:: python from qutip.core.environment import ExponentialFermionicEnvironment env_L = ExponentialFermionicEnvironment(ck_plus_L, vk_plus_L, ck_minus_L, vk_minus_L) env_R = ExponentialFermionicEnvironment(ck_plus_R, vk_plus_R, ck_minus_R, vk_minus_R) .. plot:: :context: reset :include-source: false :nofigs: # reset the context at the end qutip-5.1.1/doc/guide/heom/figures/000077500000000000000000000000001474175217300171315ustar00rootroot00000000000000qutip-5.1.1/doc/guide/heom/figures/docsfig1.png000066400000000000000000000553421474175217300213470ustar00rootroot00000000000000‰PNG  IHDRţ/z,ŸsBIT|dˆ pHYs  ŇÝ~ü8tEXtSoftwarematplotlib version3.2.2, http://matplotlib.org/–Œ‰ IDATxœěÝy\Tĺâ?đĎ ű"Ą€)–‚h(&šNVŚŠĄŠŠii–Űu)QűŠŮj7ëŢîľŇÜ*őŤŚš¤Y^و4ŃPË­4ŠÜ55EQÜežßO3€00Ë™ĺ Ÿ÷ë5ŻsšsÎsžAîĎyB€ˆˆˆH!ZgW€ˆˆˆÜ Ă)Šá‚ˆˆˆĹpADDDŠb¸ """E1\‘˘<]wŠˆˆgWƒˆˆČaN:…œœœ ď3\($""ŠŠŠÎŽ‘ĂčtşJßçc"""RĂ)Šá‚ˆˆˆĹpADDDŠb‡N""Rľ˘˘"œ={ÎŽŠŰńđđ@pp0BCCĄŐšßÁpADDŞvöěYÔŞU 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Phys. Soc. Jpn.}, year = {1989}, volume = {58}, number = {1}, pages = {101--114}, date = {1989-01}, doi = {10.1143/jpsj.58.101}, file = {:Tanimura_1989 - Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath.101.pdf:PDF}, journaltitle = {JPSJ}, owner = {wertnik}, publisher = {Physical Society of Japan}, timestamp = {2017-03-15}, } qutip-5.1.1/doc/guide/heom/history.rst000066400000000000000000000044651474175217300177310ustar00rootroot00000000000000######################## Previous implementations ######################## The current HEOM implementation in QuTiP is the latest in a succession of HEOM implementations by various contributors: HSolverDL --------- The original HEOM solver was implemented by Neill Lambert, Anubhav Vardhan, and Alexander Pitchford. In QuTiP 4.7 it was still available as ``qutip.solve.nonmarkov.dlheom_solver.HSolverDL`` but the legacy implementation was removed in QuTiP 5. It only directly provided support for the Drude-Lorentz bath although there was the possibility of sub-classing the solver to implement other baths. A compatible interface using the current implementation is still available under the same name in :class:`qutip.solver.heom.HSolverDL`. BoFiN-HEOM ---------- BoFiN-HEOM (the bosonic and fermionic HEOM solver) was a much more flexible re-write of the original QuTiP ``HSolverDL`` that added support for both bosonic and fermionic baths and for baths to be specified directly via their correlation function expansion coefficients. Its authors were Neill Lambert, Tarun Raheja, Shahnawaz Ahmed, and Alexander Pitchford. BoFiN was written outside of QuTiP and is can still be found in its original repository at https://github.com/tehruhn/bofin. The construction of the right-hand side matrix for BoFiN was slow, so BoFiN-fast, a hybrid C++ and Python implementation, was written that performed the right-hand side construction in C++. It was otherwise identical to the pure Python version. BoFiN-fast can be found at https://github.com/tehruhn/bofin_fast. BoFiN also came with an extensive set of example notebooks that are available at https://github.com/tehruhn/bofin/tree/main/examples. Current implementation ---------------------- The current implementation is a rewrite of BoFiN in pure Python. It's right-hand side construction has similar speed to BoFiN-fast, but is written in pure Python. Built-in implementations of a variety of different baths are provided, and a single solver is used for both fermionic and bosonic baths. Multiple baths of either the same kind, or a mixture of fermionic and bosonic baths, may be specified in a single problem, and there is good support for working with the auxiliary density operator (ADO) state and extracting information from it. The code was written by Neill Lambert and Simon Cross. qutip-5.1.1/doc/guide/heom/intro.rst000066400000000000000000000031471474175217300173570ustar00rootroot00000000000000############ Introduction ############ The Hierarchical Equations of Motion (HEOM) method was originally developed by Tanimura and Kubo :cite:`Tanimura_1989` in the context of physical chemistry to ''exactly'' solve a quantum system in contact with a bosonic environment, encapsulated in the Hamiltonian: .. math:: H = H_s + \sum_k \omega_k a_k^{\dagger}a_k + \hat{Q} \sum_k g_k \left(a_k + a_k^{\dagger}\right). As in other solutions to this problem, the properties of the bath are encapsulated by its temperature and its spectral density, .. math:: J(\omega) = \pi \sum_k g_k^2 \delta(\omega-\omega_k). In the HEOM, for bosonic baths, one typically chooses a Drude-Lorentz spectral density: .. math:: J_D = \frac{2\lambda \gamma \omega}{\gamma^2 + \omega^2}, or an under-damped Brownian motion spectral density: .. math:: J_U = \frac{\lambda^2 \Gamma \omega}{(\omega_c^2 - \omega^2)^2 + \Gamma^2 \omega^2}. Given the spectral density, the HEOM requires a decomposition of the bath correlation functions in terms of exponentials. Generally, such decompositions can be generated using the methods available in the :ref:`environment module `. We will go into some more detail in :doc:`bosonic`, describe how this is done with code examples, and how these expansions are passed to the solver. In addition to support for bosonic environments, QuTiP also provides support for fermionic environments which is described in :doc:`fermionic`. Both bosonic and fermionic environments are supported via a single solver, :class:`.HEOMSolver`, that supports solving for both dynamics and steady-states. qutip-5.1.1/doc/guide/heom/references.rst000066400000000000000000000000741474175217300203410ustar00rootroot00000000000000References ========== .. bibliography:: heom.bib :all: qutip-5.1.1/doc/guide/quide-basics-qobj-box.png000066400000000000000000002244741474175217300213500ustar00rootroot00000000000000‰PNG  IHDRž"/iCCPICC Profilexc``2ptqre``ČÍ+) rwRˆˆŒR`żŔŔÁŔÍ Ě`Ě`˜\\ŕŕĂyůyŠ |ťĆŔšŹ 2 UŽ +š ¨¨ęĽ¤'300ŮŮĺ%@qĆ9@śHR6˜˝Ä. rОůŇ!ě+ v„ýÄ.z¨ć H}:˜ÍÄb'AŘ2 vIjČ^çü‚ʢĚôŒ#ǔü¤T…ŕĘâ’ÔÜbĎźäü˘‚ü˘Ä’Ô Zˆű@ş! 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OQqcĹΤyuźw°ű&›ąo˛ÖźăZŰšc›ÍXźÚşŚĎÇK'a ËTź›ŠFXł čŽéDXďNĆv4X“‡ů‘äşŃŻ ÷HN )sÄňáč éWš4e="=šÜÇtZ ´xzhČÓÓßŘróŤTg„AĚL6nÄ'|ˇlˇm۶⥇}4łXƚ ďođšF7ňd łqGŐ\šňŤýćewőŮIȏ8x˜gx§Ř뒜“Çpú‘eÔ벚ĺ¨íĄŐ@ŤgD­yFÔřlń;ŽXRă}xĆŁŻoíܚ˜lŮbۡoˇţţ~ÝÚK'BcqÔ°iPkyíŘťˆrˆî4ÜÁĐ'Äł€Đfç™IÉ_+LĚ?>x@Ląâ X3fÁ^ĆáHŠşĽňTh{h5ĐjŕÓ@ë@ž1U>›‚Ü™„!fÉt&Öۋ×Ńďا˛Ózzzô  @әˆW6ß zÓ(—yĘ/óO”Ţz҄cŠx4šî$JG1źŢ¤ń=œz}YVZ ´xć5Đ:g^§ĎşDî›Đř–O˜ďŢ˝[Ž„1 _ŽHşNÎ$řG3âAˇťQŻë&żf%˜0°ÜQŇŽq wZw eş]Ĺ'l–Ă\Z ´ ´dlôzŔ¤vr&œpi‹Žd׎]r&ąÔEŁ^ţXq7ÖÍye¤;]ý},!Ői(7ČhňĺpüľžŮ ě_šeyjmh5Đj` 5Đ:1TîÝə°N\ęâňg%ŒéLčdh¨šgRlŇËđsŸaÔgHJ>ú\ dŽNSÖÁ'Wuůu|]ë܆V­Ć^­{Ô%đ› 1;á …Î…0črfÂ%OOäîˆmh5ĐjŕŮÖ@ë@žm?GËÓçoá@čH™ľI8“NN€Íu‡Ły‡Ď$') plt.show() qutip-5.1.1/doc/guide/scripts/correlation_ex2.py000066400000000000000000000006471474175217300217040ustar00rootroot00000000000000import numpy as np import matplotlib.pyplot as plt import qutip times = np.linspace(0, 10.0, 200) a = qutip.destroy(10) x = a.dag() + a H = a.dag() * a alpha = 2.5 rho0 = qutip.coherent_dm(10, alpha) corr = qutip.correlation_2op_2t(H, rho0, times, times, [np.sqrt(0.25) * a], x, x) plt.pcolor(np.real(corr)) plt.xlabel(r'Time $t_2$') plt.ylabel(r'Time $t_1$') plt.title(r'Correlation $\left$') plt.show() qutip-5.1.1/doc/guide/scripts/correlation_ex3.py000066400000000000000000000017241474175217300217020ustar00rootroot00000000000000import numpy as np import matplotlib.pyplot as plt import qutip N = 15 taus = np.linspace(0,10.0,200) a = qutip.destroy(N) H = 2 * np.pi * a.dag() * a # collapse operator G1 = 0.75 n_th = 2.00 # bath temperature in terms of excitation number c_ops = [np.sqrt(G1 * (1 + n_th)) * a, np.sqrt(G1 * n_th) * a.dag()] # start with a coherent state rho0 = qutip.coherent_dm(N, 2.0) # first calculate the occupation number as a function of time n = qutip.mesolve(H, rho0, taus, c_ops, e_ops=[a.dag() * a]).expect[0] # calculate the correlation function G1 and normalize with n to obtain g1 G1 = qutip.correlation_2op_1t(H, rho0, taus, c_ops, a.dag(), a) g1 = np.array(G1) / np.sqrt(n[0] * np.array(n)) plt.plot(taus, np.real(g1), 'b', lw=2) plt.plot(taus, n, 'r', lw=2) plt.title('Decay of a coherent state to an incoherent (thermal) state') plt.xlabel(r'$\tau$') plt.legend([ r'First-order coherence function $g^{(1)}(\tau)$', r'Occupation number $n(\tau)$', ]) plt.show() qutip-5.1.1/doc/guide/scripts/correlation_ex4.py000066400000000000000000000021161474175217300216770ustar00rootroot00000000000000import numpy as np import matplotlib.pyplot as plt import qutip N = 25 taus = np.linspace(0, 25.0, 200) a = qutip.destroy(N) H = 2 * np.pi * a.dag() * a kappa = 0.25 n_th = 2.0 # bath temperature in terms of excitation number c_ops = [np.sqrt(kappa * (1 + n_th)) * a, np.sqrt(kappa * n_th) * a.dag()] states = [ {'state': qutip.coherent_dm(N, np.sqrt(2)), 'label': "coherent state"}, {'state': qutip.thermal_dm(N, 2), 'label': "thermal state"}, {'state': qutip.fock_dm(N, 2), 'label': "Fock state"}, ] fig, ax = plt.subplots(1, 1) for state in states: rho0 = state['state'] # first calculate the occupation number as a function of time n = qutip.mesolve(H, rho0, taus, c_ops, e_ops=[a.dag() * a]).expect[0] # calculate the correlation function G2 and normalize with n(0)n(t) to # obtain g2 G2 = qutip.correlation_3op_1t(H, rho0, taus, c_ops, a.dag(), a.dag()*a, a) g2 = np.array(G2) / (n[0] * np.array(n)) ax.plot(taus, np.real(g2), label=state['label'], lw=2) ax.legend(loc=0) ax.set_xlabel(r'$\tau$') ax.set_ylabel(r'$g^{(2)}(\tau)$') plt.show() qutip-5.1.1/doc/guide/scripts/ex_bloch_animation.py000066400000000000000000000023631474175217300224240ustar00rootroot00000000000000import numpy as np import qutip def qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist): # operators and the hamiltonian sx = qutip.sigmax() sy = qutip.sigmay() sz = qutip.sigmaz() sm = qutip.sigmam() H = w * (np.cos(theta) * sz + np.sin(theta) * sx) # collapse operators c_op_list = [] n_th = 0.5 # temperature rate = gamma1 * (n_th + 1) if rate > 0.0: c_op_list.append(np.sqrt(rate) * sm) rate = gamma1 * n_th if rate > 0.0: c_op_list.append(np.sqrt(rate) * sm.dag()) rate = gamma2 if rate > 0.0: c_op_list.append(np.sqrt(rate) * sz) # evolve and calculate expectation values output = qutip.mesolve(H, psi0, tlist, c_op_list, [sx, sy, sz]) return output.expect[0], output.expect[1], output.expect[2] ## calculate the dynamics w = 1.0 * 2 * np.pi # qubit angular frequency theta = 0.2 * np.pi # qubit angle from sigma_z axis (toward sigma_x axis) gamma1 = 0.5 # qubit relaxation rate gamma2 = 0.2 # qubit dephasing rate # initial state a = 1.0 psi0 = (a*qutip.basis(2, 0) + (1-a)*qutip.basis(2, 1))/np.sqrt(a**2 + (1-a)**2) tlist = np.linspace(0, 4, 250) #expectation values for ploting sx, sy, sz = qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist) qutip-5.1.1/doc/guide/scripts/ex_steady.py000066400000000000000000000026111474175217300205630ustar00rootroot00000000000000import numpy as np import matplotlib.pyplot as plt import qutip # Define paramters N = 20 # number of basis states to consider a = qutip.destroy(N) H = a.dag() * a psi0 = qutip.basis(N, 10) # initial state kappa = 0.1 # coupling to oscillator # collapse operators c_op_list = [] n_th_a = 2 # temperature with average of 2 excitations rate = kappa * (1 + n_th_a) if rate > 0.0: c_op_list.append(np.sqrt(rate) * a) # decay operators rate = kappa * n_th_a if rate > 0.0: c_op_list.append(np.sqrt(rate) * a.dag()) # excitation operators # find steady-state solution final_state = qutip.steadystate(H, c_op_list) # find expectation value for particle number in steady state fexpt = qutip.expect(a.dag() * a, final_state) tlist = np.linspace(0, 50, 100) # monte-carlo mcdata = qutip.mcsolve(H, psi0, tlist, c_op_list, e_ops=[a.dag() * a], ntraj=100) # master eq. medata = qutip.mesolve(H, psi0, tlist, c_op_list, e_ops=[a.dag() * a]) plt.plot(tlist, mcdata.expect[0], tlist, medata.expect[0], lw=2) # plot steady-state expt. value as horizontal line (should be = 2) plt.axhline(y=fexpt, color='r', lw=1.5) plt.ylim([0, 10]) plt.xlabel('Time', fontsize=14) plt.ylabel('Number of excitations', fontsize=14) plt.legend(('Monte-Carlo', 'Master Equation', 'Steady State')) plt.title( r'Decay of Fock state $\left|10\rangle\right.$' r' in a thermal environment with $\langle n\rangle=2$' ) plt.show() qutip-5.1.1/doc/guide/scripts/floquet_ex1.py000066400000000000000000000024501474175217300210330ustar00rootroot00000000000000import numpy as np from matplotlib import pyplot import qutip delta = 0.2 * 2*np.pi eps0 = 1.0 * 2*np.pi A = 0.5 * 2*np.pi omega = 1.0 * 2*np.pi T = (2*np.pi)/omega tlist = np.linspace(0.0, 10 * T, 101) psi0 = qutip.basis(2, 0) H0 = - delta/2.0 * qutip.sigmax() - eps0/2.0 * qutip.sigmaz() H1 = A/2.0 * qutip.sigmaz() args = {'w': omega} H = [H0, [H1, lambda t, w: np.sin(w * t)]] # Create the floquet system for the time-dependent hamiltonian floquetbasis = qutip.FloquetBasis(H, T, args) # decompose the inital state in the floquet modes f_coeff = floquetbasis.to_floquet_basis(psi0) # calculate the wavefunctions using the from the floquet modes coefficients p_ex = np.zeros(len(tlist)) for n, t in enumerate(tlist): psi_t = floquetbasis.from_floquet_basis(f_coeff, t) p_ex[n] = qutip.expect(qutip.num(2), psi_t) # For reference: calculate the same thing with mesolve p_ex_ref = qutip.mesolve(H, psi0, tlist, e_ops=[qutip.num(2)], args=args).expect[0] # plot the results pyplot.plot(tlist, np.real(p_ex), 'ro', tlist, 1-np.real(p_ex), 'bo') pyplot.plot(tlist, np.real(p_ex_ref), 'r', tlist, 1-np.real(p_ex_ref), 'b') pyplot.xlabel('Time') pyplot.ylabel('Occupation probability') pyplot.legend(("Floquet $P_1$", "Floquet $P_0$", "Lindblad $P_1$", "Lindblad $P_0$")) pyplot.show() qutip-5.1.1/doc/guide/scripts/floquet_ex2.py000066400000000000000000000024671474175217300210440ustar00rootroot00000000000000import numpy as np from matplotlib import pyplot import qutip delta = 0.0 * 2*np.pi eps0 = 1.0 * 2*np.pi A = 0.25 * 2*np.pi omega = 1.0 * 2*np.pi T = 2*np.pi / omega tlist = np.linspace(0.0, 10 * T, 101) psi0 = qutip.basis(2,0) H0 = - delta/2.0 * qutip.sigmax() - eps0/2.0 * qutip.sigmaz() H1 = A/2.0 * qutip.sigmax() args = {'w': omega} H = [H0, [H1, lambda t, w: np.sin(w * t)]] # find the floquet modes for the time-dependent hamiltonian floquetbasis = qutip.FloquetBasis(H, T, args, precompute=tlist) # decompose the inital state in the floquet modes f_coeff = floquetbasis.to_floquet_basis(psi0) # calculate the wavefunctions using the from the floquet modes coefficients p_ex = np.zeros(len(tlist)) for n, t in enumerate(tlist): psi_t = floquetbasis.from_floquet_basis(f_coeff, t) p_ex[n] = qutip.expect(qutip.num(2), psi_t) # For reference: calculate the same thing with mesolve p_ex_ref = qutip.mesolve(H, psi0, tlist, e_ops=[qutip.num(2)], args=args).expect[0] # plot the results pyplot.plot(tlist, np.real(p_ex), 'ro', tlist, 1-np.real(p_ex), 'bo') pyplot.plot(tlist, np.real(p_ex_ref), 'r', tlist, 1-np.real(p_ex_ref), 'b') pyplot.xlabel('Time') pyplot.ylabel('Occupation probability') pyplot.legend(("Floquet $P_1$", "Floquet $P_0$", "Lindblad $P_1$", "Lindblad $P_0$")) pyplot.show() qutip-5.1.1/doc/guide/scripts/floquet_ex3.py000066400000000000000000000031001474175217300210260ustar00rootroot00000000000000import numpy as np from matplotlib import pyplot import qutip delta = 0.0 * 2*np.pi eps0 = 1.0 * 2*np.pi A = 0.25 * 2*np.pi omega = 1.0 * 2*np.pi T = 2*np.pi / omega tlist = np.linspace(0.0, 20 * T, 301) psi0 = qutip.basis(2,0) H0 = - delta/2.0 * qutip.sigmax() - eps0/2.0 * qutip.sigmaz() H1 = A/2.0 * qutip.sigmax() args = {'w': omega} H = [H0, [H1, lambda t, w: np.sin(w * t)]] # noise power spectrum gamma1 = 0.1 def noise_spectrum(omega): return (omega>0) * 0.5 * gamma1 * omega/(2*np.pi) # solve the floquet-markov master equation output = qutip.fmmesolve( H, psi0, tlist, [qutip.sigmax()], spectra_cb=[noise_spectrum], T=T, args=args, options={"store_floquet_states": True} ) # calculate expectation values in the computational basis p_ex = np.zeros(tlist.shape, dtype=np.complex128) for idx, t in enumerate(tlist): f_coeff_t = output.floquet_states[idx] psi_t = output.floquet_basis.from_floquet_basis(f_coeff_t, t) # Alternatively psi_t = output.states[idx] p_ex[idx] = qutip.expect(qutip.num(2), psi_t) # For reference: calculate the same thing with mesolve output = qutip.mesolve( H, psi0, tlist, [np.sqrt(gamma1) * qutip.sigmax()], e_ops=[qutip.num(2)], args=args ) p_ex_ref = output.expect[0] # plot the results pyplot.plot(tlist, np.real(p_ex), 'r--', tlist, 1-np.real(p_ex), 'b--') pyplot.plot(tlist, np.real(p_ex_ref), 'r', tlist, 1-np.real(p_ex_ref), 'b') pyplot.xlabel('Time') pyplot.ylabel('Occupation probability') pyplot.legend(("Floquet $P_1$", "Floquet $P_0$", "Lindblad $P_1$", "Lindblad $P_0$")) pyplot.show() qutip-5.1.1/doc/guide/scripts/spectrum_ex1.py000066400000000000000000000033371474175217300212230ustar00rootroot00000000000000import numpy as np from matplotlib import pyplot import qutip N = 4 # number of cavity fock states wc = wa = 1.0 * 2 * np.pi # cavity and atom frequency g = 0.1 * 2 * np.pi # coupling strength kappa = 0.75 # cavity dissipation rate gamma = 0.25 # atom dissipation rate # Jaynes-Cummings Hamiltonian a = qutip.tensor(qutip.destroy(N), qutip.qeye(2)) sm = qutip.tensor(qutip.qeye(N), qutip.destroy(2)) H = wc*a.dag()*a + wa*sm.dag()*sm + g*(a.dag()*sm + a*sm.dag()) # collapse operators n_th = 0.25 c_ops = [ np.sqrt(kappa * (1 + n_th)) * a, np.sqrt(kappa * n_th) * a.dag(), np.sqrt(gamma) * sm, ] # calculate the correlation function using the mesolve solver, and then fft to # obtain the spectrum. Here we need to make sure to evaluate the correlation # function for a sufficient long time and sufficiently high sampling rate so # that the discrete Fourier transform (FFT) captures all the features in the # resulting spectrum. tlist = np.linspace(0, 100, 5000) corr = qutip.correlation_2op_1t(H, None, tlist, c_ops, a.dag(), a) wlist1, spec1 = qutip.spectrum_correlation_fft(tlist, corr) # calculate the power spectrum using spectrum, which internally uses essolve # to solve for the dynamics (by default) wlist2 = np.linspace(0.25, 1.75, 200) * 2 * np.pi spec2 = qutip.spectrum(H, wlist2, c_ops, a.dag(), a) # plot the spectra fig, ax = pyplot.subplots(1, 1) ax.plot(wlist1 / (2 * np.pi), spec1, 'b', lw=2, label='eseries method') ax.plot(wlist2 / (2 * np.pi), spec2, 'r--', lw=2, label='me+fft method') ax.legend() ax.set_xlabel('Frequency') ax.set_ylabel('Power spectrum') ax.set_title('Vacuum Rabi splitting') ax.set_xlim(wlist2[0]/(2*np.pi), wlist2[-1]/(2*np.pi)) plt.show() qutip-5.1.1/doc/index.rst000066400000000000000000000013121474175217300152760ustar00rootroot00000000000000.. figure:: figures/logo.png :align: center :width: 7in QuTiP: Quantum Toolbox in Python ================================ This documentation contains a user guide and automatically generated API documentation for QuTiP. For more information see the `QuTiP project web page `_. Here, you can also find a collection of `tutorials for QuTiP `_. .. toctree:: :maxdepth: 3 frontmatter.rst installation.rst guide/guide.rst apidoc/apidoc.rst changelog.rst contributors.rst development/development.rst biblio.rst copyright.rst Indices and tables ==================== * :ref:`genindex` * :ref:`modindex` * :ref:`search` qutip-5.1.1/doc/installation.rst000066400000000000000000000317101474175217300166750ustar00rootroot00000000000000.. This file can be edited using retext 6.1 https://github.com/retext-project/retext .. _install: ************** Installation ************** .. _quick-start: Quick Start =========== From QuTiP version 4.6 onwards, you should be able to get a working version of QuTiP with the standard .. code-block:: bash pip install qutip It is not recommended to install any packages directly into the system Python environment; consider using ``pip`` or ``conda`` virtual environments to keep your operating system space clean, and to have more control over Python and other package versions. You do not need to worry about the details on the rest of this page unless this command did not work, but do also read the next section for the list of optional dependencies. The rest of this page covers `installation directly from conda `_, `installation from source `_, and `additional considerations when working on Windows `_. .. _install-requires: General Requirements ===================== QuTiP depends on several open-source libraries for scientific computing in the Python programming language. The following packages are currently required: .. cssclass:: table-striped +----------------+--------------+-----------------------------------------------------+ | Package | Version | Details | +================+==============+=====================================================+ | **Python** | 3.9+ | 3.6+ for version 4.7 | +----------------+--------------+-----------------------------------------------------+ | **NumPy** | 1.22+ <2.0 | 1.16+ for version 4.7 | +----------------+--------------+-----------------------------------------------------+ | **SciPy** | 1.8+ | 1.0+ for version 4.7 | +----------------+--------------+-----------------------------------------------------+ In addition, there are several optional packages that provide additional functionality: .. cssclass:: table-striped +--------------------------+--------------+-----------------------------------------------------+ | Package | Version | Details | +==========================+==============+=====================================================+ | ``matplotlib`` | 1.2.1+ | Needed for all visualisation tasks. | +--------------------------+--------------+-----------------------------------------------------+ | ``cython`` | 0.29.20+ | Needed for compiling some time-dependent | | ``setuptools`` | | Hamiltonians. Cython needs a working C++ compiler. | | ``filelock`` | | | +--------------------------+--------------+-----------------------------------------------------+ | ``cvxpy`` | 1.0+ | Needed to calculate diamond norms. | +--------------------------+--------------+-----------------------------------------------------+ | ``pytest``, | 5.3+ | For running the test suite. | | ``pytest-rerunfailures`` | | | +--------------------------+--------------+-----------------------------------------------------+ | LaTeX | TeXLive 2009+| Needed if using LaTeX in matplotlib figures, or for | | | | nice circuit drawings in IPython. | +--------------------------+--------------+-----------------------------------------------------+ | ``loky``, ``mpi4py`` | | Extra parallel map back-ends. | +--------------------------+--------------+-----------------------------------------------------+ | ``tqdm`` | | Extra progress bars back-end. | +--------------------------+--------------+-----------------------------------------------------+ In addition, there are several additional packages that are not dependencies, but may give you a better programming experience. `IPython `_ provides an improved text-based Python interpreter that is far more full-featured that the default interpreter, and runs in a terminal. If you prefer a more graphical set-up, `Jupyter `_ provides a notebook-style interface to mix code and mathematical notes together. Alternatively, `Spyder `_ is a free integrated development environment for Python, with several nice features for debugging code. QuTiP will detect if it is being used within one of these richer environments, and various outputs will have enhanced formatting. .. _install-with-conda: Installing with conda ===================== If you already have your conda environment set up, and have the ``conda-forge`` channel available, then you can install QuTiP using: .. code-block:: bash conda install qutip This will install the minimum set of dependences, but none of the optional packages. .. _adding-conda-forge: Adding the conda-forge channel ------------------------------ To install QuTiP from conda, you will need to add the conda-forge channel. The following command adds this channel with lowest priority, so conda will still try and install all other packages normally: .. code-block:: bash conda config --append channels conda-forge If you want to change the order of your channels later, you can edit your ``.condarc`` (user home folder) file manually, but it is recommended to keep ``defaults`` as the highest priority. .. _building-conda-environment: New conda environments ---------------------- The default Anaconda environment has all the Python packages needed for running QuTiP installed already, so you will only need to add the ``conda-forge`` channel and then install the package. If you have only installed Miniconda, or you want a completely clean virtual environment to install QuTiP in, the ``conda`` package manager provides a convenient way to do this. To create a conda environment for QuTiP called ``qutip-env``: .. code-block:: bash conda create -n qutip-env python qutip This will automatically install all the necessary packages, and none of the optional packages. You activate the new environment by running .. code-block:: bash conda activate qutip-env You can also install any more optional packages you want with ``conda install``, for example ``matplotlib``, ``ipython`` or ``jupyter``. .. _install-from-source: Installing from Source ====================== Official releases of QuTiP are available from the download section on `the project's web pages `_, and the latest source code is available in `our GitHub repository `_. In general we recommend users to use the latest stable release of QuTiP, but if you are interested in helping us out with development or wish to submit bug fixes, then use the latest development version from the GitHub repository. You can install from source by using the `Python-recommended PEP 517 procedure `_, or if you want more control or to have a development version, you can use the `low-level build procedure with setuptools `_. .. _build-pep517: PEP 517 Source Builds --------------------- The easiest way to build QuTiP from source is to use a PEP-517-compatible builder such as the ``build`` package available on ``pip``. These will automatically install all build dependencies for you, and the ``pip`` installation step afterwards will install the minimum runtime dependencies. You can do this by doing (for example) .. code-block:: bash pip install build python -m build pip install /dist/qutip-.whl The first command installs the reference PEP-517 build tool, the second effects the build and the third uses ``pip`` to install the built package. You will need to replace ```` with the actual path to the QuTiP source code. The string ```` will depend on the version of QuTiP, the version of Python and your operating system. It will look something like ``4.6.0-cp39-cp39-manylinux1_x86_64``, but there should only be one ``.whl`` file in the ``dist/`` directory, which will be the correct one. .. _build-setuptools: Direct Setuptools Source Builds ------------------------------- This is the method to have the greatest amount of control over the installation, but it the most error-prone and not recommended unless you know what you are doing. You first need to have all the runtime dependencies installed. The most up-to-date requirements will be listed in ``pyproject.toml`` file, in the ``build-system.requires`` key. As of the 5.0.0 release, the build requirements can be installed with .. code-block:: bash pip install setuptools wheel packaging cython 'numpy<2.0.0' scipy or similar with ``conda`` if you prefer. You will also need to have a functional C++ compiler installed on your system. This is likely already done for you if you are on Linux or macOS, but see the `section on Windows installations `_ if that is your operating system. To install QuTiP from the source code run: .. code-block:: bash pip install . If you wish to contribute to the QuTiP project, then you will want to create your own fork of `the QuTiP git repository `_, clone this to a local folder, and install it into your Python environment using: .. code-block:: bash python setup.py develop When you do ``import qutip`` in this environment, you will then load the code from your local fork, enabling you to edit the Python files and have the changes immediately available when you restart your Python interpreter, without needing to rebuild the package. Note that if you change any Cython files, you will need to rerun the build command. You should not need to use ``sudo`` (or other superuser privileges) to install into a personal virtual environment; if it feels like you need it, there is a good chance that you are installing into the system Python environment instead. .. _install-on-windows: Installation on Windows ======================= As with other operating systems, the easiest method is to use ``pip install qutip``, or use the ``conda`` procedure described above. If you want to build from source or use runtime compilation with Cython, you will need to have a working C++ compiler. You can `download the Visual Studio IDE from Microsoft `_, which has a free Community edition containing a sufficient C++ compiler. This is the recommended compiler toolchain on Windows. When installing, be sure to select the following components: - Windows "X" SDK (where "X" stands for your version: 7/8/8.1/10) - Visual Studio C++ build tools You can then follow the `installation from source `_ section as normal. .. important:: In order to prevent issues with the ``PATH`` environment variable not containing the compiler and associated libraries, it is recommended to use the developer command prompt in the Visual Studio installation folder instead of the built-in command prompt. The Community edition of Visual Studio takes around 10GB of disk space. If this is prohibitive for you, it is also possible to install `only the build tools and necessary SDKs `_ instead, which should save about 2GB of space. .. _install-verify: Verifying the Installation ========================== QuTiP includes a collection of built-in test scripts to verify that an installation was successful. To run the suite of tests scripts you must also have the ``pytest`` testing library. After installing QuTiP, leave the installation directory and call: .. code-block:: bash pytest qutip/qutip/tests This will take between 10 and 30 minutes, depending on your computer. At the end, the testing report should report a success; it is normal for some tests to be skipped, and for some to be marked "xfail" in yellow. Skips may be tests that do not run on your operating system, or tests of optional components that you have not installed the dependencies for. If any failures or errors occur, please check that you have installed all of the required modules. See the next section on how to check the installed versions of the QuTiP dependencies. If these tests still fail, then head on over to the `QuTiP Discussion Board `_ or `the GitHub issues page `_ and post a message detailing your particular issue. .. _install-about: Checking Version Information ============================ QuTiP includes an "about" function for viewing information about QuTiP and the important dependencies installed on your system. To view this information: .. code-block:: python import qutip qutip.about() qutip-5.1.1/doc/make.bat000066400000000000000000000115361474175217300150530ustar00rootroot00000000000000@ECHO OFF REM Command file for Sphinx documentation if "%SPHINXBUILD%" == "" ( set SPHINXBUILD=sphinx-build ) set BUILDDIR=_build set TEXIFY=texify set ALLSPHINXOPTS=-d %BUILDDIR%/doctrees %SPHINXOPTS% . if NOT "%PAPER%" == "" ( set ALLSPHINXOPTS=-D latex_paper_size=%PAPER% %ALLSPHINXOPTS% ) if "%1" == "" goto help if "%1" == "help" ( :help echo.Please use `make ^` where ^ is one of echo. html to make standalone HTML files echo. dirhtml to make HTML files named index.html in directories echo. singlehtml to make a single large HTML file echo. pickle to make pickle files echo. json to make JSON files echo. htmlhelp to make HTML files and a HTML help project echo. qthelp to make HTML files and a qthelp project echo. devhelp to make HTML files and a Devhelp project echo. epub to make an epub echo. latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter echo. text to make text files echo. man to make manual pages echo. changes to make an overview over all changed/added/deprecated items echo. linkcheck to check all external links for integrity echo. doctest to run all doctests embedded in the documentation if enabled goto end ) if "%1" == "clean" ( for /d %%i in (%BUILDDIR%\*) do rmdir /q /s %%i del /q /s %BUILDDIR%\* goto end ) if "%1" == "html" ( %SPHINXBUILD% -b html %ALLSPHINXOPTS% %BUILDDIR%/html if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/html. goto end ) if "%1" == "dirhtml" ( %SPHINXBUILD% -b dirhtml %ALLSPHINXOPTS% %BUILDDIR%/dirhtml if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/dirhtml. goto end ) if "%1" == "singlehtml" ( %SPHINXBUILD% -b singlehtml %ALLSPHINXOPTS% %BUILDDIR%/singlehtml if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/singlehtml. goto end ) if "%1" == "pickle" ( %SPHINXBUILD% -b pickle %ALLSPHINXOPTS% %BUILDDIR%/pickle if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can process the pickle files. goto end ) if "%1" == "json" ( %SPHINXBUILD% -b json %ALLSPHINXOPTS% %BUILDDIR%/json if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can process the JSON files. goto end ) if "%1" == "htmlhelp" ( %SPHINXBUILD% -b htmlhelp %ALLSPHINXOPTS% %BUILDDIR%/htmlhelp if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can run HTML Help Workshop with the ^ .hhp project file in %BUILDDIR%/htmlhelp. goto end ) if "%1" == "qthelp" ( %SPHINXBUILD% -b qthelp %ALLSPHINXOPTS% %BUILDDIR%/qthelp if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can run "qcollectiongenerator" with the ^ .qhcp project file in %BUILDDIR%/qthelp, like this: echo.^> qcollectiongenerator %BUILDDIR%\qthelp\QInfer.qhcp echo.To view the help file: echo.^> assistant -collectionFile %BUILDDIR%\qthelp\QInfer.ghc goto end ) if "%1" == "devhelp" ( %SPHINXBUILD% -b devhelp %ALLSPHINXOPTS% %BUILDDIR%/devhelp if errorlevel 1 exit /b 1 echo. echo.Build finished. goto end ) if "%1" == "epub" ( %SPHINXBUILD% -b epub %ALLSPHINXOPTS% %BUILDDIR%/epub if errorlevel 1 exit /b 1 echo. echo.Build finished. The epub file is in %BUILDDIR%/epub. goto end ) if "%1" == "latex" ( %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex if errorlevel 1 exit /b 1 echo. echo.Build finished; the LaTeX files are in %BUILDDIR%/latex. goto end ) if "%1" == "latexpdf" ( %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex @echo "Running LaTeX files through texify..." cd %BUILDDIR%/latex $(TEXIFY) -b --pdf @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex." ) if "%1" == "text" ( %SPHINXBUILD% -b text %ALLSPHINXOPTS% %BUILDDIR%/text if errorlevel 1 exit /b 1 echo. echo.Build finished. The text files are in %BUILDDIR%/text. goto end ) if "%1" == "man" ( %SPHINXBUILD% -b man %ALLSPHINXOPTS% %BUILDDIR%/man if errorlevel 1 exit /b 1 echo. echo.Build finished. The manual pages are in %BUILDDIR%/man. goto end ) if "%1" == "changes" ( %SPHINXBUILD% -b changes %ALLSPHINXOPTS% %BUILDDIR%/changes if errorlevel 1 exit /b 1 echo. echo.The overview file is in %BUILDDIR%/changes. goto end ) if "%1" == "linkcheck" ( %SPHINXBUILD% -b linkcheck %ALLSPHINXOPTS% %BUILDDIR%/linkcheck if errorlevel 1 exit /b 1 echo. echo.Link check complete; look for any errors in the above output ^ or in %BUILDDIR%/linkcheck/output.txt. goto end ) if "%1" == "doctest" ( %SPHINXBUILD% -b doctest -t nomock %ALLSPHINXOPTS% %BUILDDIR%/doctest if errorlevel 1 exit /b 1 echo. echo.Testing of doctests in the sources finished, look at the ^ results in %BUILDDIR%/doctest/output.txt. goto end ) :end qutip-5.1.1/doc/requirements.txt000066400000000000000000000016501474175217300167260ustar00rootroot00000000000000alabaster==0.7.16 Babel==2.14.0 backcall==0.2.0 certifi==2024.8.30 chardet==5.2.0 cycler==0.12.1 Cython==3.0.11 decorator==5.1.1 docutils==0.20.1 filelock==3.15.4 idna==3.8 imagesize==1.4.1 ipython==8.11.0 jedi==0.18.2 Jinja2==3.1.5 kiwisolver==1.4.4 MarkupSafe==2.1.2 matplotlib==3.7.1 numpy==1.26.4 numpydoc==1.8.0 packaging==24.1 parso==0.8.4 pexpect==4.9.0 pickleshare==0.7.5 Pillow==10.3.0 prompt-toolkit==3.0.47 ptyprocess==0.7.0 Pygments==2.18.0 pyparsing==3.1.4 python-dateutil==2.9.0.post0 pytz==2024.1 requests==2.32.2 scipy==1.14.1 setuptools==73.0.1 six==1.16.0 snowballstemmer==2.2.0 Sphinx==7.4.7 sphinx-rtd-theme==2.0.0 sphinxcontrib-applehelp==2.0.0 sphinxcontrib-bibtex==2.6.2 sphinxcontrib-devhelp==2.0.0 sphinxcontrib-htmlhelp==2.1.0 sphinxcontrib-jquery==4.1 sphinxcontrib-jsmath==1.0.1 sphinxcontrib-qthelp==2.0.0 sphinxcontrib-serializinghtml==1.1.10 traitlets==5.14.3 urllib3==2.2.2 wcwidth==0.2.13 wheel==0.44.0 qutip-5.1.1/doc/rtd-environment.yml000066400000000000000000000021341474175217300173160ustar00rootroot00000000000000name: rtd-environment channels: - conda-forge dependencies: - alabaster==0.7.16 - Babel==2.14.0 - backcall==0.2.0 - certifi==2024.8.30 - chardet==5.2.0 - cycler==0.12.1 - Cython==3.0.11 - decorator==5.1.1 - docutils==0.20.1 - filelock==3.15.4 - idna==3.8 - imagesize==1.4.1 - ipython==8.11.0 - jedi==0.18.2 - Jinja2==3.1.4 - kiwisolver==1.4.4 - MarkupSafe==2.1.2 - matplotlib==3.7.1 - numpy==1.26.4 - numpydoc==1.8.0 - packaging==24.1 - parso==0.8.4 - pexpect==4.9.0 - pickleshare==0.7.5 - Pillow==10.3.0 - prompt-toolkit==3.0.47 - ptyprocess==0.7.0 - Pygments==2.18.0 - pyparsing==3.1.4 - python-dateutil==2.9.0 - pytz==2024.1 - requests==2.32.2 - scipy==1.14.1 - setuptools==73.0.1 - six==1.16.0 - snowballstemmer==2.2.0 - Sphinx==7.4.7 - sphinx-rtd-theme==2.0.0 - sphinxcontrib-applehelp==2.0.0 - sphinxcontrib-bibtex==2.6.2 - sphinxcontrib-devhelp==2.0.0 - sphinxcontrib-htmlhelp==2.1.0 - sphinxcontrib-jquery==4.1 - sphinxcontrib-jsmath==1.0.1 - sphinxcontrib-qthelp==2.0.0 - sphinxcontrib-serializinghtml==1.1.10 - traitlets==5.14.3 - urllib3==2.2.2 - wcwidth==0.2.13 - wheel==0.44.0 - pip - pip: - ..[full] qutip-5.1.1/doc/static/000077500000000000000000000000001474175217300147275ustar00rootroot00000000000000qutip-5.1.1/doc/static/site.css000066400000000000000000000025501474175217300164070ustar00rootroot00000000000000/* Fix for: https://github.com/readthedocs/sphinx_rtd_theme/issues/301 */ /* Fix taken from: https://github.com/readthedocs/sphinx_rtd_theme/pull/383/ */ span.eqno { margin-left: 5px; float: right; /* position the number above the equation so that :hover is activated */ z-index: 1; position: relative; } span.eqno .headerlink { display: none; visibility: hidden; } span.eqno:hover .headerlink { display: inline-block; visibility: visible; } /* Ensure each property is on it's line. https://github.com/readthedocs/sphinx_rtd_theme/issues/1301 */ .py.property { display: block !important; } /* Improve multiline signature look https://github.com/readthedocs/sphinx_rtd_theme/issues/1529 (Solution found by the hypothesis team) */ /* don't use italics for param names; looks bad with "|" for unions */ .rst-content dl .sig-param { font-style: normal; } /* Take out pointless vertical whitespace in the signatures. */ .rst-content dl .sig dl, .rst-content dl .sig dd { margin-bottom: 0; } /* Make signature boxes full-width, with view-source and header links right-aligned. */ /* Does not works on Firefox, but does in opera. */ .rst-content dl .sig { width: -webkit-fill-available; } .rst-content .viewcode-link { display: inline-flex; float: inline-end; margin-right: 1.5em; } .rst-content .headerlink { position: absolute; right: 0.5em; } qutip-5.1.1/doc/templates/000077500000000000000000000000001474175217300154365ustar00rootroot00000000000000qutip-5.1.1/doc/templates/layout.html000066400000000000000000000002201474175217300176330ustar00rootroot00000000000000{# Import the theme's layout. #} {% extends "!layout.html" %} {# Custom CSS overrides #} {% set bootswatch_css_custom = ['_static/site.css'] %}qutip-5.1.1/pyproject.toml000066400000000000000000000022151474175217300156070ustar00rootroot00000000000000[build-system] requires = [ "setuptools", "packaging", "wheel", "cython>=0.29.20; python_version>='3.10'", "cython>=0.29.20,<3.0.0; python_version<='3.9'", # See https://numpy.org/doc/stable/user/depending_on_numpy.html for # the recommended way to build against numpy's C API: "numpy>=2.0.0", "scipy>=1.9", ] build-backend = "setuptools.build_meta" [tool.cibuildwheel] manylinux-x86_64-image = "manylinux2014" manylinux-i686-image = "manylinux2014" # Change in future version to "build" build-frontend = "pip" [tool.towncrier] directory = "doc/changes" filename = "doc/changelog.rst" name = "QuTiP" package = "qutip" [[tool.towncrier.type]] directory = "deprecation" name = "Deprecations" showcontent = true [[tool.towncrier.type]] directory = "feature" name = "Features" showcontent = true [[tool.towncrier.type]] directory = "bugfix" name = "Bug Fixes" showcontent = true [[tool.towncrier.type]] directory = "removal" name = "Removals" showcontent = true [[tool.towncrier.type]] directory = "doc" name = "Documentation" showcontent = true [[tool.towncrier.type]] directory = "misc" name = "Miscellaneous" showcontent = true qutip-5.1.1/qutip/000077500000000000000000000000001474175217300140355ustar00rootroot00000000000000qutip-5.1.1/qutip/__init__.py000066400000000000000000000030231474175217300161440ustar00rootroot00000000000000import os import warnings import qutip.settings from qutip.settings import settings import qutip.version from qutip.version import version as __version__ # ----------------------------------------------------------------------------- # Look to see if we are running with OPENMP # # Set environ variable to determin if running in parallel mode # (i.e. in parfor or parallel_map) os.environ['QUTIP_IN_PARALLEL'] = 'FALSE' # ----------------------------------------------------------------------------- # Check that import modules are compatible with requested configuration # # Check for Matplotlib try: import matplotlib except ImportError: warnings.warn("matplotlib not found: Graphics will not work.") else: del matplotlib # ----------------------------------------------------------------------------- # Load modules # from .core import * from .solver import * from .solver import nonmarkov import qutip.piqs.piqs as piqs # graphics from .bloch import * from .visualization import * from .animation import * from .matplotlib_utilities import * # library functions from .tomography import * from .wigner import * from .random_objects import * from .simdiag import * from .entropy import * from .partial_transpose import * from .continuous_variables import * from .distributions import * from . import measurement # utilities from .utilities import * from .fileio import * from .about import * from .cite import * # ----------------------------------------------------------------------------- # Clean name space # del os, warnings qutip-5.1.1/qutip/_distributions.pyx000066400000000000000000000037611474175217300176470ustar00rootroot00000000000000cimport cython from cython cimport double, complex cimport numpy as np import numpy as np from libc.math cimport pi from cmath import exp as cexp, sqrt as csqrt, pi as cpi @cython.nogil @cython.cfunc @cython.locals(x_size=np.npy_intp, j=int, i=int, k=int, temp1=complex, temp2=complex) @cython.boundscheck(False) cpdef np.ndarray[np.complex128_t, ndim=1] psi_n_single_fock_multiple_position_complex(int n, np.ndarray[np.complex128_t, ndim=1] x): """ Compute the wavefunction to a complex vector x using adapted recurrence relation. Parameters ---------- n : int Quantum state number. x : np.ndarray[np.complex128_t] Position(s) at which to evaluate the wavefunction. Returns ------- np.ndarray[np.complex128_t] The evaluated wavefunction. Examples -------- ```python >>> psi_n_single_fock_multiple_position_complex(0, np.array([1.0 + 1.0j, 2.0 + 2.0j])) array([ 0.40583486-0.63205035j, -0.49096842+0.56845369j]) >>> psi_n_single_fock_multiple_position_complex(61, np.array([1.0 + 1.0j, 2.0 + 2.0j])) array([-7.56548941e+03+9.21498621e+02j, -1.64189542e+08-3.70892077e+08j]) ``` References ---------- - PĂŠrez-JordĂĄ, J. M. (2017). On the recursive solution of the quantum harmonic oscillator. *European Journal of Physics*, 39(1), 015402. doi:10.1088/1361-6404/aa9584 """ x_size = x.shape[0] cdef np.ndarray[np.complex128_t, ndim=2] result = np.zeros((n + 1, x_size), dtype=np.complex128) pi_025 = pi ** (-0.25) for j in range(x_size): result[0, j] = pi_025 * cexp(-(x[j] ** 2) / 2) for i in range(n): temp1 = csqrt(2 * (i + 1)) temp2 = csqrt(i / (i + 1)) if(i == 0): for k in range(x_size): result[i + 1, k] = 2 * x[k] * (result[i, k] / temp1) else: for k in range(x_size): result[i + 1, k] = 2 * x[k] * (result[i, k] / temp1) - temp2 * result[i - 1, k] return result[-1, :] qutip-5.1.1/qutip/_mkl/000077500000000000000000000000001474175217300147575ustar00rootroot00000000000000qutip-5.1.1/qutip/_mkl/__init__.py000066400000000000000000000000011474175217300170570ustar00rootroot00000000000000 qutip-5.1.1/qutip/_mkl/spmv.py000066400000000000000000000022541474175217300163210ustar00rootroot00000000000000import numpy as np from ctypes import POINTER, c_int, c_char, byref from numpy.ctypeslib import ndpointer import qutip.settings as qset zcsrgemv = qset.mkl_lib.mkl_cspblas_zcsrgemv def mkl_spmv(A, x): """ sparse csr_spmv using MKL """ m, _ = A.shape # Pointers to data of the matrix data = A.data.ctypes.data_as(ndpointer(np.complex128, ndim=1, flags='C')) indptr = A.indptr.ctypes.data_as(POINTER(c_int)) indices = A.indices.ctypes.data_as(POINTER(c_int)) # Allocate output, using same conventions as input if x.ndim == 1: y = np.empty(m, dtype=np.complex128, order='C') elif x.ndim == 2 and x.shape[1] == 1: y = np.empty((m, 1), dtype=np.complex128, order='C') else: raise Exception('Input vector must be 1D row or 2D column vector') # Now call MKL. This returns the answer in the last argument, which shares # memory with y. zcsrgemv( byref(c_char(bytes(b'N'))), byref(c_int(m)), data, indptr, indices, x.ctypes.data_as(ndpointer(np.complex128, ndim=1, flags='C')), y.ctypes.data_as(ndpointer(np.complex128, ndim=1, flags='C')), ) return y qutip-5.1.1/qutip/_mkl/spsolve.py000066400000000000000000000310751474175217300170320ustar00rootroot00000000000000import sys import numpy as np import scipy.sparse as sp from ctypes import c_int, byref from numpy.ctypeslib import ndpointer import time from qutip.settings import settings as qset # Load solver functions from mkl_lib pardiso = qset.mkl_lib.pardiso pardiso_delete = qset.mkl_lib.pardiso_handle_delete if sys.maxsize > 2**32: #Running 64-bit pardiso_64 = qset.mkl_lib.pardiso_64 pardiso_delete_64 = qset.mkl_lib.pardiso_handle_delete_64 def _pardiso_parameters(hermitian, has_perm, max_iter_refine, scaling_vectors, weighted_matching): iparm = np.zeros(64, dtype=np.int32) iparm[0] = 1 # Do not use default values iparm[1] = 3 # Use openmp nested dissection if has_perm: iparm[4] = 1 iparm[7] = max_iter_refine # Max number of iterative refinements if hermitian: iparm[9] = 8 else: iparm[9] = 13 if not hermitian: iparm[10] = int(scaling_vectors) iparm[12] = int(weighted_matching) # Non-symmetric weighted matching iparm[17] = -1 iparm[20] = 1 iparm[23] = 1 # Parallel factorization iparm[26] = 0 # Check matrix structure iparm[34] = 1 # Use zero-based indexing return iparm # Set error messages pardiso_error_msgs = { '-1': 'Input inconsistant', '-2': 'Out of memory', '-3': 'Reordering problem', '-4': 'Zero pivot, numerical factorization or iterative refinement problem', '-5': 'Unclassified internal error', '-6': 'Reordering failed', '-7': 'Diagonal matrix is singular', '-8': '32-bit integer overflow', '-9': 'Not enough memory for OOC', '-10': 'Error opening OOC files', '-11': 'Read/write error with OOC files', '-12': 'Pardiso-64 called from 32-bit library', } def _default_solver_args(): return { 'hermitian': False, 'posdef': False, 'max_iter_refine': 10, 'scaling_vectors': True, 'weighted_matching': True, 'return_info': False, } class mkl_lu: """ Object pointing to LU factorization of a sparse matrix generated by mkl_splu. Methods ------- solve(b, verbose=False) Solve system of equations using given RHS vector 'b'. Returns solution ndarray with same shape as input. info() Returns the statistics of the factorization and solution in the lu.info attribute. delete() Deletes the allocated solver memory. """ def __init__(self, np_pt=None, dim=None, is_complex=None, data=None, indptr=None, indices=None, iparm=None, np_iparm=None, mtype=None, perm=None, np_perm=None, factor_time=None): self._np_pt = np_pt self._dim = dim self._is_complex = is_complex self._data = data self._indptr = indptr self._indices = indices self._iparm = iparm self._np_iparm = np_iparm self._mtype = mtype self._perm = perm self._np_perm = np_perm self._factor_time = factor_time self._solve_time = None def solve(self, b, verbose=None): b_shp = b.shape if b.ndim == 2 and b.shape[1] == 1: b = b.ravel() nrhs = 1 elif b.ndim == 2 and b.shape[1] != 1: nrhs = b.shape[1] b = b.ravel(order='F') else: b = b.ravel() nrhs = 1 data_type = np.complex128 if self._is_complex else np.float64 if b.dtype != data_type: b = b.astype(np.complex128, copy=False) # Create solution array (x) and pointers to x and b x = np.zeros(b.shape, dtype=data_type, order='C') np_x = x.ctypes.data_as(ndpointer(data_type, ndim=1, flags='C')) np_b = b.ctypes.data_as(ndpointer(data_type, ndim=1, flags='C')) error = np.zeros(1, dtype=np.int32) np_error = error.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) # Call solver _solve_start = time.time() pardiso( self._np_pt, byref(c_int(1)), byref(c_int(1)), byref(c_int(self._mtype)), byref(c_int(33)), byref(c_int(self._dim)), self._data, self._indptr, self._indices, self._np_perm, byref(c_int(nrhs)), self._np_iparm, byref(c_int(0)), np_b, np_x, np_error, ) self._solve_time = time.time() - _solve_start if error[0] != 0: raise Exception(pardiso_error_msgs[str(error[0])]) if verbose: print('Solution Stage') print('--------------') print('Solution time: ', round(self._solve_time, 4)) print('Solution memory (Mb): ', round(self._iparm[16]/1024, 4)) print('Number of iterative refinements:', self._iparm[6]) print('Total memory (Mb): ', round(sum(self._iparm[15:17])/1024, 4)) print() return np.reshape(x, b_shp, order=('C' if nrhs == 1 else 'F')) def info(self): info = {'FactorTime': self._factor_time, 'SolveTime': self._solve_time, 'Factormem': round(self._iparm[15]/1024, 4), 'Solvemem': round(self._iparm[16]/1024, 4), 'IterRefine': self._iparm[6]} return info def delete(self): # Delete all data error = np.zeros(1, dtype=np.int32) np_error = error.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) pardiso( self._np_pt, byref(c_int(1)), byref(c_int(1)), byref(c_int(self._mtype)), byref(c_int(-1)), byref(c_int(self._dim)), self._data, self._indptr, self._indices, self._np_perm, byref(c_int(1)), self._np_iparm, byref(c_int(0)), byref(c_int(0)), byref(c_int(0)), np_error, ) if error[0] == -10: raise Exception('Error freeing solver memory') _MATRIX_TYPE_NAMES = { 4: 'Complex Hermitian positive-definite', -4: 'Complex Hermitian indefinite', 2: 'Real symmetric positive-definite', -2: 'Real symmetric indefinite', 11: 'Real non-symmetric', 13: 'Complex non-symmetric', } def _mkl_matrix_type(dtype, solver_args): if not solver_args['hermitian']: return 13 if dtype == np.complex128 else 11 out = 4 if dtype == np.complex128 else 2 return out if solver_args['posdef'] else -out def mkl_splu(A, perm=None, verbose=False, **kwargs): """ Returns the LU factorization of the sparse matrix A. Parameters ---------- A : csr_matrix Sparse input matrix. perm : ndarray (optional) User defined matrix factorization permutation. verbose : bool {False, True} Report factorization details. Returns ------- lu : mkl_lu Returns object containing LU factorization with a solve method for solving with a given RHS vector. """ if not sp.isspmatrix_csr(A): raise TypeError('Input matrix must be in sparse CSR format.') if A.shape[0] != A.shape[1]: raise Exception('Input matrix must be square') dim = A.shape[0] solver_args = _default_solver_args() if set(kwargs) - set(solver_args): raise ValueError( "Unknown keyword arguments pass to mkl_splu: {!r}" .format(set(kwargs) - set(solver_args)) ) solver_args.update(kwargs) # If hermitian, then take upper-triangle of matrix only if solver_args['hermitian']: B = sp.triu(A, format='csr') A = B # This gets around making a full copy of A in triu is_complex = bool(A.dtype == np.complex128) if not is_complex: A = sp.csr_matrix(A, dtype=np.float64, copy=False) data_type = A.dtype # Create pointer to internal memory pt = np.zeros(64, dtype=int) np_pt = pt.ctypes.data_as(ndpointer(int, ndim=1, flags='C')) # Create pointers to sparse matrix arrays data = A.data.ctypes.data_as(ndpointer(data_type, ndim=1, flags='C')) indptr = A.indptr.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) indices = A.indices.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) # Setup perm array if perm is None: perm = np.zeros(dim, dtype=np.int32) has_perm = 0 else: has_perm = 1 np_perm = perm.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) # setup iparm iparm = _pardiso_parameters( solver_args['hermitian'], has_perm, solver_args['max_iter_refine'], solver_args['scaling_vectors'], solver_args['weighted_matching'], ) np_iparm = iparm.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) # setup call parameters mtype = _mkl_matrix_type(data_type, solver_args) if verbose: print('Solver Initialization') print('---------------------') print('Input matrix type: ', _MATRIX_TYPE_NAMES[mtype]) print('Input matrix shape:', A.shape) print('Input matrix NNZ: ', A.nnz) print() b = np.zeros(1, dtype=data_type) # Input dummy RHS at this phase np_b = b.ctypes.data_as(ndpointer(data_type, ndim=1, flags='C')) x = np.zeros(1, dtype=data_type) # Input dummy solution at this phase np_x = x.ctypes.data_as(ndpointer(data_type, ndim=1, flags='C')) error = np.zeros(1, dtype=np.int32) np_error = error.ctypes.data_as(ndpointer(np.int32, ndim=1, flags='C')) # Call solver _factor_start = time.time() pardiso( np_pt, byref(c_int(1)), byref(c_int(1)), byref(c_int(mtype)), byref(c_int(12)), byref(c_int(dim)), data, indptr, indices, np_perm, byref(c_int(1)), np_iparm, byref(c_int(0)), np_b, np_x, np_error, ) _factor_time = time.time() - _factor_start if error[0] != 0: raise Exception(pardiso_error_msgs[str(error[0])]) if verbose: print('Analysis and Factorization Stage') print('--------------------------------') print('Factorization time: ', round(_factor_time, 4)) print('Factorization memory (Mb):', round(iparm[15]/1024, 4)) print('NNZ in LU factors: ', iparm[17]) print() return mkl_lu(np_pt, dim, is_complex, data, indptr, indices, iparm, np_iparm, mtype, perm, np_perm, _factor_time) def mkl_spsolve(A, b, perm=None, verbose=False, **kwargs): """ Solves a sparse linear system of equations using the Intel MKL Pardiso solver. Parameters ---------- A : csr_matrix Sparse matrix. b : ndarray or sparse matrix The vector or matrix representing the right hand side of the equation. If a vector, b.shape must be (n,) or (n, 1). perm : ndarray (optional) User defined matrix factorization permutation. Returns ------- x : ndarray or csr_matrix The solution of the sparse linear equation. If b is a vector, then x is a vector of size A.shape[1] If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1]) """ lu = mkl_splu(A, perm=perm, verbose=verbose, **kwargs) b_is_sparse = sp.isspmatrix(b) b_shp = b.shape if b_is_sparse and b.shape[1] == 1: b = b.toarray() b_is_sparse = False elif b_is_sparse and b.shape[1] != 1: nrhs = b.shape[1] if lu._is_complex: b = sp.csc_matrix(b, dtype=np.complex128, copy=False) else: b = sp.csc_matrix(b, dtype=np.float64, copy=False) # Do dense RHS solving if not b_is_sparse: x = lu.solve(b, verbose=verbose) # Solve each RHS vec individually and convert to sparse else: data_segs = [] row_segs = [] col_segs = [] for j in range(nrhs): bj = b[:, j].toarray().ravel() xj = lu.solve(bj) w = np.flatnonzero(xj) segment_length = w.shape[0] row_segs.append(w) col_segs.append(np.ones(segment_length, dtype=np.int32)*j) data_segs.append(np.asarray(xj[w], dtype=xj.dtype)) sp_data = np.concatenate(data_segs) sp_row = np.concatenate(row_segs) sp_col = np.concatenate(col_segs) x = sp.csr_matrix((sp_data, (sp_row, sp_col)), shape=b_shp) info = lu.info() lu.delete() return (x, info) if kwargs.get('return_info', False) else x qutip-5.1.1/qutip/about.py000066400000000000000000000061401474175217300155220ustar00rootroot00000000000000""" Command line output of information on QuTiP and dependencies. """ __all__ = ['about'] import sys import os import importlib import platform import numpy import scipy import inspect import qutip from qutip.settings import _blas_info, settings def about(): """ About box for QuTiP. Gives version numbers for QuTiP, NumPy, SciPy, Cython, and MatPlotLib and information about installed QuTiP family packages. """ print("") print("QuTiP: Quantum Toolbox in Python") print("================================") print("Copyright (c) QuTiP team 2011 and later.") print( "Current admin team: Alexander Pitchford, " "Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, Eric Giguère, " "Boxi Li, Simon Cross, Asier Galicia, Paul Menczel, " "and Patrick Hopf." ) print( "Board members: Daniel Burgarth, Robert Johansson, Anton F. Kockum, " "Franco Nori and Will Zeng." ) print("Original developers: R. J. Johansson & P. D. Nation.") print("Previous lead developers: Chris Granade & A. Grimsmo.") print("Currently developed through wide collaboration. " "See https://github.com/qutip for details.") print("") print("QuTiP Version: %s" % qutip.__version__) print("Numpy Version: %s" % numpy.__version__) print("Scipy Version: %s" % scipy.__version__) try: import Cython cython_ver = Cython.__version__ except ImportError: cython_ver = 'None' print("Cython Version: %s" % cython_ver) try: import matplotlib matplotlib_ver = matplotlib.__version__ except ImportError: matplotlib_ver = 'None' print("Matplotlib Version: %s" % matplotlib_ver) print("Python Version: %d.%d.%d" % sys.version_info[0:3]) print("Number of CPUs: %s" % settings.num_cpus) print("BLAS Info: %s" % _blas_info()) # print("OPENMP Installed: %s" % str(qutip.settings.has_openmp)) print("INTEL MKL Ext: %s" % settings.mkl_lib_location) print("Platform Info: %s (%s)" % (platform.system(), platform.machine())) qutip_install_path = os.path.dirname(inspect.getsourcefile(qutip)) print("Installation path: %s" % qutip_install_path) print() # family packages print("Installed QuTiP family packages") print("-------------------------------") print() entrypoints = importlib.metadata.entry_points(group="qutip.family") if not entrypoints: print("No QuTiP family packages installed.") for ep in entrypoints: family_mod = ep.load() try: pkg, version = family_mod.version() except Exception as exc: pkg, version = ep.name, [str(exc)] print("%s: %s" % (pkg, version)) print() # citation longbar = "=" * 80 cite_msg = "For your convenience a bibtex reference can be easily" cite_msg += " generated using `qutip.cite()`" print(longbar) print("Please cite QuTiP in your publication.") print(longbar) print(cite_msg) if __name__ == "__main__": about() qutip-5.1.1/qutip/animation.py000066400000000000000000000457551474175217300164060ustar00rootroot00000000000000""" Functions to animate results of quantum dynamics simulations, """ __all__ = ['anim_wigner_sphere', 'anim_hinton', 'anim_sphereplot', 'anim_matrix_histogram', 'anim_fock_distribution', 'anim_wigner', 'anim_spin_distribution', 'anim_qubism', 'anim_schmidt'] from . import (plot_wigner_sphere, hinton, sphereplot, matrix_histogram, plot_fock_distribution, plot_wigner, plot_spin_distribution, plot_qubism, plot_schmidt) from .solver import Result from numpy import sqrt def _result_state(obj): if isinstance(obj, Result): obj = obj.states if len(obj) == 0: raise ValueError('Nothing to visualize. You might have forgotten ' 'to set options={"store_states": True}.') return obj def anim_wigner_sphere(wigners, reflections=False, *, cmap=None, colorbar=True, fig=None, ax=None): """Animate a coloured Bloch sphere. Parameters ---------- wigners : list of transformations The wigner transformation at `steps` different theta and phi. reflections : bool, default: False If the reflections of the sphere should be plotted as well. cmap : a matplotlib colormap instance, optional Color map to use when plotting. colorbar : bool, default: True Whether (True) or not (False) a colorbar should be attached. fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The ax context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. Notes ----- Special thanks to Russell P Rundle for writing this function. """ fig, ani = plot_wigner_sphere(wigners, reflections, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_hinton(rhos, x_basis=None, y_basis=None, color_style="scaled", label_top=True, *, cmap=None, colorbar=True, fig=None, ax=None): """Draws an animation of Hinton diagram. Parameters ---------- rhos : :class:`.Result` or list of :class:`.Qobj` Input density matrix or superoperator. .. note:: Hinton plots of superoperators are currently only supported for qubits. x_basis : list of strings, optional list of x ticklabels to represent x basis of the input. y_basis : list of strings, optional list of y ticklabels to represent y basis of the input. color_style : str, {"scaled", "threshold", "phase"}, default: "scaled" Determines how colors are assigned to each square: - If set to ``"scaled"`` (default), each color is chosen by passing the absolute value of the corresponding matrix element into `cmap` with the sign of the real part. - If set to ``"threshold"``, each square is plotted as the maximum of `cmap` for the positive real part and as the minimum for the negative part of the matrix element; note that this generalizes `"threshold"` to complex numbers. - If set to ``"phase"``, each color is chosen according to the angle of the corresponding matrix element. label_top : bool, default: True If True, x ticklabels will be placed on top, otherwise they will appear below the plot. cmap : a matplotlib colormap instance, optional Color map to use when plotting. colorbar : bool, default: True Whether (True) or not (False) a colorbar should be attached. fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The ax context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. Raises ------ ValueError Input argument is not a quantum object. """ rhos = _result_state(rhos) fig, ani = hinton(rhos, x_basis, y_basis, color_style, label_top, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_sphereplot(V, theta, phi, *, cmap=None, colorbar=True, fig=None, ax=None): """animation of a matrices of values on a sphere Parameters ---------- V : list of array instances Data set to be plotted theta : float Angle with respect to z-axis. Its range is between 0 and pi phi : float Angle in x-y plane. Its range is between 0 and 2*pi cmap : a matplotlib colormap instance, optional Color map to use when plotting. colorbar : bool, default: True Whether (True) or not (False) a colorbar should be attached. fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The axes context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. """ fig, ani = sphereplot(V, theta, phi, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_matrix_histogram(Ms, x_basis=None, y_basis=None, limits=None, bar_style='real', color_limits=None, color_style='real', options=None, *, cmap=None, colorbar=True, fig=None, ax=None): """ Draw an animation of a histogram for the matrix M, with the given x and y labels. Parameters ---------- Ms : list of matrices or :class:`.Result` The matrix to visualize x_basis : list of strings, optional list of x ticklabels y_basis : list of strings, optional list of y ticklabels limits : list/array with two float numbers, optional The z-axis limits [min, max] bar_style : str, {"real", "img", "abs", "phase"}, default: "real" - If set to ``"real"`` (default), each bar is plotted as the real part of the corresponding matrix element - If set to ``"img"``, each bar is plotted as the imaginary part of the corresponding matrix element - If set to ``"abs"``, each bar is plotted as the absolute value of the corresponding matrix element - If set to ``"phase"`` (default), each bar is plotted as the angle of the corresponding matrix element color_limits : list/array with two float numbers, optional The limits of colorbar [min, max] color_style : str, {"real", "img", "abs", "phase"}, default: "real" Determines how colors are assigned to each square: - If set to ``"real"`` (default), each color is chosen according to the real part of the corresponding matrix element. - If set to ``"img"``, each color is chosen according to the imaginary part of the corresponding matrix element. - If set to ``"abs"``, each color is chosen according to the absolute value of the corresponding matrix element. - If set to ``"phase"``, each color is chosen according to the angle of the corresponding matrix element. cmap : a matplotlib colormap instance, optional Color map to use when plotting. colorbar : bool, default: True show colorbar fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The axes context in which the plot will be drawn. options : dict, optional A dictionary containing extra options for the plot. The names (keys) and values of the options are described below: 'zticks' : list of numbers, optional A list of z-axis tick locations. 'bars_spacing' : float, default: 0.1 spacing between bars. 'bars_alpha' : float, default: 1. transparency of bars, should be in range 0 - 1 'bars_lw' : float, default: 0.5 linewidth of bars' edges. 'bars_edgecolor' : color, default: 'k' The colors of the bars' edges. Examples: 'k', (0.1, 0.2, 0.5) or '#0f0f0f80'. 'shade' : bool, default: True Whether to shade the dark sides of the bars (True) or not (False). The shading is relative to plot's source of light. 'azim' : float, default: -35 The azimuthal viewing angle. 'elev' : float, default: 35 The elevation viewing angle. 'stick' : bool, default: False Changes xlim and ylim in such a way that bars next to XZ and YZ planes will stick to those planes. This option has no effect if ``ax`` is passed as a parameter. 'cbar_pad' : float, default: 0.04 The fraction of the original axes between the colorbar and the new image axes. (i.e. the padding between the 3D figure and the colorbar). 'cbar_to_z' : bool, default: False Whether to set the color of maximum and minimum z-values to the maximum and minimum colors in the colorbar (True) or not (False). 'threshold': float, optional Threshold for when bars of smaller height should be transparent. If not set, all bars are colored according to the color map. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. Raises ------ ValueError Input argument is not valid. """ Ms = _result_state(Ms) fig, ani = matrix_histogram(Ms, x_basis, y_basis, limits, bar_style, color_limits, color_style, options, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_fock_distribution(rhos, fock_numbers=None, color="green", unit_y_range=True, *, fig=None, ax=None): """ Animation of the Fock distribution for a density matrix (or ket) that describes an oscillator mode. Parameters ---------- rhos : :class:`.Result` or list of :class:`.Qobj` The density matrix (or ket) of the state to visualize. fock_numbers : list of strings, optional list of x ticklabels to represent fock numbers color : color or list of colors, default: "green" The colors of the bar faces. unit_y_range : bool, default: True Set y-axis limits [0, 1] or not fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The axes context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. """ rhos = _result_state(rhos) fig, ani = plot_fock_distribution(rhos, fock_numbers, color, unit_y_range, fig=fig, ax=ax) return fig, ani def anim_wigner(rhos, xvec=None, yvec=None, method='clenshaw', projection='2d', g=sqrt(2), sparse=False, parfor=False, *, cmap=None, colorbar=False, fig=None, ax=None): """ Animation of the Wigner function for a density matrix (or ket) that describes an oscillator mode. Parameters ---------- rhos : :class:`.Result` or list of :class:`.Qobj` The density matrix (or ket) of the state to visualize. xvec : array_like, optional x-coordinates at which to calculate the Wigner function. yvec : array_like, optional y-coordinates at which to calculate the Wigner function. Does not apply to the 'fft' method. method : str {'clenshaw', 'iterative', 'laguerre', 'fft'}, default: 'clenshaw' The method used for calculating the wigner function. See the documentation for qutip.wigner for details. projection: str {'2d', '3d'}, default: '2d' Specify whether the Wigner function is to be plotted as a contour graph ('2d') or surface plot ('3d'). g : float Scaling factor for `a = 0.5 * g * (x + iy)`, default `g = sqrt(2)`. See the documentation for qutip.wigner for details. sparse : bool {False, True} Flag for sparse format. See the documentation for qutip.wigner for details. parfor : bool {False, True} Flag for parallel calculation. See the documentation for qutip.wigner for details. cmap : a matplotlib cmap instance, optional The colormap. colorbar : bool, default: False Whether (True) or not (False) a colorbar should be attached to the Wigner function graph. fig : a matplotlib Figure instance, optional The Figure canvas in which the plot will be drawn. ax : a matplotlib axes instance, optional The axes context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. """ rhos = _result_state(rhos) fig, ani = plot_wigner(rhos, xvec, yvec, method=method, g=g, sparse=sparse, parfor=parfor, projection=projection, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_spin_distribution(Ps, THETA, PHI, projection='2d', *, cmap=None, colorbar=False, fig=None, ax=None): """ Animation of a spin distribution (given as meshgrid data). Parameters ---------- Ps : list of matrices Distribution values as a meshgrid matrix. THETA : matrix Meshgrid matrix for the theta coordinate. Its range is between 0 and pi PHI : matrix Meshgrid matrix for the phi coordinate. Its range is between 0 and 2*pi projection: str {'2d', '3d'}, default: '2d' Specify whether the spin distribution function is to be plotted as a 2D projection where the surface of the unit sphere is mapped on the unit disk ('2d') or surface plot ('3d'). cmap : a matplotlib cmap instance, optional The colormap. colorbar : bool, default: False Whether (True) or not (False) a colorbar should be attached to the Wigner function graph. fig : a matplotlib figure instance, optional The figure canvas on which the plot will be drawn. ax : a matplotlib axis instance, optional The axis context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. """ fig, ani = plot_spin_distribution(Ps, THETA, PHI, projection, cmap=cmap, colorbar=colorbar, fig=fig, ax=ax) return fig, ani def anim_qubism(kets, theme='light', how='pairs', grid_iteration=1, legend_iteration=0, *, fig=None, ax=None): """ Animation of Qubism plot for pure states of many qudits. Works best for spin chains, especially with even number of particles of the same dimension. Allows to see entanglement between first 2k particles and the rest. .. note:: colorblind_safe does not apply because of its unique colormap Parameters ---------- kets : :class:`.Result` or list of :class:`.Qobj` Pure states for animation. theme : str {'light', 'dark'}, default: 'light' Set coloring theme for mapping complex values into colors. See: complex_array_to_rgb. how : str {'pairs', 'pairs_skewed', 'before_after'}, default: 'pairs' Type of Qubism plotting. Options: - 'pairs' - typical coordinates, - 'pairs_skewed' - for ferromagnetic/antriferromagnetic plots, - 'before_after' - related to Schmidt plot (see also: plot_schmidt). grid_iteration : int, default: 1 Helper lines to be drawn on plot. Show tiles for 2*grid_iteration particles vs all others. legend_iteration : int or 'grid_iteration' or 'all', default: 0 Show labels for first ``2*legend_iteration`` particles. Option 'grid_iteration' sets the same number of particles as for grid_iteration. Option 'all' makes label for all particles. Typically it should be 0, 1, 2 or perhaps 3. fig : a matplotlib figure instance, optional The figure canvas on which the plot will be drawn. ax : a matplotlib axis instance, optional The axis context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. Notes ----- See also [1]_. References ---------- .. [1] J. Rodriguez-Laguna, P. Migdal, M. Ibanez Berganza, M. Lewenstein and G. Sierra, *Qubism: self-similar visualization of many-body wavefunctions*, `New J. Phys. 14 053028 `_, arXiv:1112.3560 (2012), open access. """ kets = _result_state(kets) fig, ani = plot_qubism(kets, theme, how, grid_iteration, legend_iteration, fig=fig, ax=ax) return fig, ani def anim_schmidt(kets, theme='light', splitting=None, labels_iteration=(3, 2), *, fig=None, ax=None): """ Animation of Schmidt decomposition. Converts a state into a matrix (A_ij -> A_i^j), where rows are first particles and columns - last. See also: plot_qubism with how='before_after' for a similar plot. .. note:: colorblind_safe does not apply because of its unique colormap Parameters ---------- ket : :class:`.Result` or list of :class:`.Qobj` Pure states for animation. theme : str {'light', 'dark'}, default: 'light' Set coloring theme for mapping complex values into colors. See: complex_array_to_rgb. splitting : int, optional Plot for a number of first particles versus the rest. If not given, it is (number of particles + 1) // 2. labels_iteration : int or pair of ints, default: (3, 2) Number of particles to be shown as tick labels, for first (vertical) and last (horizontal) particles, respectively. fig : a matplotlib figure instance, optional The figure canvas on which the plot will be drawn. ax : a matplotlib axis instance, optional The axis context in which the plot will be drawn. Returns ------- fig, ani : tuple A tuple of the matplotlib figure and the animation instance used to produce the figure. """ kets = _result_state(kets) fig, ani = plot_schmidt(kets, theme, splitting, labels_iteration, fig=fig, ax=ax) return fig, ani qutip-5.1.1/qutip/bloch.py000066400000000000000000001076771474175217300155200ustar00rootroot00000000000000__all__ = ['Bloch'] import os from typing import Literal import numpy as np from numpy import (outer, cos, sin, ones) from packaging.version import parse as parse_version from . import Qobj, expect, sigmax, sigmay, sigmaz try: import matplotlib import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from matplotlib.patches import FancyArrowPatch from mpl_toolkits.mplot3d import proj3d # Define a custom _axes3D function based on the matplotlib version. # The auto_add_to_figure keyword is new for matplotlib>=3.4. if parse_version(matplotlib.__version__) >= parse_version('3.4'): def _axes3D(fig, *args, **kwargs): ax = Axes3D(fig, *args, auto_add_to_figure=False, **kwargs) return fig.add_axes(ax) else: def _axes3D(*args, **kwargs): return Axes3D(*args, **kwargs) class Arrow3D(FancyArrowPatch): def __init__(self, xs, ys, zs, *args, **kwargs): FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs) self._verts3d = xs, ys, zs def draw(self, renderer): xs3d, ys3d, zs3d = self._verts3d xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, self.axes.M) self.set_positions((xs[0], ys[0]), (xs[1], ys[1])) FancyArrowPatch.draw(self, renderer) def do_3d_projection(self, renderer=None): # only called by matplotlib >= 3.5 xs3d, ys3d, zs3d = self._verts3d xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, self.axes.M) self.set_positions((xs[0], ys[0]), (xs[1], ys[1])) return np.min(zs) except ImportError: pass try: from IPython.display import display except ImportError: pass class Bloch: r""" Class for plotting data on the Bloch sphere. Valid data can be either points, vectors, or Qobj objects. Attributes ---------- axes : matplotlib.axes.Axes User supplied Matplotlib axes for Bloch sphere animation. fig : matplotlib.figure.Figure User supplied Matplotlib Figure instance for plotting Bloch sphere. font_color : str, default 'black' Color of font used for Bloch sphere labels. font_size : int, default 20 Size of font used for Bloch sphere labels. frame_alpha : float, default 0.1 Sets transparency of Bloch sphere frame. frame_color : str, default 'gray' Color of sphere wireframe. frame_width : int, default 1 Width of wireframe. point_color : list, default ["b", "r", "g", "#CC6600"] List of colors for Bloch sphere point markers to cycle through, i.e. by default, points 0 and 4 will both be blue ('b'). point_marker : list, default ["o", "s", "d", "^"] List of point marker shapes to cycle through. point_size : list, default [25, 32, 35, 45] List of point marker sizes. Note, not all point markers look the same size when plotted! sphere_alpha : float, default 0.2 Transparency of Bloch sphere itself. sphere_color : str, default '#FFDDDD' Color of Bloch sphere. figsize : list, default [7, 7] Figure size of Bloch sphere plot. Best to have both numbers the same; otherwise you will have a Bloch sphere that looks like a football. vector_color : list, ["g", "#CC6600", "b", "r"] List of vector colors to cycle through. vector_width : int, default 5 Width of displayed vectors. vector_style : str, default '-\|>' Vector arrowhead style (from matplotlib's arrow style). vector_mutation : int, default 20 Width of vectors arrowhead. view : list, default [-60, 30] Azimuthal and Elevation viewing angles. xlabel : list, default ["$x$", ""] List of strings corresponding to +x and -x axes labels, respectively. xlpos : list, default [1.1, -1.1] Positions of +x and -x labels respectively. ylabel : list, default ["$y$", ""] List of strings corresponding to +y and -y axes labels, respectively. ylpos : list, default [1.2, -1.2] Positions of +y and -y labels respectively. zlabel : list, default ['$\\left\|0\\right>$', '$\\left\|1\\right>$'] List of strings corresponding to +z and -z axes labels, respectively. zlpos : list, default [1.2, -1.2] Positions of +z and -z labels respectively. """ def __init__(self, fig=None, axes=None, view=None, figsize=None, background=False): # Figure and axes self.fig = fig self._ext_fig = fig is not None self.axes = axes # Background axes, default = False self.background = background # The size of the figure in inches, default = [5,5]. self.figsize = figsize if figsize else [5, 5] # Azimuthal and Elvation viewing angles, default = [-60,30]. self.view = view if view else [-60, 30] # Color of Bloch sphere, default = #FFDDDD self.sphere_color = '#FFDDDD' # Transparency of Bloch sphere, default = 0.2 self.sphere_alpha = 0.2 # Color of wireframe, default = 'gray' self.frame_color = 'gray' # Width of wireframe, default = 1 self.frame_width = 1 # Transparency of wireframe, default = 0.2 self.frame_alpha = 0.2 # Labels for x-axis (in LaTex), default = ['$x$', ''] self.xlabel = ['$x$', ''] # Position of x-axis labels, default = [1.2, -1.2] self.xlpos = [1.2, -1.2] # Labels for y-axis (in LaTex), default = ['$y$', ''] self.ylabel = ['$y$', ''] # Position of y-axis labels, default = [1.1, -1.1] self.ylpos = [1.2, -1.2] # Labels for z-axis (in LaTex), # default = [r'$\left\|0\right>$', r'$\left|1\right>$'] self.zlabel = [r'$\left|0\right>$', r'$\left|1\right>$'] # Position of z-axis labels, default = [1.2, -1.2] self.zlpos = [1.2, -1.2] # ---font options--- # Color of fonts, default = 'black' self.font_color = 'black' # Size of fonts, default = 20 self.font_size = 20 # ---vector options--- # List of colors for Bloch vectors, default = ['b','g','r','y'] self.vector_default_color = ['g', '#CC6600', 'b', 'r'] # List that stores the display colors for each vector self.vector_color = [] # Width of Bloch vectors, default = 5 self.vector_width = 3 # Style of Bloch vectors, default = '-\|>' (or 'simple') self.vector_style = '-|>' # Sets the width of the vectors arrowhead self.vector_mutation = 20 # ---point options--- # List of colors for Bloch point markers, default = ['b','g','r','y'] self.point_default_color = ['b', 'r', 'g', '#CC6600'] # Old variable used in V4 to customise the color of the points self.point_color = None # List that stores the display colors for each set of points self._inner_point_color = [] # Size of point markers, default = 25 self.point_size = [25, 32, 35, 45] # Shape of point markers, default = ['o','^','d','s'] self.point_marker = ['o', 's', 'd', '^'] # ---data lists--- # Data for point markers self.points = [] # Data for Bloch vectors self.vectors = [] # Transparency of vectors, alpha value from 0 to 1 self.vector_alpha = [] # Data for annotations self.annotations = [] # Number of times sphere has been saved self.savenum = 0 # Style of points, 'm' for multiple colors, 's' for single color self.point_style = [] # Transparency of points, alpha value from 0 to 1 self.point_alpha = [] # Data for line segment self._lines = [] # Data for arcs and arc style self._arcs = [] def set_label_convention(self, convention): """Set x, y and z labels according to one of conventions. Parameters ---------- convention : string One of the following: - "original" - "xyz" - "sx sy sz" - "01" - "polarization jones" - "polarization jones letters" see also: https://en.wikipedia.org/wiki/Jones_calculus - "polarization stokes" see also: https://en.wikipedia.org/wiki/Stokes_parameters """ ketex = "$\\left.|%s\\right\\rangle$" # \left.| is on purpose, so that every ket has the same size if convention == "original": self.xlabel = ['$x$', ''] self.ylabel = ['$y$', ''] self.zlabel = ['$\\left|0\\right>$', '$\\left|1\\right>$'] elif convention == "xyz": self.xlabel = ['$x$', ''] self.ylabel = ['$y$', ''] self.zlabel = ['$z$', ''] elif convention == "sx sy sz": self.xlabel = ['$s_x$', ''] self.ylabel = ['$s_y$', ''] self.zlabel = ['$s_z$', ''] elif convention == "01": self.xlabel = ['', ''] self.ylabel = ['', ''] self.zlabel = ['$\\left|0\\right>$', '$\\left|1\\right>$'] elif convention == "polarization jones": self.xlabel = [ketex % "\\nearrow\\hspace{-1.46}\\swarrow", ketex % "\\nwarrow\\hspace{-1.46}\\searrow"] self.ylabel = [ketex % "\\circlearrowleft", ketex % "\\circlearrowright"] self.zlabel = [ketex % "\\leftrightarrow", ketex % "\\updownarrow"] elif convention == "polarization jones letters": self.xlabel = [ketex % "D", ketex % "A"] self.ylabel = [ketex % "L", ketex % "R"] self.zlabel = [ketex % "H", ketex % "V"] elif convention == "polarization stokes": self.ylabel = ["$\\nearrow\\hspace{-1.46}\\swarrow$", "$\\nwarrow\\hspace{-1.46}\\searrow$"] self.zlabel = ["$\\circlearrowleft$", "$\\circlearrowright$"] self.xlabel = ["$\\leftrightarrow$", "$\\updownarrow$"] else: raise Exception("No such convention.") def __str__(self): s = "" s += "Bloch data:\n" s += "-----------\n" s += "Number of points: " + str(len(self.points)) + "\n" s += "Number of vectors: " + str(len(self.vectors)) + "\n" s += "\n" s += "Bloch sphere properties:\n" s += "------------------------\n" s += "font_color: " + str(self.font_color) + "\n" s += "font_size: " + str(self.font_size) + "\n" s += "frame_alpha: " + str(self.frame_alpha) + "\n" s += "frame_color: " + str(self.frame_color) + "\n" s += "frame_width: " + str(self.frame_width) + "\n" s += "point_default_color:" + str(self.point_default_color) + "\n" s += "point_marker: " + str(self.point_marker) + "\n" s += "point_size: " + str(self.point_size) + "\n" s += "sphere_alpha: " + str(self.sphere_alpha) + "\n" s += "sphere_color: " + str(self.sphere_color) + "\n" s += "figsize: " + str(self.figsize) + "\n" s += "vector_default_color:" + str(self.vector_default_color) + "\n" s += "vector_width: " + str(self.vector_width) + "\n" s += "vector_style: " + str(self.vector_style) + "\n" s += "vector_mutation: " + str(self.vector_mutation) + "\n" s += "view: " + str(self.view) + "\n" s += "xlabel: " + str(self.xlabel) + "\n" s += "xlpos: " + str(self.xlpos) + "\n" s += "ylabel: " + str(self.ylabel) + "\n" s += "ylpos: " + str(self.ylpos) + "\n" s += "zlabel: " + str(self.zlabel) + "\n" s += "zlpos: " + str(self.zlpos) + "\n" return s def _repr_png_(self): from IPython.core.pylabtools import print_figure self.render() fig_data = print_figure(self.fig, 'png') plt.close(self.fig) return fig_data def _repr_svg_(self): from IPython.core.pylabtools import print_figure self.render() fig_data = print_figure(self.fig, 'svg') plt.close(self.fig) return fig_data def clear(self): """Resets Bloch sphere data sets to empty. """ self.points = [] self.vectors = [] self.point_style = [] self.point_alpha = [] self.vector_alpha = [] self.annotations = [] self.vector_color = [] self.point_color = None self._lines = [] self._arcs = [] def add_points(self, points, meth: Literal['s', 'm', 'l'] = 's', colors=None, alpha=1.0): """Add a list of data points to bloch sphere. Parameters ---------- points : array_like Collection of data points. meth : {'s', 'm', 'l'} Type of points to plot, use 'm' for multicolored, 'l' for points connected with a line. colors : array_like Optional array with colors for the points. A single color for meth 's', and list of colors for meth 'm' alpha : float, default=1. Transparency value for the vectors. Values between 0 and 1. Notes ----- When using ``meth=l`` in QuTiP 4.6, the line transparency defaulted to ``0.75`` and there was no way to alter it. When the ``alpha`` parameter was added in QuTiP 4.7, the default became ``alpha=1.0`` for values of ``meth``. """ points = np.asarray(points) if points.ndim == 1: points = points[:, np.newaxis] if points.ndim != 2 or points.shape[0] != 3: raise ValueError("The included points are not valid. Points must " "be equivalent to a 2D array where the first " "index represents the x,y,z values and the " "second index iterates over the points.") if meth not in ['s', 'm', 'l']: raise ValueError(f"The value for meth = {meth} is not valid." " Please use 's', 'l' or 'm'.") if meth == 's' and points.shape[1] == 1: points = np.append(points[:, :1], points, axis=1) self.point_style.append(meth) self.points.append(points) self.point_alpha.append(alpha) self._inner_point_color.append(colors) def add_states(self, state, kind: Literal['vector', 'point'] = 'vector', colors=None, alpha=1.0): """Add a state vector Qobj to Bloch sphere. Parameters ---------- state : :obj:`.Qobj` or array_like Input state vector or list. kind : {'vector', 'point'} Type of object to plot. colors : array_like Optional array with colors for the states. alpha : float, default=1. Transparency value for the vectors. Values between 0 and 1. """ state = np.asarray(state) if state.ndim == 0: state = state[np.newaxis] if state.ndim != 1: raise ValueError("The included states are not valid. " "State should be a Qobj or a list of Qobj.") if colors is not None: colors = np.asarray(colors) if colors.ndim == 0: colors = colors[np.newaxis] if colors.shape != state.shape: raise ValueError("The included colors are not valid. " "colors must be equivalent to a 1D array " "with the same size as the number of states.") else: colors = np.array([None] * state.size) for k, st in enumerate(state): vec = [expect(sigmax(), st), expect(sigmay(), st), expect(sigmaz(), st)] if kind == 'vector': self.add_vectors(vec, colors=[colors[k]], alpha=alpha) elif kind == 'point': self.add_points(vec, colors=[colors[k]], alpha=alpha) def add_vectors(self, vectors, colors=None, alpha=1.0): """Add a list of vectors to Bloch sphere. Parameters ---------- vectors : array_like Array with vectors of unit length or smaller. colors : array_like Optional array with colors for the vectors. alpha : float, default=1. Transparency value for the vectors. Values between 0 and 1. """ vectors = np.asarray(vectors) if vectors.ndim == 1: vectors = vectors[np.newaxis, :] if vectors.ndim != 2 or vectors.shape[1] != 3: raise ValueError( "The included vectors are not valid. Vectors must " "be equivalent to a 2D array where the first " "index represents the iteration over the vectors and the " "second index represents the position in 3D of vector head.") n_vectors = vectors.shape[0] if colors is None: colors = np.array([None] * n_vectors) else: colors = np.asarray(colors) if colors.ndim != 1 or colors.size != n_vectors: raise ValueError("The included colors are not valid. colors must " "be equivalent to a 1D array with the same " "size as the number of vectors. ") for k, vec in enumerate(vectors): self.vectors.append(vec) self.vector_alpha.append(alpha) self.vector_color.append(colors[k]) def add_annotation(self, state_or_vector, text, **kwargs): """ Add a text or LaTeX annotation to Bloch sphere, parametrized by a qubit state or a vector. Parameters ---------- state_or_vector : :obj:`.Qobj`/array/list/tuple Position for the annotaion. Qobj of a qubit or a vector of 3 elements. text : str Annotation text. You can use LaTeX, but remember to use raw string e.g. r"$\\langle x \\rangle$" or escape backslashes e.g. "$\\\\langle x \\\\rangle$". kwargs : Options as for mplot3d.axes3d.text, including: fontsize, color, horizontalalignment, verticalalignment. """ if isinstance(state_or_vector, Qobj): vec = [expect(sigmax(), state_or_vector), expect(sigmay(), state_or_vector), expect(sigmaz(), state_or_vector)] elif isinstance(state_or_vector, (list, np.ndarray, tuple)) \ and len(state_or_vector) == 3: vec = state_or_vector else: raise Exception("Position needs to be specified by a qubit " + "state or a 3D vector.") self.annotations.append({'position': vec, 'text': text, 'opts': kwargs}) def add_arc(self, start, end, fmt="b", steps=None, **kwargs): """Adds an arc between two points on a sphere. The arc is set to be blue solid curve by default. The start and end points must be on the same sphere (i.e. have the same radius) but need not be on the unit sphere. Parameters ---------- start : :obj:`.Qobj` or array-like Array with cartesian coordinates of the first point, or a state vector or density matrix that can be mapped to a point on or within the Bloch sphere. end : :obj:`.Qobj` or array-like Array with cartesian coordinates of the second point, or a state vector or density matrix that can be mapped to a point on or within the Bloch sphere. fmt : str, default: "b" A matplotlib format string for rendering the arc. steps : int, default: None The number of segments to use when rendering the arc. The default uses 100 steps times the distance between the start and end points, with a minimum of 2 steps. **kwargs : dict Additional parameters to pass to the matplotlib .plot function when rendering this arc. """ if isinstance(start, Qobj): pt1 = [ expect(sigmax(), start), expect(sigmay(), start), expect(sigmaz(), start), ] else: pt1 = start if isinstance(end, Qobj): pt2 = [ expect(sigmax(), end), expect(sigmay(), end), expect(sigmaz(), end), ] else: pt2 = end pt1 = np.asarray(pt1) pt2 = np.asarray(pt2) len1 = np.linalg.norm(pt1) len2 = np.linalg.norm(pt2) if len1 < 1e-12 or len2 < 1e-12: raise ValueError('Polar and azimuthal angles undefined at origin.') elif abs(len1 - len2) > 1e-12: raise ValueError("Points not on the same sphere.") elif (pt1 == pt2).all(): raise ValueError( "Start and end represent the same point. No arc can be formed." ) elif (pt1 == -pt2).all(): raise ValueError( "Start and end are diagonally opposite, no unique arc is" " possible." ) if steps is None: steps = int(np.linalg.norm(pt1 - pt2) * 100) steps = max(2, steps) t = np.linspace(0, 1, steps) # All the points in this line are contained in the plane defined # by pt1, pt2 and the origin. line = pt1[:, np.newaxis] * t + pt2[:, np.newaxis] * (1 - t) # Normalize all the points in the line so that are distance len1 from # the origin. arc = line * len1 / np.linalg.norm(line, axis=0) self._arcs.append([arc, fmt, kwargs]) def add_line(self, start, end, fmt="k", **kwargs): """Adds a line segment connecting two points on the bloch sphere. The line segment is set to be a black solid line by default. Parameters ---------- start : :obj:`.Qobj` or array-like Array with cartesian coordinates of the first point, or a state vector or density matrix that can be mapped to a point on or within the Bloch sphere. end : :obj:`.Qobj` or array-like Array with cartesian coordinates of the second point, or a state vector or density matrix that can be mapped to a point on or within the Bloch sphere. fmt : str, default: "k" A matplotlib format string for rendering the line. **kwargs : dict Additional parameters to pass to the matplotlib .plot function when rendering this line. """ if isinstance(start, Qobj): pt1 = [ expect(sigmax(), start), expect(sigmay(), start), expect(sigmaz(), start), ] else: pt1 = start if isinstance(end, Qobj): pt2 = [ expect(sigmax(), end), expect(sigmay(), end), expect(sigmaz(), end), ] else: pt2 = end pt1 = np.asarray(pt1) pt2 = np.asarray(pt2) x = [pt1[1], pt2[1]] y = [-pt1[0], -pt2[0]] z = [pt1[2], pt2[2]] v = [x, y, z] self._lines.append([v, fmt, kwargs]) def make_sphere(self): """ Plots Bloch sphere and data sets. """ self.render() def run_from_ipython(self): try: __IPYTHON__ return True except NameError: return False def _is_inline_backend(self): backend = matplotlib.get_backend() return backend == "module://matplotlib_inline.backend_inline" def render(self): """ Render the Bloch sphere and its data sets in on given figure and axes. """ if not self._ext_fig and not self._is_inline_backend(): # If no external figure was supplied, we check to see if the # figure we created in a previous call to .render() has been # closed, and re-create if has been. This has the unfortunate # side effect of losing any modifications made to the axes or # figure, but the alternative is to crash the matplotlib backend. # # The inline backend used by, e.g. jupyter notebooks, is happy to # use closed figures so we leave those figures intact. if ( self.fig is not None and not plt.fignum_exists(self.fig.number) ): self.fig = None self.axes = None if self.fig is None: self.fig = plt.figure(figsize=self.figsize) if self._is_inline_backend(): # We immediately close the inline figure do avoid displaying # the figure twice when .show() calls display. plt.close(self.fig) if self.axes is None: self.axes = _axes3D(self.fig, azim=self.view[0], elev=self.view[1]) # Clearing the axes is horrifically slow and loses a lot of the # axes state, but matplotlib doesn't seem to provide a better way # to redraw Axes3D. :/ self.axes.clear() self.axes.grid(False) if self.background: self.axes.set_xlim3d(-1.3, 1.3) self.axes.set_ylim3d(-1.3, 1.3) self.axes.set_zlim3d(-1.3, 1.3) else: self.axes.set_axis_off() self.axes.set_xlim3d(-0.7, 0.7) self.axes.set_ylim3d(-0.7, 0.7) self.axes.set_zlim3d(-0.7, 0.7) # Manually set aspect ratio to fit a square bounding box. # Matplotlib did this stretching for < 3.3.0, but not above. if parse_version(matplotlib.__version__) >= parse_version('3.3'): self.axes.set_box_aspect((1, 1, 1)) if not self.background: self.plot_axes() self.plot_back() self.plot_points() self.plot_vectors() self.plot_lines() self.plot_arcs() self.plot_front() self.plot_axes_labels() self.plot_annotations() # Trigger an update of the Bloch sphere if it is already shown: self.fig.canvas.draw() def plot_back(self): # back half of sphere u = np.linspace(0, np.pi, 25) v = np.linspace(0, np.pi, 25) x = outer(cos(u), sin(v)) y = outer(sin(u), sin(v)) z = outer(ones(np.size(u)), cos(v)) self.axes.plot_surface(x, y, z, rstride=2, cstride=2, color=self.sphere_color, linewidth=0, alpha=self.sphere_alpha) # wireframe self.axes.plot_wireframe(x, y, z, rstride=5, cstride=5, color=self.frame_color, alpha=self.frame_alpha) # equator self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='z', lw=self.frame_width, color=self.frame_color) self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='x', lw=self.frame_width, color=self.frame_color) def plot_front(self): # front half of sphere u = np.linspace(-np.pi, 0, 25) v = np.linspace(0, np.pi, 25) x = outer(cos(u), sin(v)) y = outer(sin(u), sin(v)) z = outer(ones(np.size(u)), cos(v)) self.axes.plot_surface(x, y, z, rstride=2, cstride=2, color=self.sphere_color, linewidth=0, alpha=self.sphere_alpha) # wireframe self.axes.plot_wireframe(x, y, z, rstride=5, cstride=5, color=self.frame_color, alpha=self.frame_alpha) # equator self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='z', lw=self.frame_width, color=self.frame_color) self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='x', lw=self.frame_width, color=self.frame_color) def plot_axes(self): # axes span = np.linspace(-1.0, 1.0, 2) self.axes.plot(span, 0 * span, zs=0, zdir='z', label='X', lw=self.frame_width, color=self.frame_color) self.axes.plot(0 * span, span, zs=0, zdir='z', label='Y', lw=self.frame_width, color=self.frame_color) self.axes.plot(0 * span, span, zs=0, zdir='y', label='Z', lw=self.frame_width, color=self.frame_color) def plot_axes_labels(self): # axes labels opts = {'fontsize': self.font_size, 'color': self.font_color, 'horizontalalignment': 'center', 'verticalalignment': 'center'} self.axes.text(0, -self.xlpos[0], 0, self.xlabel[0], **opts) self.axes.text(0, -self.xlpos[1], 0, self.xlabel[1], **opts) self.axes.text(self.ylpos[0], 0, 0, self.ylabel[0], **opts) self.axes.text(self.ylpos[1], 0, 0, self.ylabel[1], **opts) self.axes.text(0, 0, self.zlpos[0], self.zlabel[0], **opts) self.axes.text(0, 0, self.zlpos[1], self.zlabel[1], **opts) for a in (self.axes.xaxis.get_ticklines() + self.axes.xaxis.get_ticklabels()): a.set_visible(False) for a in (self.axes.yaxis.get_ticklines() + self.axes.yaxis.get_ticklabels()): a.set_visible(False) for a in (self.axes.zaxis.get_ticklines() + self.axes.zaxis.get_ticklabels()): a.set_visible(False) def plot_vectors(self): # -X and Y data are switched for plotting purposes for k, vec in enumerate(self.vectors): xs3d = vec[1] * np.array([0, 1]) ys3d = -vec[0] * np.array([0, 1]) zs3d = vec[2] * np.array([0, 1]) alpha = self.vector_alpha[k] color = self.vector_color[k] if color is None: idx = k % len(self.vector_default_color) color = self.vector_default_color[idx] # decorated style, with arrow heads a = Arrow3D(xs3d, ys3d, zs3d, mutation_scale=self.vector_mutation, lw=self.vector_width, arrowstyle=self.vector_style, color=color, alpha=alpha) self.axes.add_artist(a) def plot_points(self): # -X and Y data are switched for plotting purposes for k, points in enumerate(self.points): points = np.asarray(points) num_points = points.shape[1] dist = np.linalg.norm(points, axis=0) if not np.allclose(dist, dist[0], rtol=1e-12): indperm = np.argsort(dist) else: indperm = np.arange(num_points) s = self.point_size[np.mod(k, len(self.point_size))] marker = self.point_marker[np.mod(k, len(self.point_marker))] style = self.point_style[k] if self._inner_point_color[k] is not None: color = self._inner_point_color[k] elif self.point_color is not None: color = self.point_color elif self.point_style[k] in ['s', 'l']: color = [self.point_default_color[ k % len(self.point_default_color) ]] elif self.point_style[k] == 'm': length = np.ceil(num_points/len(self.point_default_color)) color = np.tile(self.point_default_color, length.astype(int)) color = color[indperm] color = list(color) if self.point_style[k] in ['s', 'm']: self.axes.scatter(np.real(points[1][indperm]), -np.real(points[0][indperm]), np.real(points[2][indperm]), s=s, marker=marker, color=color, alpha=self.point_alpha[k], edgecolor=None, zdir='z', ) elif self.point_style[k] == 'l': color = color[k % len(color)] self.axes.plot(np.real(points[1]), -np.real(points[0]), np.real(points[2]), color=color, alpha=self.point_alpha[k], zdir='z', ) def plot_annotations(self): # -X and Y data are switched for plotting purposes for annotation in self.annotations: vec = annotation['position'] opts = {'fontsize': self.font_size, 'color': self.font_color, 'horizontalalignment': 'center', 'verticalalignment': 'center'} opts.update(annotation['opts']) self.axes.text(vec[1], -vec[0], vec[2], annotation['text'], **opts) def plot_lines(self): for line, fmt, kw in self._lines: self.axes.plot(line[0], line[1], line[2], fmt, **kw) def plot_arcs(self): for arc, fmt, kw in self._arcs: self.axes.plot(arc[1, :], -arc[0, :], arc[2, :], fmt, **kw) def show(self): """ Display Bloch sphere and corresponding data sets. Notes ----- When using inline plotting in Jupyter notebooks, any figure created in a notebook cell is displayed after the cell executes. Thus if you create a figure yourself and use it create a Bloch sphere with ``b = Bloch(..., fig=fig)`` and then call ``b.show()`` in the same cell, then the figure will be displayed twice. If you do create your own figure, the simplest solution to this is to not call ``.show()`` in the cell you create the figure in. """ self.render() if self.run_from_ipython(): display(self.fig) else: self.fig.show() def save(self, name=None, format='png', dirc=None, dpin=None): """Saves Bloch sphere to file of type ``format`` in directory ``dirc``. Parameters ---------- name : str Name of saved image. Must include path and format as well. i.e. '/Users/Me/Desktop/bloch.png' This overrides the 'format' and 'dirc' arguments. format : str Format of output image. dirc : str Directory for output images. Defaults to current working directory. dpin : int Resolution in dots per inch. Returns ------- File containing plot of Bloch sphere. """ self.render() # Conditional variable for first argument to savefig # that is set in subsequent if-elses complete_path = "" if dirc: if not os.path.isdir(os.getcwd() + "/" + str(dirc)): os.makedirs(os.getcwd() + "/" + str(dirc)) if name is None: if dirc: complete_path = os.getcwd() + "/" + str(dirc) + '/bloch_' \ + str(self.savenum) + '.' + format else: complete_path = os.getcwd() + '/bloch_' + \ str(self.savenum) + '.' + format else: complete_path = name if dpin: self.fig.savefig(complete_path, dpi=dpin) else: self.fig.savefig(complete_path) self.savenum += 1 if self.fig: plt.close(self.fig) def _hide_tick_lines_and_labels(axis): ''' Set visible property of ticklines and ticklabels of an axis to False ''' for a in axis.get_ticklines() + axis.get_ticklabels(): a.set_visible(False) qutip-5.1.1/qutip/cite.py000066400000000000000000000024411474175217300153340ustar00rootroot00000000000000""" Citation generator for QuTiP """ import os __all__ = ['cite'] def cite(save=False, path=None): """ Citation information and bibtex generator for QuTiP Parameters ---------- save: bool The flag specifying whether to save the .bib file. path: str The complete directory path to generate the bibtex file. If not specified then the citation will be generated in cwd """ citation = """\ @misc{qutip5, title = {{QuTiP} 5: The Quantum Toolbox in {Python}}, author = {Lambert, Neill and Giguère, Eric and Menczel, Paul and Li, Boxi and Hopf, Patrick and SuĂĄrez, Gerardo and Gali, Marc and Lishman, Jake and Gadhvi, Rushiraj and Agarwal, Rochisha and Galicia, Asier and Shammah, Nathan and Nation, Paul D. and Johansson, J. R. and Ahmed, Shahnawaz and Cross, Simon and Pitchford, Alexander and Nori, Franco}, year={2024}, eprint={2412.04705}, archivePrefix={arXiv}, primaryClass={quant-ph}, url={https://arxiv.org/abs/2412.04705}, doi={10.48550/arXiv.2412.04705}, }""" print(citation) if not path: path = os.getcwd() if save: filename = "qutip.bib" with open(os.path.join(path, filename), 'w') as f: f.write("\n".join(citation)) if __name__ == "__main__": cite() qutip-5.1.1/qutip/continuous_variables.py000066400000000000000000000205141474175217300206470ustar00rootroot00000000000000""" This module contains a collection functions for calculating continuous variable quantities from fock-basis representation of the state of multi-mode fields. """ __all__ = ['correlation_matrix', 'covariance_matrix', 'correlation_matrix_field', 'correlation_matrix_quadrature', 'wigner_covariance_matrix', 'logarithmic_negativity'] from . import expect import numpy as np def correlation_matrix(basis, rho=None): r""" Given a basis set of operators :math:`\{a\}_n`, calculate the correlation matrix: .. math:: C_{mn} = \langle a_m a_n \rangle Parameters ---------- basis : list List of operators that defines the basis for the correlation matrix. rho : Qobj, optional Density matrix for which to calculate the correlation matrix. If `rho` is `None`, then a matrix of correlation matrix operators is returned instead of expectation values of those operators. Returns ------- corr_mat : ndarray A 2-dimensional *array* of correlation values or operators. """ if rho is None: # return array of operators out = np.empty((len(basis), len(basis)), dtype=object) for i, op2 in enumerate(basis): out[i, :] = [op1 * op2 for op1 in basis] return out else: # return array of expectation values return np.array([[expect(op1 * op2, rho) for op1 in basis] for op2 in basis]) def covariance_matrix(basis, rho, symmetrized=True): r""" Given a basis set of operators :math:`\{a\}_n`, calculate the covariance matrix: .. math:: V_{mn} = \frac{1}{2}\langle a_m a_n + a_n a_m \rangle - \langle a_m \rangle \langle a_n\rangle or, if of the optional argument `symmetrized=False`, .. math:: V_{mn} = \langle a_m a_n\rangle - \langle a_m \rangle \langle a_n\rangle Parameters ---------- basis : list List of operators that defines the basis for the covariance matrix. rho : Qobj Density matrix for which to calculate the covariance matrix. symmetrized : bool, default: True Flag indicating whether the symmetrized (default) or non-symmetrized correlation matrix is to be calculated. Returns ------- corr_mat : ndarray A 2-dimensional array of covariance values. """ if symmetrized: return np.array([[0.5 * expect(op1 * op2 + op2 * op1, rho) - expect(op1, rho) * expect(op2, rho) for op1 in basis] for op2 in basis]) else: return np.array([[expect(op1 * op2, rho) - expect(op1, rho) * expect(op2, rho) for op1 in basis] for op2 in basis]) def correlation_matrix_field(a1, a2, rho=None): """ Calculates the correlation matrix for given field operators :math:`a_1` and :math:`a_2`. If a density matrix is given the expectation values are calculated, otherwise a matrix with operators is returned. Parameters ---------- a1 : Qobj Field operator for mode 1. a2 : Qobj Field operator for mode 2. rho : Qobj, optional Density matrix for which to calculate the covariance matrix. Returns ------- cov_mat : ndarray Array of complex numbers or Qobj's A 2-dimensional *array* of covariance values, or, if rho=0, a matrix of operators. """ basis = [a1, a1.dag(), a2, a2.dag()] return correlation_matrix(basis, rho) def correlation_matrix_quadrature(a1, a2, rho=None, g=np.sqrt(2)): """ Calculate the quadrature correlation matrix with given field operators :math:`a_1` and :math:`a_2`. If a density matrix is given the expectation values are calculated, otherwise a matrix with operators is returned. Parameters ---------- a1 : Qobj Field operator for mode 1. a2 : Qobj Field operator for mode 2. rho : Qobj, optional Density matrix for which to calculate the covariance matrix. g : float, default: sqrt(2) Scaling factor for ``a = 0.5 * g * (x + iy)``, default ``g = sqrt(2)``. The value of ``g`` is related to the value of ``hbar`` in the commutation relation ``[x, y] = i * hbar`` via ``hbar=2/g ** 2`` giving the default value ``hbar=1``. Returns ------- corr_mat : ndarray Array of complex numbers or Qobj's A 2-dimensional *array* of covariance values for the field quadratures, or, if rho=0, a matrix of operators. """ x1 = (a1 + a1.dag()) / g p1 = -1j * (a1 - a1.dag()) / g x2 = (a2 + a2.dag()) / g p2 = -1j * (a2 - a2.dag()) / g basis = [x1, p1, x2, p2] return correlation_matrix(basis, rho) def wigner_covariance_matrix(a1=None, a2=None, R=None, rho=None, g=np.sqrt(2)): r""" Calculates the Wigner covariance matrix :math:`V_{ij} = \frac{1}{2}(R_{ij} + R_{ji})`, given the quadrature correlation matrix :math:`R_{ij} = \langle R_{i} R_{j}\rangle - \langle R_{i}\rangle \langle R_{j}\rangle`, where :math:`R = (q_1, p_1, q_2, p_2)^T` is the vector with quadrature operators for the two modes. Alternatively, if ``R = None``, and if annihilation operators ``a1`` and ``a2`` for the two modes are supplied instead, the quadrature correlation matrix is constructed from the annihilation operators before then the covariance matrix is calculated. Parameters ---------- a1 : Qobj, optional Field operator for mode 1. a2 : Qobj, optional Field operator for mode 2. R : ndarray, optional The quadrature correlation matrix. rho : Qobj, optional Density matrix for which to calculate the covariance matrix. g : float, default: sqrt(2) Scaling factor for ``a = 0.5 * g * (x + iy)``, default ``g = sqrt(2)``. The value of ``g`` is related to the value of ``hbar`` in the commutation relation ``[x, y] = i * hbar`` via ``hbar=2/g ** 2`` giving the default value ``hbar=1``. Returns ------- cov_mat : ndarray A 2-dimensional array of covariance values. """ if R is not None: if rho is None: return np.array([[0.5 * np.real(R[i, j] + R[j, i]) for i in range(4)] for j in range(4)], dtype=np.float64) else: return np.array([[0.5 * np.real(expect(R[i, j] + R[j, i], rho)) for i in range(4)] for j in range(4)], dtype=np.float64) elif a1 is not None and a2 is not None: if rho is not None: x1 = (a1 + a1.dag()) / g p1 = -1j * (a1 - a1.dag()) / g x2 = (a2 + a2.dag()) / g p2 = -1j * (a2 - a2.dag()) / g return covariance_matrix([x1, p1, x2, p2], rho) else: raise ValueError("Must give rho if using field operators " + "(a1 and a2)") else: raise ValueError("Must give either field operators (a1 and a2) " + "or a precomputed correlation matrix (R)") def logarithmic_negativity(V, g=np.sqrt(2)): """ Calculates the logarithmic negativity given a symmetrized covariance matrix, see :func:`qutip.continuous_variables.covariance_matrix`. Note that the two-mode field state that is described by `V` must be Gaussian for this function to applicable. Parameters ---------- V : ndarray The covariance matrix. g : float, default: sqrt(2) Scaling factor for ``a = 0.5 * g * (x + iy)``, default ``g = sqrt(2)``. The value of ``g`` is related to the value of ``hbar`` in the commutation relation ``[x, y] = i * hbar`` via ``hbar=2/g ** 2`` giving the default value ``hbar=1``. Returns ------- N : float The logarithmic negativity for the two-mode Gaussian state that is described by the the Wigner covariance matrix V. """ A = 0.5 * V[0:2, 0:2] * g ** 2 B = 0.5 * V[2:4, 2:4] * g ** 2 C = 0.5 * V[0:2, 2:4] * g ** 2 sigma = np.linalg.det(A) + np.linalg.det(B) - 2 * np.linalg.det(C) nu_ = sigma / 2 - np.sqrt(sigma ** 2 - 4 * np.linalg.det(V)) / 2 if nu_ < 0.0: return 0.0 nu = np.sqrt(nu_) lognu = -np.log(2 * nu) logneg = max(0, lognu) return logneg qutip-5.1.1/qutip/control.py000066400000000000000000000006571474175217300160770ustar00rootroot00000000000000"""Module replicating the qutip_qtrl package from within qutip.""" import sys try: import qutip_qtrl del qutip_qtrl sys.modules["qutip.control"] = sys.modules["qutip_qtrl"] except ImportError: raise ImportError( "Importing 'qutip.control' requires the 'qutip_qtrl' package. " "Install it with `pip install qutip-qtrl` (for more details, go to " "https://qutip-qtrl.readthedocs.io/)." ) qutip-5.1.1/qutip/core/000077500000000000000000000000001474175217300147655ustar00rootroot00000000000000qutip-5.1.1/qutip/core/__init__.py000066400000000000000000000007351474175217300171030ustar00rootroot00000000000000from .options import * from .coefficient import * from .qobj import * from .cy.qobjevo import * from .environment import * from .expect import * from .tensor import * from .states import * from .operators import * from .metrics import * from .superoperator import * from .superop_reps import * from .subsystem_apply import * from .blochredfield import * from .energy_restricted import * from .properties import * from . import gates del cy # File in cy are not public facing qutip-5.1.1/qutip/core/_brtensor.pyx000066400000000000000000000274721474175217300175400ustar00rootroot00000000000000#cython: language_level=3 cimport cython import qutip.core.data as _data from qutip.core.data cimport Dense, CSR, Data, idxint, csr from qutip.core.cy.qobjevo cimport QobjEvo from qutip.core.cy.coefficient cimport Coefficient from qutip.core.cy._element cimport _BaseElement, _MapElement, _ProdElement from qutip.core._brtools cimport _EigenBasisTransform from qutip.core.qobj import Qobj import numpy as np from libcpp.vector cimport vector from libc.math cimport fabs, fmin __all__ = [] cpdef enum TensorType: SPARSE = 0 DENSE = 1 DATA = 2 @cython.boundscheck(False) @cython.wraparound(False) cpdef Data _br_term_data(Data A, double[:, ::1] spectrum, double[:, ::1] skew, double cutoff): """ Compute the contribution of A to the Bloch Redfield tensor. Computation are done using dispatched function. """ cdef object cutoff_arr cdef int nrows = A.shape[0], a, b, c, d cdef Data S, I, AS, AST, out, C cdef type cls = type(A) S = _data.to(cls, _data.mul(_data.Dense(spectrum), 0.5)) I = _data.identity[cls](nrows) AS = _data.multiply(A, S) AST = _data.multiply(A, _data.transpose(S)) out = _data.kron(AST, _data.transpose(A)) out = _data.add(out, _data.kron(A, _data.transpose(AS))) out = _data.sub(out, _data.kron(I, _data.transpose(_data.matmul(AS, A)))) out = _data.sub(out, _data.kron(_data.matmul(A, AST), I)) if cutoff == np.inf: return out # The cutoff_arr should be sparse most of the time, but it depend on the # cutoff and we cannot easily guess a nnz to make it efficiently... # But there is probably room from improvement. cutoff_arr = np.zeros((nrows*nrows, nrows*nrows), dtype=np.complex128) for a in range(nrows): for b in range(nrows): for c in range(nrows): for d in range(nrows): if fabs(skew[a, b] - skew[c, d]) < cutoff: cutoff_arr[a * nrows + b, c * nrows + d] = 1. C = _data.to(cls, _data.Dense(cutoff_arr, copy=False)) return _data.multiply(out, C) @cython.boundscheck(False) @cython.wraparound(False) cpdef Dense _br_term_dense(Data A, double[:, ::1] spectrum, double[:, ::1] skew, double cutoff): """ Compute the contribution of A to the Bloch Redfield tensor. Allocate a Dense array and fill it. """ cdef size_t nrows = A.shape[0] cdef size_t a, b, c, d, k # matrix indexing variables cdef double complex elem cdef double complex[:,:] A_mat, ac_term, bd_term cdef object np2term cdef Dense out cdef double complex[::1, :] out_array if type(A) is Dense: A_mat = A.as_ndarray() else: A_mat = A.to_array() out = _data.dense.zeros(nrows*nrows, nrows*nrows) out_array = out.as_ndarray() np2term = np.zeros((nrows, nrows, 2), dtype=np.complex128) ac_term = np2term[:, :, 0] bd_term = np2term[:, :, 1] for a in range(nrows): for b in range(nrows-1, -1, -1): if fabs(skew[a, b]) < cutoff: for k in range(nrows): ac_term[a, b] += A_mat[a, k] * A_mat[k, b] * spectrum[a, k] bd_term[a, b] += A_mat[a, k] * A_mat[k, b] * spectrum[b, k] # TODO: we could use openmp to speed up. for a in range(nrows): for b in range(nrows): for c in range(nrows): for d in range(nrows): if fabs(skew[a, b] - skew[c, d]) < cutoff: elem = A_mat[a, c] * A_mat[d, b] * 0.5 elem *= (spectrum[c, a] + spectrum[d, b]) if a == c: elem = elem - 0.5 * ac_term[d, b] if b == d: elem = elem - 0.5 * bd_term[a, c] out_array[a * nrows + b, c * nrows + d] = elem return out @cython.boundscheck(False) @cython.wraparound(False) cpdef CSR _br_term_sparse(Data A, double[:, :] spectrum, double[:, ::1] skew, double cutoff): """ Compute the contribution of A to the Bloch Redfield tensor. Create it as coo pointers and return as CSR. """ cdef size_t nrows = A.shape[0] cdef size_t a, b, c, d, k, d_min # matrix indexing variables cdef double complex elem, ac_elem, bd_elem cdef double complex[:,:] A_mat, ac_term, bd_term cdef double dskew cdef object np2term cdef vector[idxint] coo_rows, coo_cols cdef vector[double complex] coo_data if type(A) is Dense: A_mat = A.as_ndarray() else: A_mat = A.to_array() np2term = np.zeros((nrows, nrows, 2), dtype=np.complex128) ac_term = np2term[:, :, 0] bd_term = np2term[:, :, 1] for a in range(nrows): for b in range(nrows-1, -1, -1): if fabs(skew[a, b]) < cutoff: for k in range(nrows): ac_term[a, b] += A_mat[a, k] * A_mat[k, b] * spectrum[a, k] bd_term[a, b] += A_mat[a, k] * A_mat[k, b] * spectrum[b, k] elif skew[a, b] > cutoff: break # skew[a,b] = w[a] - w[b] # (w[a] - w[b] - w[c] + w[d]) < cutoff # w's are sorted so we can skip part of the loop. for a in range(nrows): for b in range(nrows): d_min = 0 for c in range(nrows): if skew[a, b] - skew[c, nrows-1] <= -cutoff: break for d in range(d_min, nrows): dskew = skew[a, b] - skew[c, d] if -dskew > cutoff: d_min = d elif fabs(dskew) < cutoff: elem = (A_mat[a, c] * A_mat[d, b]) * 0.5 elem *= (spectrum[c, a] + spectrum[d, b]) if a == c: elem -= 0.5 * ac_term[d, b] if b == d: elem -= 0.5 * bd_term[a, c] if elem != 0: coo_rows.push_back(a * nrows + b) coo_cols.push_back(c * nrows + d) coo_data.push_back(elem) elif dskew >= cutoff: break return csr.from_coo_pointers( coo_rows.data(), coo_cols.data(), coo_data.data(), nrows*nrows, nrows*nrows, coo_rows.size() ) cdef class _BlochRedfieldElement(_BaseElement): """ Element for individual Bloch Redfield collapse term. The tensor is computed in the ``eig_basis``, but is returned in the outside basis unless ``eig_basis`` is True. The ``matmul_data_t`` method also act on a state expected to be in that basis. It transform the state instead of the tensor as it is usually faster, the state being a density matrix in most cases. Diffenrent term can share a same instance of the eigen transform tool (``H`` as _EigenBasisTransform) so that the Hamiltonian is diagonalized only once even when needed by multiple terms. """ cdef readonly _EigenBasisTransform H cdef readonly QobjEvo a_op cdef readonly Coefficient spectra cdef readonly double sec_cutoff cdef readonly size_t nrows cdef readonly (idxint, idxint) shape cdef readonly list dims cdef readonly object np_datas cdef readonly double[:, ::1] skew cdef readonly double[:, ::1] spectrum cdef readonly bint eig_basis cdef readonly TensorType tensortype def __init__(self, H, a_op, spectra, sec_cutoff, eig_basis=False, dtype=None): if isinstance(H, _EigenBasisTransform): self.H = H else: self.H = _EigenBasisTransform(H) self.a_op = a_op self.spectra = spectra self.sec_cutoff = sec_cutoff self.eig_basis = eig_basis self.nrows = a_op.shape[0] self.dims = [a_op.dims, a_op.dims] dtype = dtype or ('dense' if sec_cutoff >= np.inf else 'sparse') self.tensortype = { 'sparse': SPARSE, 'dense': DENSE, 'data': DATA }[dtype] # Allocate some array # Let numpy manage memory self.np_datas = [np.zeros((self.nrows, self.nrows), dtype=np.float64), np.zeros((self.nrows, self.nrows), dtype=np.float64)] self.skew = self.np_datas[0] self.spectrum = self.np_datas[1] cpdef double _compute_spectrum(self, double t) except *: "Compute the skew, spectrum and dw_min" cdef Coefficient spec cdef double dw_min = np.inf eigvals = self.H.eigenvalues(t) for col in range(0, self.nrows): self.skew[col, col] = 0. self.spectrum[col, col] = self.spectra(t, w=0).real for row in range(col, self.nrows): dw = eigvals[row] - eigvals[col] self.skew[row, col] = dw self.skew[col, row] = -dw if dw != 0: dw_min = fmin(fabs(dw), dw_min) self.spectrum[row, col] = self.spectra(t, w=dw).real self.spectrum[col, row] = self.spectra(t, w=-dw).real return dw_min cdef Data _br_term(self, Data A_eig, double cutoff): if self.tensortype == DENSE: return _br_term_dense(A_eig, self.spectrum, self.skew, cutoff) elif self.tensortype == SPARSE: return _br_term_sparse(A_eig, self.spectrum, self.skew, cutoff) elif self.tensortype == DATA: return _br_term_data(A_eig, self.spectrum, self.skew, cutoff) raise ValueError('Invalid tensortype') cpdef object qobj(self, t): return Qobj(self.data(t), dims=self.dims, copy=False, superrep="super") cpdef object coeff(self, t): return 1. cpdef Data data(self, t): cdef size_t i cdef double cutoff = self.sec_cutoff * self._compute_spectrum(t) A_eig = self.H.to_eigbasis(t, self.a_op._call(t)) BR_eig = self._br_term(A_eig, cutoff) if self.eig_basis: return BR_eig return self.H.from_eigbasis(t, BR_eig) cdef Data matmul_data_t(self, t, Data state, Data out=None): cdef size_t i cdef double cutoff = self.sec_cutoff * self._compute_spectrum(t) cdef Data A_eig, BR_eig if not self.eig_basis: state = self.H.to_eigbasis(t, state) if not self.eig_basis and out is not None: out = self.H.to_eigbasis(t, out) A_eig = self.H.to_eigbasis(t, self.a_op._call(t)) BR_eig = self._br_term(A_eig, cutoff) out = _data.add(_data.matmul(BR_eig, state), out) if not self.eig_basis: out = self.H.from_eigbasis(t, out) return out def linear_map(self, f, anti=False): return _MapElement(self, [f]) def replace_arguments(self, args, cache=None): if cache is None: return _BlochRedfieldElement( self.H, QobjEvo(self.a_op, args=args), self.spectra, self.sec_cutoff ) H = None for old, new in cache: if old is self: return new if old is self.H: H = new if H is None: H = _EigenBasisTransform(QobjEvo(self.H.oper, args=args), type(self.H.oper) is CSR) new = _BlochRedfieldElement( H, QobjEvo(self.a_op, args=args), self.spectra.replace_arguments(**args), self.sec_cutoff ) cache.append((self, new)) cache.append((self.H, H)) return new def __matmul__(left, right): return _ProdElement(left, right, []) def __mul__(left, right): cdef _MapElement out if type(left) is _BlochRedfieldElement: out = _MapElement(left, [], right) if type(right) is _BlochRedfieldElement: out = _MapElement(right, [], left) return out qutip-5.1.1/qutip/core/_brtools.pxd000066400000000000000000000016521474175217300173310ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.cy.qobjevo cimport QobjEvo from qutip.core.cy.coefficient cimport Coefficient from qutip.core.data cimport Data cdef class SpectraCoefficient(Coefficient): cdef Coefficient coeff_t cdef Coefficient coeff_w cdef double w cpdef Data matmul_var_data(Data left, Data right, int transleft, int transright) cdef class _EigenBasisTransform: cdef: QobjEvo oper int size readonly bint isconstant double _t object _eigvals # np.ndarray Data _evecs, _evecs_inv cpdef object eigenvalues(self, double t) cpdef Data evecs(self, double t) cpdef Data to_eigbasis(self, double t, Data fock) cpdef Data from_eigbasis(self, double t, Data eig) cdef Data _inv(self, double t) cdef void _compute_eigen(self, double t) except * cdef Data _S_converter(self, double t) cdef Data _S_converter_inverse(self, double t) qutip-5.1.1/qutip/core/_brtools.pyx000066400000000000000000000262241474175217300173600ustar00rootroot00000000000000#cython: language_level=3 from libc.math cimport fabs, fmin from libc.float cimport DBL_MAX cimport numpy as cnp import numpy as np cimport cython from qutip.core.cy.qobjevo cimport QobjEvo from qutip.core.cy.coefficient cimport Coefficient from qutip.core.data cimport Data, Dense, idxint import qutip.core.data as _data from qutip.core import Qobj from scipy.linalg cimport cython_blas as blas __all__ = ['SpectraCoefficient'] cdef class SpectraCoefficient(Coefficient): """ Change a Coefficient with `t` dependence to one with `w` dependence to use in Bloch-Redfield tensor to allow array based coefficients to be used as spectral functions. If 2 coefficients are passed, the first one is the frequence response and the second is the time response. """ def __init__(self, Coefficient coeff_w, Coefficient coeff_t=None, double w=0): self.coeff_t = coeff_t self.coeff_w = coeff_w self.w = w cdef complex _call(self, double t) except *: if self.coeff_t is None: return self.coeff_w(self.w) return self.coeff_t(t) * self.coeff_w(self.w) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return SpectraCoefficient(self.coeff_t, self.coeff_w, self.w) def replace_arguments(self, _args=None, *, w=None, **kwargs): if _args: kwargs.update(_args) if kwargs: return SpectraCoefficient( self.coeff_w.replace(**kwargs), self.coeff_t.replace(**kwargs) if self.coeff_t else None, kwargs.get('w', w or self.w) ) if w is not None: return SpectraCoefficient(self.coeff_w, self.coeff_t, w) return self cdef Data _apply_trans(Data original, int trans): """helper function for matmul_var_data, apply transform.""" cdef Data out if trans == 0: out = original elif trans == 1: out = original.transpose() elif trans == 2: out = original.conj() elif trans == 3: out = original.adjoint() return out cdef char _fetch_trans_code(int trans): """helper function for matmul_var_Dense, fetch the blas flag byte""" if trans == 0: return b'N' elif trans == 1: return b'T' elif trans == 3: return b'C' cpdef Data matmul_var_data(Data left, Data right, int transleft, int transright): """ matmul which input matrices can be transposed or adjoint. out = transleft(left) @ transright(right) with trans[left, right]: 0 : Normal 1 : Transpose 2 : Conjugate 3 : Adjoint """ # Should this be supported in data.matmul? # A.dag() @ A is quite common. cdef int size cdef double complex beta cdef char left_code, right_code if ( type(left) is Dense and type(right) is Dense and left.shape[0] == left.shape[1] and left.shape[0] == right.shape[0] and left.shape[0] == right.shape[1] ): return matmul_var_Dense(left, right, transleft, transright) left = _apply_trans(left, transleft) right = _apply_trans(right, transright) return _data.matmul(left, right) cdef Dense matmul_var_Dense(Dense left, Dense right, int transleft, int transright): """ matmul which input matrices can be transposed or adjoint. out = transleft(left) @ transright(right) with trans[left, right]: 0 : Normal 1 : Transpose 2 : Conjugate 3 : Adjoint """ # blas support matmul for normal, transpose, adjoint for fortran ordered # matrices. if not ( left.shape[0] == left.shape[1] and left.shape[0] == right.shape[0] and left.shape[0] == right.shape[1] ): raise ValueError("Only implemented for square operators") cdef Dense out, a, b cdef double complex alpha = 1., beta = 0. cdef int tleft, tright, size = left.shape[0] # Since fortran to C equivalent to transpose, fix the codes to fortran tleft = transleft ^ (not left.fortran) tright = transright ^ (not right.fortran) # blas.zgemm does not support adjoint. if tleft + tright == 5: # adjoint and conjugate, we can't transpose the output to use zgemm out = matmul_var_data(left, right, transleft-2, transright-2) return out.conj() if tleft == 2 or tright == 2: # Need a conjugate, we compute the transpose of the desired results. # A.conj @ B^op -> (B^T^op @ A.dag)^T out = _data.dense.empty(left.shape[0], right.shape[1], False) a, b = right, left tleft, tright = tright ^ 1, tleft ^ 1 else: out = _data.dense.empty(left.shape[0], right.shape[1], True) a, b = left, right left_code = _fetch_trans_code(tleft) right_code = _fetch_trans_code(tright) blas.zgemm(&left_code, &right_code, &size, &size, &size, &alpha, ( a).data, &size, ( b).data, &size, &beta, ( out).data, &size) return out class _eigen_qevo: """ Callable function to represent the eigenvectors of a QobjEvo at a time ``t``. """ def __init__(self, qevo): self.qevo = QobjEvo(qevo) # Force a copy self.args = None # This is a base conversion operator, the eigen basis part of the dims # are flat. self.out_dims = [qevo.dims[0], [qevo.shape[1]]] def __call__(self, t, args): if args is not self.args: self.args = args self.qevo.arguments(self.args) _, data = _data.eigs(self.qevo._call(t), True, True) return Qobj(data, copy=False, dims=self.out_dims) cdef class _EigenBasisTransform: """ For an hermitian operator, compute the eigenvalues and eigenstates and do the base change to and from that eigenbasis. parameter --------- oper : QobjEvo Hermitian operator for which to compute the eigenbasis. sparse : bool [False] Whether to use sparse solver for eigen decomposition. """ def __init__(self, QobjEvo oper, bint sparse=False): if oper.dims[0] != oper.dims[1]: raise ValueError if type(oper(0).data) in (_data.CSR, _data.Dia) and not sparse: oper = oper.to(Dense) self.oper = oper self.isconstant = oper.isconstant self.size = oper.shape[0] if oper.isconstant: self._eigvals, self._evecs = _data.eigs(self.oper._call(0), True, True) else: self._evecs = None self._eigvals = None self._t = np.nan self._evecs_inv = None def as_Qobj(self): """Make an Qobj or QobjEvo of the eigenvectors.""" if self.isconstant: return Qobj(self.evecs(0), dims=self.oper.dims) else: return QobjEvo(_eigen_qevo(self.oper)) cdef void _compute_eigen(self, double t) except *: if self._t != t and not self.isconstant: self._t = t self._evecs_inv = None self._eigvals, self._evecs = _data.eigs(self.oper._call(t), True, True) cpdef object eigenvalues(self, double t): """ Return the eigenvalues at ``t``. """ self._compute_eigen(t) return self._eigvals cpdef Data evecs(self, double t): """ Return the eigenstates at ``t``. """ self._compute_eigen(t) return self._evecs cdef Data _inv(self, double t): if self._evecs_inv is None: self._evecs_inv = self.evecs(t).adjoint() return self._evecs_inv cdef Data _S_converter(self, double t): return _data.kron_transpose(self.evecs(t), self._inv(t)) cdef Data _S_converter_inverse(self, double t): return _data.kron_transpose(self._inv(t), self.evecs(t)) cpdef Data to_eigbasis(self, double t, Data fock): """ Do the transformation of the :cls:`Qobj` ``fock`` to the basis where ``oper(t)`` is diagonalized. """ # For Hermitian operator, the inverse of evecs is the adjoint matrix. # Blas include A.dag @ B in one operation. We use it if we can so we # don't make unneeded copy of evecs. cdef Data temp if fock.shape[0] == self.size and fock.shape[1] == 1: return matmul_var_data(self.evecs(t), fock, 3, 0) elif fock.shape[0] == self.size**2 and fock.shape[1] == 1: if type(fock) is Dense and ( fock).fortran: fock = _data.column_unstack_dense(fock, self.size, True) temp = _data.matmul(matmul_var_data(self.evecs(t), fock, 3, 0), self.evecs(t)) fock = _data.column_stack_dense(fock, True) else: fock = _data.column_unstack(fock, self.size) temp = _data.matmul(matmul_var_data(self.evecs(t), fock, 3, 0), self.evecs(t)) if type(temp) is Dense: return _data.column_stack_dense(temp, True) return _data.column_stack(temp) elif fock.shape[0] == self.size and fock.shape[0] == fock.shape[1]: return _data.matmul(matmul_var_data(self.evecs(t), fock, 3, 0), self.evecs(t)) elif fock.shape[0] == self.size**2 and fock.shape[0] == fock.shape[1]: temp = self._S_converter_inverse(t) return _data.matmul(matmul_var_data(temp, fock, 3, 0), temp) raise ValueError("Could not convert the Qobj's data to eigenbasis: " "can't guess type from shape.") cpdef Data from_eigbasis(self, double t, Data eig): """ Do the transformation of the :cls:`Qobj` ``eig`` in the basis where ``oper(t)`` is diagonalized to the outside basis. """ cdef Data temp if eig.shape[0] == self.size and eig.shape[1] == 1: return _data.matmul(self.evecs(t), eig) elif eig.shape[0] == self.size**2 and eig.shape[1] == 1: if type(eig) is Dense and ( eig).fortran: eig = _data.column_unstack_dense(eig, self.size, True) temp = matmul_var_data(_data.matmul(self.evecs(t), eig), self.evecs(t), 0, 3) eig = _data.column_stack_dense(eig, True) else: eig = _data.column_unstack(eig, self.size) temp = matmul_var_data(_data.matmul(self.evecs(t), eig), self.evecs(t), 0, 3) if type(temp) is Dense: return _data.column_stack_dense(temp, True) return _data.column_stack(temp) elif eig.shape[0] == self.size and eig.shape[0] == eig.shape[1]: temp = self.evecs(t) return matmul_var_data(_data.matmul(temp, eig), temp, 0, 3) elif eig.shape[0] == self.size**2 and eig.shape[0] == eig.shape[1]: temp = self._S_converter_inverse(t) return _data.matmul(temp, matmul_var_data(eig, temp, 0, 3)) raise ValueError("Could not convert the Qobj's data from eigenbasis: " "can't guess type from shape.") qutip-5.1.1/qutip/core/blochredfield.py000066400000000000000000000203541474175217300201310ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations import os import inspect import numpy as np from typing import overload from qutip.settings import settings as qset from . import Qobj, QobjEvo, liouvillian, coefficient, sprepost from ._brtools import SpectraCoefficient, _EigenBasisTransform from .cy.coefficient import InterCoefficient, Coefficient from ._brtensor import _BlochRedfieldElement from ..typing import CoeffProtocol __all__ = ['bloch_redfield_tensor', 'brterm'] @overload def bloch_redfield_tensor( H: Qobj, a_ops: list[tuple[Qobj, Coefficient | str | CoeffProtocol]], c_ops: list[Qobj] = None, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> Qobj: ... @overload def bloch_redfield_tensor( H: Qobj | QobjEvo, a_ops: list[tuple[Qobj | QobjEvo, Coefficient | str | CoeffProtocol]], c_ops: list[Qobj | QobjEvo] = None, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> QobjEvo: ... def bloch_redfield_tensor( H: Qobj | QobjEvo, a_ops: list[tuple[Qobj | QobjEvo, Coefficient | str | CoeffProtocol]], c_ops: list[Qobj | QobjEvo] = None, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> Qobj | QobjEvo: """ Calculates the Bloch-Redfield tensor for a system given a set of operators and corresponding spectral functions that describes the system's coupling to its environment. Parameters ---------- H : :class:`qutip.Qobj`, :class:`qutip.QobjEvo` System Hamiltonian. a_ops : list of (a_op, spectra) Nested list of system operators that couple to the environment, and the corresponding bath spectra. a_op : :class:`qutip.Qobj`, :class:`qutip.QobjEvo` The operator coupling to the environment. Must be hermitian. spectra : :obj:`.Coefficient`, func, str The corresponding bath spectra. Can be a :obj:`.Coefficient` using an 'w' args, a function of the frequency or a string. The :class:`SpectraCoefficient` can be used for array based coefficient. The spectra can depend on ``t`` if the corresponding ``a_op`` is a :obj:`.QobjEvo`. Example: .. code-block:: a_ops = [ (a+a.dag(), coefficient('w>0', args={"w": 0})), (QobjEvo(a+a.dag()), 'w > exp(-t)'), (QobjEvo([b+b.dag(), lambda t: ...]), lambda w: ...)), (c+c.dag(), SpectraCoefficient(coefficient(ws, tlist=ts))), ] c_ops : list List of system collapse operators. sec_cutoff : float {0.1} Cutoff for secular approximation. Use ``-1`` if secular approximation is not used when evaluating bath-coupling terms. fock_basis : bool {False} Whether to return the tensor in the input basis or the diagonalized basis. sparse_eigensolver : bool {False} Whether to use the sparse eigensolver br_dtype : ['sparse', 'dense', 'data'] Which data type to use when computing the brtensor. With a cutoff 'sparse' is usually the most efficient. Returns ------- R, [evecs]: :class:`qutip.Qobj`, tuple of :class:`qutip.Qobj` If ``fock_basis``, return the Bloch Redfield tensor in the laboratory basis. Otherwise return the Bloch Redfield tensor in the diagonalized Hamiltonian basis and the eigenvectors of the Hamiltonian as hstacked column. """ R = liouvillian(H, c_ops) H_transform = _EigenBasisTransform(QobjEvo(H), sparse_eigensolver) if fock_basis: for (a_op, spectra) in a_ops: R += brterm(H_transform, a_op, spectra, sec_cutoff, True, br_dtype=br_dtype) return R else: # When the Hamiltonian is time-dependent, the transformation of `L` to # eigenbasis is not optimized. if isinstance(R, QobjEvo): # The `sprepost` will be computed 2 times for each parts of `R`. # Compressing the QobjEvo will lower the number of parts. R.compress() evec = H_transform.as_Qobj() R = sprepost(evec, evec.dag()) @ R @ sprepost(evec.dag(), evec) for (a_op, spectra) in a_ops: R += brterm(H_transform, a_op, spectra, sec_cutoff, False, br_dtype=br_dtype)[0] return R, H_transform.as_Qobj() @overload def brterm( H: Qobj, a_op: Qobj, spectra: Coefficient | CoeffProtocol | str, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> Qobj: ... @overload def brterm( H: Qobj | QobjEvo, a_op: Qobj | QobjEvo, spectra: Coefficient | CoeffProtocol | str, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> QobjEvo: ... def brterm( H: Qobj | QobjEvo, a_op: Qobj | QobjEvo, spectra: Coefficient | CoeffProtocol | str, sec_cutoff: float = 0.1, fock_basis: bool = False, sparse_eigensolver: bool = False, br_dtype: str = 'sparse', ) -> Qobj | QobjEvo: """ Calculates the contribution of one coupling operator to the Bloch-Redfield tensor. Parameters ---------- H : :class:`qutip.Qobj`, :class:`qutip.QobjEvo` System Hamiltonian. a_op : :class:`qutip.Qobj`, :class:`qutip.QobjEvo` The operator coupling to the environment. Must be hermitian. spectra : :obj:`.Coefficient`, func, str The corresponding bath spectra. Can be a :obj:`.Coefficient` using an 'w' args, a function of the frequency or a string. The :class:`SpectraCoefficient` can be used for array based coefficient. The spectra can depend on ``t`` if the corresponding ``a_op`` is a :obj:`.QobjEvo`. Example: coefficient('w>0', args={"w": 0}) SpectraCoefficient(coefficient(array, tlist=...)) sec_cutoff : float {0.1} Cutoff for secular approximation. Use ``-1`` if secular approximation is not used when evaluating bath-coupling terms. fock_basis : bool {False} Whether to return the tensor in the input basis or the diagonalized basis. sparse_eigensolver : bool {False} Whether to use the sparse eigensolver on the Hamiltonian. br_dtype : ['sparse', 'dense', 'data'] Which data type to use when computing the brtensor. With a cutoff 'sparse' is usually the most efficient. Returns ------- R, [evecs]: :obj:`.Qobj`, :obj:`.QobjEvo` or tuple If ``fock_basis``, return the Bloch Redfield tensor in the outside basis. Otherwise return the Bloch Redfield tensor in the diagonalized Hamiltonian basis and the eigenvectors of the Hamiltonian as hstacked column. The tensors and, if given, evecs, will be :obj:`.QobjEvo` if the ``H`` and ``a_op`` is time dependent, :obj:`.Qobj` otherwise. """ if isinstance(H, _EigenBasisTransform): Hdiag = H else: Hdiag = _EigenBasisTransform(QobjEvo(H), sparse=sparse_eigensolver) # convert spectra to Coefficient if isinstance(spectra, str): spectra = coefficient(spectra, args={'w': 0}) elif isinstance(spectra, InterCoefficient): spectra = SpectraCoefficient(spectra) elif isinstance(spectra, Coefficient): pass elif callable(spectra): sig = inspect.signature(spectra) if tuple(sig.parameters.keys()) == ("w",): spectra = SpectraCoefficient(coefficient(spectra)) else: spectra = coefficient(spectra, args={'w': 0}) else: raise TypeError("a_ops's spectra not known") sec_cutoff = sec_cutoff if sec_cutoff >= 0 else np.inf R = QobjEvo(_BlochRedfieldElement(Hdiag, QobjEvo(a_op), spectra, sec_cutoff, not fock_basis, dtype=br_dtype)) if ( ((isinstance(H, _EigenBasisTransform) and H.isconstant) or isinstance(H, Qobj)) and isinstance(a_op, Qobj) ): R = R(0) return R if fock_basis else (R, Hdiag.as_Qobj()) qutip-5.1.1/qutip/core/coefficient.py000066400000000000000000000651021474175217300176210ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations import numpy as np from numpy.typing import ArrayLike import scipy import scipy.interpolate import os import sys import re import dis import hashlib import glob import importlib import warnings import numbers from collections import defaultdict try: from setuptools import setup, Extension from Cython.Build import cythonize import filelock except ImportError: pass from ..settings import settings as qset from .options import QutipOptions from .data import Data from .cy.coefficient import ( Coefficient, InterCoefficient, FunctionCoefficient, StrFunctionCoefficient, ConjCoefficient, NormCoefficient, ConstantCoefficient ) from qutip.typing import CoefficientLike __all__ = ["coefficient", "CompilationOptions", "Coefficient", "clean_compiled_coefficient"] class StringParsingWarning(Warning): pass def _return(base, **kwargs): return base # The `coefficient` function is dispatcher for the type of the `base` to the # function that created the `Coefficient` object. `coefficient_builders` stores # the map `type -> function(base, **kw)`. Optional module can add their # `Coefficient` specializations here. coefficient_builders = { Coefficient: _return, np.ndarray: InterCoefficient, scipy.interpolate.PPoly: InterCoefficient.from_PPoly, scipy.interpolate.BSpline: InterCoefficient.from_Bspline, numbers.Number: ConstantCoefficient, } def coefficient( base: CoefficientLike, *, tlist: ArrayLike = None, args: dict = {}, args_ctypes: dict = {}, order: int = 3, compile_opt: dict = None, function_style: str = None, boundary_conditions: tuple | str = None, **kwargs ): """Build ``Coefficient`` for time dependent systems: ``` QobjEvo = Qobj + Qobj * Coefficient + Qobj * Coefficient + ... ``` The coefficients can be a function, a string or a numpy array. Other packages may add support for other kind of coefficients. For function based coefficients, the function signature must be either: * ``f(t, ...)`` where the other arguments are supplied as ordinary "pythonic" arguments (e.g. ``f(t, w, a=5)``) * ``f(t, args)`` where the arguments are supplied in a "dict" named ``args`` By default the signature style is controlled by the ``qutip.settings.core["function_coefficient_style"]`` setting, but it may be overriden here by specifying either ``function_style="pythonic"`` or ``function_style="dict"``. *Examples*: - pythonic style function signature:: def f1_t(t, w): return np.exp(-1j * t * w) coeff1 = coefficient(f1_t, args={"w": 1.}) - dict style function signature:: def f2_t(t, args): return np.exp(-1j * t * args["w"]) coeff2 = coefficient(f2_t, args={"w": 1.}) For string based coeffients, the string must be a compilable python code resulting in a complex. The following symbols are defined: sin, cos, tan, asin, acos, atan, pi, sinh, cosh, tanh, asinh, acosh, atanh, exp, log, log10, erf, zerf, sqrt, real, imag, conj, abs, norm, arg, proj, numpy as np, scipy.special as spe (python interface) and cython_special (scipy cython interface) *Examples*:: coeff = coefficient('exp(-1j*w1*t)', args={"w1":1.}) 'args' is needed for string coefficient at compilation. It is a dict of (name:object). The keys must be a valid variables string. Compilation options can be passed as "compile_opt=CompilationOptions(...)". For numpy array format, the array must be an 1d of dtype float or complex. A list of times (float64) at which the coeffients must be given (tlist). The coeffients array must have the same len as the tlist. The time of the tlist do not need to be equidistant, but must be sorted. By default, a cubic spline interpolation will be used to compute the coefficient at time t. The keyword ``order`` sets the order of the interpolation. When ``order = 0``, the interpolation is step function that evaluates to the most recent value. *Examples*:: tlist = np.logspace(-5,0,100) H = QobjEvo(np.exp(-1j*tlist), tlist=tlist) ``scipy.interpolate``'s ``CubicSpline``, ``PPoly`` and ``Bspline`` are also converted to interpolated coefficients (the same kind of coefficient created from ``ndarray``). Other interpolation methods from scipy are converted to a function-based coefficient (the same kind of coefficient created from callables). Parameters ---------- base : object Base object to make into a Coefficient. args : dict, optional Dictionary of arguments to pass to the function or string coefficient. order : int, default=3 Order of the spline for array based coefficient. tlist : iterable, optional Times for each element of an array based coefficient. function_style : str {"dict", "pythonic", None}, optional Function signature of function based coefficients. args_ctypes : dict, optional C type for the args when compiling array based coefficients. compile_opt : CompilationOptions, optional Sets of options for the compilation of string based coefficients. boundary_conditions: 2-tupule, str or None, optional Specify boundary conditions for spline interpolation. **kwargs Extra arguments to pass the the coefficients. """ kwargs.update({ "tlist": tlist, 'args': args, 'args_ctypes': args_ctypes, 'order': order, 'compile_opt': compile_opt, 'function_style': function_style, 'boundary_conditions': boundary_conditions }) for type_ in coefficient_builders: if isinstance(base, type_): return coefficient_builders[type_](base, **kwargs) if callable(base): op = FunctionCoefficient(base, args.copy(), style=function_style) if not isinstance(op(0), numbers.Number): raise TypeError("The coefficient function must return a number") return op else: raise ValueError("coefficient format not understood") def norm(coeff): """ return a Coefficient with is the norm: |c|^2. """ return NormCoefficient(coeff) def conj(coeff): """ return a Coefficient with is the conjugate. """ return ConjCoefficient(coeff) def const(value): """ return a Coefficient with a constant value. """ return ConstantCoefficient(value) # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # %%%%%%%%% Everything under this is for string compilation %%%%%%%%% # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WARN_MISSING_MODULE = [0] class CompilationOptions(QutipOptions): """ Options that control compilation of string based coefficient to Cython. These options can be set globaly: ``settings.compile["compiler_flags"] = "-O1"`` In a ``with`` block: ``with CompilationOptions(use_cython=False):`` Or as an instance: ``coefficient(coeff, compile_opt=CompilationOptions(recompile=True))`` ******************** Compilation options: ******************** use_cython: bool Whether to compile strings as cython code or use python's ``exec``. recompile : bool Do not use previously made files but build a new one. try_parse: bool [True] Whether to try parsing the string for reuse and static typing. static_types : bool [True] Whether to use C types for constant and args. accept_int : None, bool Whether to use the type ``int`` for integer constants and args or upgrade it to ``float`` or ``complex``. If `None`, it will only use ``int`` when subscription is found in the code. accept_float : bool Whether to use the type ``float`` or upgrade them to ``complex``. compiler_flags : str Flags to pass to the compiler, ex: "-Wall -O3"... Flags not matching your comiler and OS may cause compilation to fail. Use "recompile=True", when trying to if the string pattern was previously used. link_flags : str Libraries to link to pass to the compiler. They can not be used to add function to the string coefficient. extra_import : str Cython code to add at the head of the file. Can be used to add extra import or cimport code, ex: extra_import="from scipy.linalg import det" extra_import="from qutip.core.data cimport CSR" clean_on_error : bool [True] When writing a cython file that cannot be imported, erase it. build_dir: str [None] cythonize's build_dir. """ _link_flags = "" _compiler_flags = "" if sys.platform == 'win32': _compiler_flags = '' elif sys.platform == 'darwin': _compiler_flags = '-w -O3 -funroll-loops -mmacosx-version-min=10.9' _link_flags += '-mmacosx-version-min=10.9' else: _compiler_flags = '-w -O3 -funroll-loops' try: import cython import filelock import setuptools _use_cython = True except ImportError: _use_cython = False WARN_MISSING_MODULE[0] = 1 _options = { "use_cython": _use_cython, "try_parse": True, "static_types": True, "accept_int": None, "accept_float": None, "recompile": False, "compiler_flags": _compiler_flags, "link_flags": _link_flags, "extra_import": "", "clean_on_error": True, "build_dir": None, } _settings_name = "compile" # Create the default instance in settings. qset.compile = CompilationOptions() # Version number of the Coefficient COEFF_VERSION = "1.2" try: root = os.path.join(qset.tmproot, f"qutip_coeffs_{COEFF_VERSION}") qset.coeffroot = root except OSError: qset.coeffroot = "." def clean_compiled_coefficient(all=False): """ Remove previouly compiled string Coefficient. Parameter: ---------- all: bool If not `all`, it will remove only previous version. """ import glob import shutil tmproot = qset.tmproot active = qset.coeffroot folders = glob.glob(os.path.join(tmproot, 'qutip_coeffs_') + "*") if all: shutil.rmtree(active) for folder in folders: if folder != active: shutil.rmtree(folder) # Recreate the empty folder. qset.coeffroot = qset.coeffroot def proj(x): if np.isfinite(x): return (x) else: return np.inf + 0j * np.imag(x) str_env = { "sin": np.sin, "cos": np.cos, "tan": np.tan, "asin": np.arcsin, "acos": np.arccos, "atan": np.arctan, "pi": np.pi, "sinh": np.sinh, "cosh": np.cosh, "tanh": np.tanh, "asinh": np.arcsinh, "acosh": np.arccosh, "atanh": np.arctanh, "exp": np.exp, "log": np.log, "log10": np.log10, "erf": scipy.special.erf, "zerf": scipy.special.erf, "sqrt": np.sqrt, "real": np.real, "imag": np.imag, "conj": np.conj, "abs": np.abs, "norm": lambda x: np.abs(x)**2, "arg": np.angle, "proj": proj, "np": np, "spe": scipy.special} def coeff_from_str(base, args, args_ctypes, compile_opt=None, **_): """ Entry point for string based coefficients - Test if the string is valid - Parse: "cos(a*t)" and "cos( w1 * t )" should be recognised as the same compiled object. - Verify if already compiled and compile if not """ # First, a sanity check before thinking of compiling if compile_opt is None: compile_opt = qset.compile if not compile_opt['extra_import']: try: env = {"t": 0} env.update(args) exec(base, str_env, env) except Exception as err: raise Exception("Invalid string coefficient") from err coeff = None # Do we compile? if not compile_opt['use_cython']: if WARN_MISSING_MODULE[0]: warnings.warn( "`cython`, `setuptools` and `filelock` are required for " "compilation of string coefficents. Falling back on `eval`.") # Only warns once. WARN_MISSING_MODULE[0] = 0 return StrFunctionCoefficient(base, args) # Parsing tries to make the code in common pattern parsed, variables, constants, raw = try_parse(base, args, args_ctypes, compile_opt) # Once parsed, the code should be unique enough to get a filename hash_ = hashlib.sha256(bytes(parsed, encoding='utf8')) file_name = "qtcoeff_" + hash_.hexdigest()[:30] # See if it already exist and import it. if not compile_opt['recompile']: coeff = try_import(file_name, parsed) if not coeff and qset.coeff_write_ok: # Previously compiled coefficient not available: create the cython code code = make_cy_code(parsed, variables, constants, raw, compile_opt) try: coeff = compile_code(code, file_name, parsed, compile_opt) except PermissionError: pass if coeff is None: # We don't use cython or compilation failed return StrFunctionCoefficient(base, args) keys = [key for _, key, _ in variables] const = [fromstr(val) for _, val, _ in constants] return coeff(base, keys, const, args) coefficient_builders[str] = coeff_from_str def try_import(file_name, parsed_in): """ Import the compiled coefficient if existing and check for name collision. """ try: mod = importlib.import_module(file_name) except ModuleNotFoundError: # Coefficient does not exist, to compile as file_name return None if mod.parsed_code == parsed_in: # Coefficient found! return mod.StrCoefficient else: raise ValueError("string hash collision, change the string " "or clean files in qutip.settings.coeffroot") def make_cy_code(code, variables, constants, raw, compile_opt): """ Generate the code for the string coefficients. """ cdef_cte = "" init_cte = "" copy_cte = "" for i, (name, val, ctype) in enumerate(constants): cdef_cte += " {} {}\n".format(ctype, name[5:]) copy_cte += " out.{} = {}\n".format(name[5:], name) init_cte += " {} = cte[{}]\n".format(name, i) cdef_var = "" init_var = "" init_arg = "" replace_var = "" call_var = "" copy_var = "" for i, (name, val, ctype) in enumerate(variables): cdef_var += " str key{}\n".format(i) cdef_var += " {} {}\n".format(ctype, name[5:]) copy_var += " out.key{} = self.key{}\n".format(i, i) copy_var += " out.{} = {}\n".format(name[5:], name) if not raw: init_var += " self.key{} = var[{}]\n".format(i, i) else: init_var += " self.key{} = '{}'\n".format(i, val) init_arg += " {} = args[self.key{}]\n".format(name, i) replace_var += " if self.key{} in kwargs:\n".format(i) replace_var += (" out.{}" " = kwargs[self.key{}]\n".format(name[5:], i)) if raw: call_var += " cdef {} {} = {}\n".format(ctype, val, name) code = f"""#cython: language_level=3 # This file is generated automatically by QuTiP. import numpy as np import scipy.special as spe from scipy.special cimport cython_special cimport cython from qutip.core.cy.coefficient cimport Coefficient from qutip.core.cy.math cimport erf, zerf from qutip.core.cy.complex_math cimport * from qutip.core.data cimport Data cdef double pi = 3.14159265358979323 {compile_opt['extra_import']} parsed_code = "{code}" @cython.auto_pickle(True) cdef class StrCoefficient(Coefficient): \"\"\" String compiled as a :obj:`.Coefficient` using cython. \"\"\" cdef: str codeString {cdef_cte}{cdef_var} def __init__(self, base, var, cte, args): self.codeString = base {init_cte}{init_var}{init_arg} cpdef Coefficient copy(self): \"\"\"Return a copy of the :obj:`.Coefficient`.\"\"\" cdef StrCoefficient out = StrCoefficient.__new__(StrCoefficient) out.codeString = self.codeString {copy_cte}{copy_var} return out def replace_arguments(self, _args=None, **kwargs): \"\"\" Return a :obj:`.Coefficient` with args changed for :obj:`.Coefficient` built from 'str' or a python function. Or a the :obj:`.Coefficient` itself if the :obj:`.Coefficient` does not use arguments. New arguments can be passed as a dict or as keywords. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. \"\"\" cdef StrCoefficient out if _args: kwargs.update(_args) if kwargs: out = self.copy() {replace_var} return out return self @cython.initializedcheck(False) @cython.cdivision(True) cdef complex _call(self, double t) except *: {call_var} return {code} """ return code def compile_code(code, file_name, parsed, c_opt): pwd = os.getcwd() os.chdir(qset.coeffroot) # Files with the same name, but differents extension than the pyx file, are # erased during cythonization process, breaking filelock. # Adding a prefix make them safe to use. lock = filelock.FileLock("compile_lock_" + file_name + ".lock") try: lock.acquire(timeout=0) for file in glob.glob(file_name + "*"): os.remove(file) file_ = open(file_name + ".pyx", "w") file_.writelines(code) file_.close() oldargs = sys.argv try: sys.argv = ["setup.py", "build_ext", "--inplace"] coeff_file = Extension( file_name, sources=[file_name + ".pyx"], extra_compile_args=c_opt['compiler_flags'].split(), extra_link_args=c_opt['link_flags'].split(), include_dirs=[np.get_include()], language='c++' ) ext_modules = cythonize( coeff_file, force=True, build_dir=c_opt['build_dir'] ) setup(ext_modules=ext_modules) except Exception as e: if c_opt['clean_on_error']: for file in glob.glob(file_name + "*"): os.remove(file) raise Exception("Could not compile") from e finally: sys.argv = oldargs except filelock.Timeout: with lock: # We wait for the lock to be released and then retry the import. pass finally: lock.release() os.chdir(pwd) return try_import(file_name, parsed) # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # %%%%%%%%% Everything under this is for parsing string %%%%%%%%% # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # Parsing here is extracting constants and args name to replace them with # attribute of the Coefficient so similar string like: # "2.*cos(a*t)", "5.2 * cos(w1 *t)", "5 * cos(w3 * t)" # are all reconized as the same compiled object and only compiled once. # Weakness: # typing: "1" and "1j" or the type of args ("w1") make different object # complex: "1+1j" is seens as cte(double) + cte(complex) # negative: "-1" is not seens as a constant but "- constant" # # int and double can be seens as complex with flags in CompilationOptions def fromstr(base): """Read a varibles in a string""" ls = {} exec("out = " + base, {}, ls) return ls["out"] typeCodes = { "Data": "_datalayer", "complex": "_cpl", "double": "_dbl", "int": "_int", "str": "_str", "object": "_obj" } def compileType(value): """Obtain the index of typeCodes that correspond to the value 4.5 -> 'double'...""" if isinstance(value, Data): ctype = "Data" elif isinstance(value, numbers.Integral): ctype = "int" elif isinstance(value, numbers.Real): ctype = "double" elif isinstance(value, numbers.Complex): ctype = "complex" elif isinstance(value, str): ctype = "str" else: ctype = "object" return ctype def find_type_from_str(chars): """ '1j' -> complex """ try: lc = {} exec("out = " + chars, {}, lc) return compileType(lc["out"]) except Exception: return None def fix_type(ctype, accept_int, accept_float): """int and double could be complex to limit the number of compiled object. change the types is we choose not to support all. """ if ctype == "int" and not accept_int: ctype = "double" if ctype == "double" and not accept_float: ctype = "complex" return ctype def extract_constant(code): """Look for floating and complex constants and replace them with variable. """ code = " " + code + " " contants = [] code = extract_cte_pattern(code, contants, "[^0-9a-zA-Z_][0-9]*[.]?[0-9]+e[+-]?[0-9]*[j]?") code = extract_cte_pattern(code, contants, "[^0-9a-zA-Z_][0-9]+[.]?[0-9]*e[+-]?[0-9]*[j]?") code = extract_cte_pattern(code, contants, "[^0-9a-zA-Z_][0-9]+[.]?[0-9]*[j]?") code = extract_cte_pattern(code, contants, "[^0-9a-zA-Z_][0-9]*[.]?[0-9]+[j]?") return code, contants def extract_cte_pattern(code, constants, pattern): """replace the constant following a pattern with variable""" const_strs = re.findall(pattern, code) for cte in const_strs: name = " _cte_temp{}_ ".format(len(constants)) code = code.replace(cte, cte[0] + name, 1) constants.append((name[1:-1], cte[1:], find_type_from_str(cte[1:]))) return code def space_parts(code, names): """Force spacing: single space between element""" for name in names: code = re.sub("(?<=[^0-9a-zA-Z_])" + name + "(?=[^0-9a-zA-Z_])", " " + name + " ", code) code = " ".join(code.split()) return code def parse(code, args, compile_opt): """ Read the code and rewrite it in a reutilisable form: Ins: '2.*cos(a*t)', {"a":5+1j} Outs: code = 'self._cte_dbl0 * cos ( self._arg_cpl0 * t )' variables = [('self._arg_cpl0', 'a', 'complex')] ordered_constants = [('self._cte_dbl0', 2, 'double')] """ code, constants = extract_constant(code) names = re.findall("[0-9a-zA-Z_]+", code) code = space_parts(code, names) constants_names = [const[0] for const in constants] new_code = [] ordered_constants = [] variables = [] typeCounts = defaultdict(lambda: 0) accept_int = compile_opt['accept_int'] accept_float = compile_opt['accept_float'] if accept_int is None: # If there is a subscript: a[b] int are always accepted to be safe # with TypeError. # Also comparison is not supported for complex. accept_int = "SUBSCR" in dis.Bytecode(code).dis() if accept_float is None: accept_float = "COMPARE_OP" in dis.Bytecode(code).dis() for word in code.split(): if word not in names: # syntax new_code.append(word) elif word in args: # find first if the variable is use more than once and reuse var_name = [var_name for var_name, name, _ in variables if word == name] if var_name: var_name = var_name[0] else: ctype = compileType(args[word]) ctype = fix_type(ctype, accept_int, accept_float) var_name = ("self._arg" + typeCodes[ctype] + str(typeCounts[ctype])) typeCounts[ctype] += 1 variables.append((var_name, word, ctype)) new_code.append(var_name) elif word in constants_names: name, val, ctype = constants[int(word[9:-1])] ctype = fix_type(ctype, accept_int, accept_float) cte_name = "self._cte" + typeCodes[ctype] +\ str(len(ordered_constants)) new_code.append(cte_name) ordered_constants.append((cte_name, val, ctype)) else: # Hopefully a buildin or known object new_code.append(word) code = " ".join(new_code) return code, variables, ordered_constants def use_hinted_type(variables, code, args_ctypes): variables_manually_typed = [] for i, (name, key, type_) in enumerate(variables): if key in args_ctypes: new_name = "self._custom_" + args_ctypes[key] + str(i) code = code.replace(name, new_name) variables_manually_typed.append((new_name, key, args_ctypes[key])) else: variables_manually_typed.append((name, key, type_)) return code, variables_manually_typed def try_parse(code, args, args_ctypes, compile_opt): """ Try to parse and verify that the result is still usable. """ if not compile_opt['try_parse']: variables = [("self." + name, name, "object") for name in args if name in code] code, variables = use_hinted_type(variables, code, args_ctypes) return code, variables, [], True ncode, variables, constants = parse(code, args, compile_opt) if not compile_opt['static_types']: # Fallback to object variables = [(f, s, "object") for f, s, _ in variables] constants = [(f, s, "object") for f, s, _ in constants] ncode, variables = use_hinted_type(variables, ncode, args_ctypes) if ( (compile_opt['extra_import'] and not compile_opt['extra_import'].isspace()) or test_parsed(ncode, variables, constants, args) ): return ncode, variables, constants, False else: warnings.warn("Could not find c types", StringParsingWarning) remaped_variable = [] for _, name, ctype in variables: remaped_variable.append(("self." + name, name, "object")) return code, remaped_variable, [], True def test_parsed(code, variables, constants, args): """ Test if parsed code broke anything. """ class DummySelf: pass [setattr(DummySelf, cte[0][5:], fromstr(cte[1])) for cte in constants] [setattr(DummySelf, var[0][5:], args[var[1]]) for var in variables] loc_env = {"t": 0, 'self': DummySelf} try: exec(code, str_env, loc_env) except Exception: return False return True qutip-5.1.1/qutip/core/cy/000077500000000000000000000000001474175217300154005ustar00rootroot00000000000000qutip-5.1.1/qutip/core/cy/__init__.py000066400000000000000000000000001474175217300174770ustar00rootroot00000000000000qutip-5.1.1/qutip/core/cy/_element.pxd000066400000000000000000000021501474175217300177030ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data cimport CSR, Dense, Data from qutip.core.cy.coefficient cimport Coefficient from qutip.core.data.base cimport idxint from libcpp cimport bool cdef class _BaseElement: cdef Data _data cpdef Data data(self, t) cpdef object qobj(self, t) cpdef object coeff(self, t) cdef Data matmul_data_t(_BaseElement self, t, Data state, Data out=?) cdef class _ConstantElement(_BaseElement): cdef readonly object _qobj cdef class _EvoElement(_BaseElement): cdef readonly object _qobj cdef readonly Coefficient _coefficient cdef class _FuncElement(_BaseElement): cdef readonly object _func cdef readonly dict _args cdef readonly tuple _previous cdef readonly bint _f_pythonic cdef readonly set _f_parameters cdef class _MapElement(_BaseElement): cdef readonly _FuncElement _base cdef readonly list _transform cdef readonly double complex _coeff cdef class _ProdElement(_BaseElement): cdef readonly _BaseElement _left cdef readonly _BaseElement _right cdef readonly list _transform cdef readonly bool _conj qutip-5.1.1/qutip/core/cy/_element.pyx000066400000000000000000000512611474175217300177370ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False #cython: wraparound=False #cython: initializedcheck=False #cython: cdvision=True #cython: c_api_binop_methods=True from .. import data as _data from qutip.core.cy.coefficient import coefficient_function_parameters from qutip.core.data cimport Dense, Data, dense from qutip.core.data.matmul cimport * from math import nan as Nan cdef extern from "" namespace "std" nogil: double complex conj(double complex x) __all__ = ['_ConstantElement', '_EvoElement', '_FuncElement', '_MapElement', '_ProdElement'] cdef class _BaseElement: """ The representation of a single time-dependent term in the list of terms used by QobjEvo and solvers to describe operators. Conceptually each term is given by ``coeff(t) * qobj(t)`` where ``coeff`` is a complex coefficient and ``qobj`` is a :obj:`.Qobj`. Both are functions of time. :meth:`~_BaseElement.coeff` returns the coefficient at ``t``. :meth:`~_BaseElement.qobj` returns the :obj:`.Qobj`. For example, a :obj:`.QobjEvo` instance created by:: QobjEvo([sigmax(), [sigmay(), 'cos(pi * t)']]) would contain one :obj:`~_BaseElement` instance for the ``sigmax()`` term, and one for the ``[sigmay(), 'cos(pi*t)']`` term. :obj:`~_BaseElement` defines the interface to time-dependent terms. Sub-classes implement terms defined in different ways. For example, :obj:`~_ConstantElement` implements a term that consists only of a constant :obj:`.Qobj` (i.e. where there is no dependence on ``t``), :obj:`~_EvoElement` implements a term that consists of a time-dependet :obj:`.Coefficient` times a constant :obj:`.Qobj`, and so on. .. note:: There are three methods to return the factors of the term. :meth:`~_BaseElement.coeff` and :meth:`~_BaseElement.qobj` return the coefficient and operator factors respectively. They are separate to avoid constructing an intermediate Python object when called from Cython code (which may take as long as the rest of the call). :meth:`~BaseElement.data` is equivalent to ``.qobj(t).data`` and provides a convenience method for this common operation. .. note:: All :obj:`~_BaseElement` instances are immutable and methods that would modify an object return a new instance instead. """ cpdef Data data(self, t): """ Returns the underlying :obj:`~Data` of the :obj:`.Qobj` component of the term at time ``t``. Parameters ---------- t : double The time, ``t``. Returns ------- :obj:`~Data` The underlying data of the :obj:`.Qobj` component of the term at time ``t``. """ raise NotImplementedError( "Sub-classes of _BaseElement should implement .data(t)." ) cpdef object qobj(self, t): """ Returns the :obj:`.Qobj` component of the term at time ``t``. Parameters ---------- t : float The time, ``t``. Returns ------- :obj:`.Qobj` The :obj:`.Qobj` component of the term at time ``t``. """ raise NotImplementedError( "Sub-classes of _BaseElement should implement .qobj(t)." ) cpdef object coeff(self, t): """ Returns the complex coefficient of the term at time ``t``. Parameters ---------- t : float The time, ``t``. Returns ------- complex The complex coefficient of the term at time ``t``. """ raise NotImplementedError( "Sub-classes of _BaseElement should implement .coeff(t)." ) cdef Data matmul_data_t(_BaseElement self, t, Data state, Data out=None): """ Possibly in-place multiplication and addition. Multiplies a given state by the elemen's value at time ``t`` and adds the result to ``out``. Equivalent to:: out += self.coeff(t) * self.qobj(t) @ state Sub-classes may override :meth:`~matmul_data_t` to provide an more efficient implementation. Parameters ---------- t : double The time, ``t``. state : :obj:`~Data` The state to multiply by the element term. out : :obj:`~Data` or ``NULL`` The output to add the result of the multiplication to. If ``NULL``, the result of the multiplication is returned directly (i.e. ``out`` is assumed to be the zero matrix). Returns ------- data The result of ``self.coeff(t) * self.qobj(t) @ state + out``, with the addition possibly having been performed in-place on ``out``. .. note:: Because of the possibly but not definitely in-place behaviour of this function, the result should always be assigned to some variable and surrounding code should assume that ``out`` maybe have been modified and that the result may be a reference to ``out``. The safest is simply to write ``out = elem.matmul_data_t(t, state, out)``. .. note:: This method would ideally be implemented using a special function dispatched by the data layer so that it did not have to special case the ``Dense`` operation itself, but the data layer dispatch does not yet support in-place operations. Once it does this method should be updated to use the new support. """ if out is None: return _data.matmul(self.data(t), state, self.coeff(t)) elif type(state) is Dense and type(out) is Dense: imatmul_data_dense(self.data(t), state, self.coeff(t), out) return out else: return _data.add( out, _data.matmul(self.data(t), state, self.coeff(t)) ) def linear_map(self, f, anti=False): """ Return a new element representing a linear transformation ``f`` of the :obj:`.Qobj` portion of this element and possibly a complex conjucation of the coefficient portion (when ``f`` is an antilinear map). If this element represents ``coeff * qobj`` the returned element represents ``coeff * f(obj)`` (if ``anti=False``) or ``conj(coeff) * f(obj)`` (if ``anti=True``). Parameters ---------- f : function The linear transformation to apply to the :obj:`.Qobj` of this element. anti : bool Whether to take the complex conjugate of the coefficient. Default is ``False``. Should be set to ``True`` if ``f`` is an antilinear map such as the adjoint (i.e. dagger). Returns ------- _BaseElement A new element with the transformation applied. """ raise NotImplementedError( "Sub-classes of _BaseElement should implement .linear_map(t)." ) def replace_arguments(self, args, cache=None): """ Return a copy of the element with the (possible) additional arguments to any time-dependent functions updated to the given argument values. The arguments of any contained :obj:`.Coefficient` instances are also replaced. If the operation does not modify this element, the original element may be returned. Parameters ---------- args : dict A dictionary of arguments to update. Keys are the names of the arguments and values are the new argument values. Arguments not included retain their original values. cache : list or ``None`` A cache to add updated elements to. Unmodified elements are not added to the cache. If a cache is supplied and ``.replace_arguments`` would be called again on the same element with the same arguments, the new element from the cache will be returned instead. By default the cache is ``None`` and no caching is performed. Cache users should supply either ``cache=[]`` (which activates caching) or an existing cache (for example, if making calls on sub-elements of some composite element). Returns ------- _BaseElement A new element with the arguments replaced, or possibly this element if it would not be modified. Example ------- If ``elem`` is a product element for ``op * op.dag()`` it will contain two references to the same element for ``op``. Calling:: elem = elem.replace_arguments({"theta": 3.1416}) will return a new element that contains two *different* copies of ``op.replace_arguments({"theta": 3.1416})``. This will cause ``op`` to be evaluated *twice* when ``elem.qobj(t)`` is called. Calling instead:: elem = elem.replace_arguments({"theta": 3.1416}, cache=[]) will return a new element that contains two references to *one* copy of ``op.replace_arguments({"theta": 3.1416})``, which will improve performance when calling ``elem.qobj(t)`` later. """ raise NotImplementedError( "Sub-classes of _BaseElement should implement .replace_arguments(t)." ) def __call__(self, t, args=None): if args: cache = [] new = self.replace_arguments(args, cache) return new.qobj(t) * new.coeff(t) return self.qobj(t) * self.coeff(t) @property def dtype(self): return None cdef class _ConstantElement(_BaseElement): """ Constant part of a list format :obj:`.QobjEvo`. A constant :obj:`.QobjEvo` will contain one `_ConstantElement`:: qevo = QobjEvo(H0) qevo.elements = [_ConstantElement(H0)] """ def __init__(self, qobj): self._qobj = qobj self._data = self._qobj.data def __mul__(left, right): if type(left) is _ConstantElement: return _ConstantElement((<_ConstantElement> left)._qobj * right) elif type(right) is _ConstantElement: return _ConstantElement((<_ConstantElement> right)._qobj * left) return NotImplemented def __matmul__(left, right): if type(left) is _ConstantElement and type(right) is _ConstantElement: return _ConstantElement( (<_ConstantElement> left)._qobj @ (<_ConstantElement> right)._qobj ) return NotImplemented cpdef Data data(self, t): return self._data cpdef object qobj(self, t): return self._qobj cpdef object coeff(self, t): return 1. def linear_map(self, f, anti=False): return _ConstantElement(f(self._qobj)) def replace_arguments(self, args, cache=None): return self def __call__(self, t, args=None): return self._qobj @property def dtype(self): return type(self._data) cdef class _EvoElement(_BaseElement): """ A pair of a :obj:`.Qobj` and a :obj:`.Coefficient` from the list format time-dependent operator:: qevo = QobjEvo([[H0, coeff0], [H1, coeff1]]) qevo.elements = [_EvoElement(H0, coeff0), _EvoElement(H1, coeff1)] """ def __init__(self, qobj, coefficient): self._qobj = qobj self._data = self._qobj.data self._coefficient = coefficient def __mul__(left, right): cdef _EvoElement base cdef object factor if type(left) is _EvoElement: base = left factor = right if type(right) is _EvoElement: base = right factor = left return _EvoElement(base._qobj * factor, base._coefficient) def __matmul__(left, right): if isinstance(left, _EvoElement) and isinstance(right, _EvoElement): coefficient = left._coefficient * right._coefficient elif isinstance(left, _EvoElement) and isinstance(right, _ConstantElement): coefficient = left._coefficient elif isinstance(right, _EvoElement) and isinstance(left, _ConstantElement): coefficient = right._coefficient else: return NotImplemented return _EvoElement(left._qobj * right._qobj, coefficient) cpdef Data data(self, t): return self._data cpdef object qobj(self, t): return self._qobj cpdef object coeff(self, t): return self._coefficient(t) def linear_map(self, f, anti=False): return _EvoElement( f(self._qobj), self._coefficient.conj() if anti else self._coefficient, ) def replace_arguments(self, args, cache=None): return _EvoElement( self._qobj, self._coefficient.replace_arguments(args) ) @property def dtype(self): return type(self._data) cdef class _FuncElement(_BaseElement): """ Used with :obj:`.QobjEvo` to build an evolution term from a function with either the signature: :: func(t: float, ...) -> Qobj or the older QuTiP 4 style signature: :: func(t: float, args: dict) -> Qobj In the new style, ``func`` may accept arbitrary named arguments and is called as ``func(t, **args)``. A :obj:`.QobjEvo` created from such a function contains one :obj:`_FuncElement`: :: qevo = QobjEvo(func, args=args) qevo.elements = [_FuncElement(func, args)] Each :obj:`_FuncElement` consists of an immutable pair ``(func, args)`` of function and argument. This class has a basic capacity to memoize calls to ``func`` by saving the result of the last call :: op = QobjEvo(func, args=args) (op.dag() * op)(t) calls ``func`` only once. Parameters ---------- func : callable(t : float, ...) -> Qobj Function returning the element value at time ``t``. args : dict Values of the arguments to pass to ``func``. style : {None, "pythonic", "dict", "auto"} The style of the signature used. If style is ``None``, the value of ``qutip.settings.core["function_coefficient_style"]`` is used. Otherwise the supplied value overrides the global setting. The parameters ``_f_pythonic`` and ``_f_parameters`` override function style and parameter detection and are not intended to be part of the public interface. """ _UNSET = object() def __init__(self, func, args, style=None, _f_pythonic=_UNSET, _f_parameters=_UNSET): if _f_pythonic is self._UNSET or _f_parameters is self._UNSET: if not (_f_pythonic is self._UNSET and _f_parameters is self._UNSET): raise TypeError( "_f_pythonic and _f_parameters should always be given together." ) _f_pythonic, _f_parameters = coefficient_function_parameters( func, style=style) if _f_parameters is not None: args = {k: args[k] for k in _f_parameters & args.keys()} else: args = args.copy() self._func = func self._args = args self._f_pythonic = _f_pythonic self._f_parameters = _f_parameters self._previous = (Nan, None) def __mul__(left, right): cdef _MapElement out if type(left) is _FuncElement: out = _MapElement(left, [], right) if type(right) is _FuncElement: out = _MapElement(right, [], left) return out def __matmul__(left, right): return _ProdElement(left, right, []) cpdef Data data(self, t): return self.qobj(t).data cpdef object qobj(self, t): cdef double _t cdef object _qobj _t, _qobj = self._previous if t == _t: return _qobj if self._f_pythonic: _qobj = self._func(t, **self._args) else: _qobj = self._func(t, self._args) self._previous = (t, _qobj) return _qobj cpdef object coeff(self, t): return 1. def linear_map(self, f, anti=False): return _MapElement(self, [f]) def replace_arguments(_FuncElement self, args, cache=None): if self._f_parameters is not None: args = {k: args[k] for k in self._f_parameters & args.keys()} if not args: return self if cache is not None: for old, new in cache: if old is self: return new new = _FuncElement( self._func, {**self._args, **args}, _f_pythonic=self._f_pythonic, _f_parameters=self._f_parameters, ) if cache is not None: cache.append((self, new)) return new cdef class _MapElement(_BaseElement): """ :obj:`_FuncElement` decorated with linear tranformations. Linear tranformations available in :obj:`.QobjEvo` include transpose, adjoint, conjugate, convertion and product with number:: ``` op = QobjEvo(f, args=args) op2 = op.conj().dag() * 2 ``` Then ``op2.elements`` is:: ``[_MapElement(_FuncElement(f, args), [conj, dag], 2)]`` """ def __init__(self, _FuncElement base, transform, coeff=1.): self._base = base self._transform = transform self._coeff = coeff def __mul__(left, right): cdef _MapElement out, self cdef double complex factor if type(left) is _MapElement: self = left factor = right elif type(right) is _MapElement: self = right factor = left return _MapElement( self._base, self._transform.copy(), self._coeff*factor ) def __matmul__(left, right): return _ProdElement(left, right, []) cpdef Data data(self, t): return self.qobj(t).data cpdef object qobj(self, t): out = self._base.qobj(t) for func in self._transform: out = func(out) return out cpdef object coeff(self, t): return self._coeff def linear_map(self, f, anti=False): return _MapElement( self._base, self._transform + [f], conj(self._coeff) if anti else self._coeff ) def replace_arguments(_MapElement self, args, cache=None): return _MapElement( self._base.replace_arguments(args, cache=cache), self._transform.copy(), self._coeff, ) cdef class _ProdElement(_BaseElement): """ Product of a :obj:`_FuncElement` or :obj:`_MapElement` with other :obj:`_BaseElement`. Include a stack of linear transformation to be applied after the product:: ``op = QobjEvo(f) * qobj1`` Then ``op.elements`` is:: ``[_ProdElement(_FuncElement(f, {}), _ConstantElement(qobj1))]`` """ def __init__(self, left, right, transform, conj=False): self._left = left self._right = right self._conj = conj self._transform = transform def __mul__(left, right): cdef _ProdElement self cdef double complex factor if type(left) is _ProdElement: self = left factor = right if type(right) is _ProdElement: self = right factor = left return _ProdElement(self._left, self._right * factor, self._transform.copy(), self._conj) def __matmul__(left, right): return _ProdElement(left, right, []) cpdef Data data(self, t): return self.qobj(t).data cpdef object qobj(self, t): out = self._left.qobj(t) @ self._right.qobj(t) for func in self._transform: out = func(out) return out cpdef object coeff(self, t): cdef double complex out = self._left.coeff(t) * self._right.coeff(t) return conj(out) if self._conj else out cdef Data matmul_data_t(_ProdElement self, t, Data state, Data out=None): cdef Data temp if not self._transform: temp = self._right.matmul_data_t(t, state) out = self._left.matmul_data_t(t, temp, out) return out elif type(state) is Dense and type(out) is Dense: imatmul_data_dense(self.data(t), state, self.coeff(t), out) return out else: return _data.add( out, _data.matmul(self.data(t), state, self.coeff(t)) ) def linear_map(self, f, anti=False): return _ProdElement( self._left, self._right, self._transform + [f], self._conj ^ anti ) def replace_arguments(_ProdElement self, args, cache=None): return _ProdElement( self._left.replace_arguments(args, cache=cache), self._right.replace_arguments(args, cache=cache), self._transform.copy(), self._conj ) qutip-5.1.1/qutip/core/cy/coefficient.pxd000066400000000000000000000002461474175217300203750ustar00rootroot00000000000000#cython: language_level=3 cdef class Coefficient: cdef readonly dict args cdef double complex _call(self, double t) except * cpdef Coefficient copy(self) qutip-5.1.1/qutip/core/cy/coefficient.pyx000066400000000000000000000624711474175217300204320ustar00rootroot00000000000000#cython: language_level=3 #cython: c_api_binop_methods=True import inspect import pickle import scipy from scipy.interpolate import make_interp_spline import numpy as np cimport numpy as cnp cimport cython import qutip cdef extern from "" namespace "std" nogil: double complex conj(double complex x) double norm(double complex x) __all__ = [ "Coefficient", "InterCoefficient", "FunctionCoefficient", "StrFunctionCoefficient", "ConjCoefficient", "NormCoefficient" ] def coefficient_function_parameters(func, style=None): """ Return the function style (either "pythonic" or not) and a list of additional parameters accepted. Used by :obj:`FunctionCoefficient` and :obj:`_FuncElement` to determine the call signature of the supplied function based on the given style (or ``qutip.settings.core["function_coefficient_style"]`` if no style is given) and the signature of the given function. Parameters ---------- func : function The :obj:`FunctionCoefficient` to inspect. The first argument of the function is assumed to be ``t`` (the time at which to evaluate the coefficient). The remaining arguments depend on the signature style (see below). style : {None, "pythonic", "dict", "auto"} The style of the signature used. If style is ``None``, the value of ``qutip.settings.core["function_coefficient_style"]`` is used. Otherwise the supplied value overrides the global setting. Returns ------- (f_pythonic, f_parameters) f_pythonic : bool True if the function should be called as ``f(t, **kw)`` and False if the function should be called as ``f(t, kw_dict)``. f_parameters : set or None The set of parameters (other than ``t``) of the function or ``None`` if the function accepts arbitrary parameters. """ sig = inspect.signature(func) f_has_kw = any(p.kind == p.VAR_KEYWORD for p in sig.parameters.values()) if style is None: style = qutip.settings.core["function_coefficient_style"] if style == "auto": if tuple(sig.parameters.keys()) == ("t", "args") and not f_has_kw: # if the signature is exactly f(t, args), then assume parameters # are supplied in an argument dictionary style = "dict" else: style = "pythonic" if style == "dict" or f_has_kw: # f might accept any parameter f_parameters = None else: # f accepts only t and the named parameters f_parameters = set(list(sig.parameters.keys())[1:]) return (style == "pythonic", f_parameters) cdef class Coefficient: """ `Coefficient` are the time-dependant scalar of a `[Qobj, coeff]` pair composing time-dependant operator in list format for :obj:`.QobjEvo`. :obj:`.Coefficient` are immutable. """ def __init__(self, args, **_): self.args = args def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return self def __call__(self, t, dict _args=None, **kwargs): """ Return the coefficient value at time `t`. Stored arguments can overwriten with `_args` or as keywords parameters. Parameters ---------- t : float Time at which to evaluate the :obj:`.Coefficient`. _args : dict Dictionary of arguments to use instead of the stored ones. **kwargs Arguments to overwrite for this call. """ if _args is not None or kwargs: return ( self.replace_arguments(_args, **kwargs))._call(t) return self._call(t) cdef double complex _call(self, double t) except *: """Core computation of the :obj:`.Coefficient`.""" # All Coefficient sub-classes should overwrite this or __call__ return complex(self(t)) def __add__(left, right): if ( isinstance(left, InterCoefficient) and isinstance(right, InterCoefficient) ): return add_inter(left, right) if isinstance(left, Coefficient) and isinstance(right, Coefficient): return SumCoefficient(left.copy(), right.copy()) return NotImplemented def __mul__(left, right): if isinstance(left, Coefficient) and isinstance(right, Coefficient): return MulCoefficient(left.copy(), right.copy()) if isinstance(left, qutip.Qobj): return qutip.QobjEvo([left.copy(), right.copy()]) if isinstance(right, qutip.Qobj): return qutip.QobjEvo([right.copy(), left.copy()]) return NotImplemented cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return pickle.loads(pickle.dumps(self)) def conj(self): """ Return a conjugate :obj:`.Coefficient` of this""" return ConjCoefficient(self) def _cdc(self): """ Return a :obj:`.Coefficient` being the norm of this""" return NormCoefficient(self) @cython.auto_pickle(True) cdef class FunctionCoefficient(Coefficient): """ :obj:`.Coefficient` wrapping a Python function. Parameters ---------- func : callable(t : float, ...) -> complex Function returning the coefficient value at time ``t``. args : dict Values of the arguments to pass to ``func``. style : {None, "pythonic", "dict", "auto"} The style of function signature used. If style is ``None``, the value of ``qutip.settings.core["function_coefficient_style"]`` is used. Otherwise the supplied value overrides the global setting. The parameters ``_f_pythonic`` and ``_f_parameters`` override function style and parameter detection and are not intended to be part of the public interface. """ cdef object func cdef bint _f_pythonic cdef set _f_parameters _UNSET = object() def __init__(self, func, dict args, style=None, _f_pythonic=_UNSET, _f_parameters=_UNSET, **_): if _f_pythonic is self._UNSET or _f_parameters is self._UNSET: if not (_f_pythonic is self._UNSET and _f_parameters is self._UNSET): raise TypeError( "_f_pythonic and _f_parameters should " "always be given together." ) _f_pythonic, _f_parameters = coefficient_function_parameters( func, style=style) if _f_parameters is not None: args = {k: args[k] for k in _f_parameters & args.keys()} else: args = args.copy() self.func = func self.args = args self._f_pythonic = _f_pythonic self._f_parameters = _f_parameters def __call__(self, t, dict _args=None, **kwargs): if _args is not None or kwargs: return self.replace_arguments(_args, **kwargs)(t) if self._f_pythonic: return self.func(t, **self.args) return self.func(t, self.args) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return FunctionCoefficient( self.func, self.args.copy(), _f_pythonic=self._f_pythonic, _f_parameters=self._f_parameters, ) def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ if _args: kwargs.update(_args) if self._f_parameters is not None: kwargs = {k: kwargs[k] for k in self._f_parameters & kwargs.keys()} if not kwargs: return self return FunctionCoefficient( self.func, {**self.args, **kwargs}, _f_pythonic=self._f_pythonic, _f_parameters=self._f_parameters, ) def proj(x): if np.isfinite(x): return (x) else: return np.inf + 0j * np.imag(x) cdef class StrFunctionCoefficient(Coefficient): """ A :obj:`.Coefficient` defined by a string containing a simple Python expression. The string should contain a compilable Python expression that results in a complex number. The time ``t`` is available as a local variable, as are the individual arguments (i.e. the keys of ``args``). The ``args`` dictionary itself is not accessible. The following symbols are defined: ``sin``, ``cos``, ``tan``, ``asin``, ``acos``, ``atan``, ``pi``, ``sinh``, ``cosh``, ``tanh``, ``asinh``, ``acosh``, ``atanh``, ``exp``, ``log``, ``log10``, ``erf``, ``zerf``, ``sqrt``, ``real``, ``imag``, ``conj``, ``abs``, ``norm``, ``arg``, ``proj``, ``numpy`` as ``np`` and ``scipy.special`` as ``spe``. Examples -------- >>> StrFunctionCoefficient("sin(w * pi * t)", {'w': 1j}) Parameters ---------- base : str A string representing a compilable Python expression that results in a complex number. args : dict A dictionary of variable used in the code string. It may include unused variables. """ cdef object func cdef str base str_env = { "sin": np.sin, "cos": np.cos, "tan": np.tan, "asin": np.arcsin, "acos": np.arccos, "atan": np.arctan, "pi": np.pi, "sinh": np.sinh, "cosh": np.cosh, "tanh": np.tanh, "asinh": np.arcsinh, "acosh": np.arccosh, "atanh": np.arctanh, "exp": np.exp, "log": np.log, "log10": np.log10, "erf": scipy.special.erf, "zerf": scipy.special.erf, "sqrt": np.sqrt, "real": np.real, "imag": np.imag, "conj": np.conj, "abs": np.abs, "norm": lambda x: np.abs(x)**2, "arg": np.angle, "proj": proj, "np": np, "spe": scipy.special} def __init__(self, base, dict args, **_): args2var = "\n".join([" {} = args['{}']".format(key, key) for key in args]) code = f""" def coeff(t, args): {args2var} return {base}""" lc = {} exec(code, self.str_env, lc) self.base = base self.func = lc["coeff"] self.args = args cdef complex _call(self, double t) except *: return self.func(t, self.args) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return StrFunctionCoefficient(self.base, self.args.copy()) def __reduce__(self): return (StrFunctionCoefficient, (self.base, self.args)) def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ if _args: kwargs.update(_args) if kwargs: return StrFunctionCoefficient(self.base, {**self.args, **kwargs}) return self cdef class InterCoefficient(Coefficient): """ A :obj:`.Coefficient` built from an interpolation of a numpy array. Parameters ---------- coeff_arr : np.ndarray The array of coefficient values to interpolate. tlist : np.ndarray An array of times corresponding to each coefficient value. The times must be increasing, but do not need to be uniformly spaced. order : int Order of the interpolation. Order ``0`` uses the previous (i.e. left) value. The order will be reduced to ``len(tlist) - 1`` if it is larger. boundary_conditions : 2-Tuple, str or None, optional Boundary conditions for spline evaluation. Default value is `None`. Correspond to `bc_type` of scipy.interpolate.make_interp_spline. Refer to Scipy's documentation for further details: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.make_interp_spline.html """ cdef int order cdef double dt cdef double[::1] tlist cdef complex[:, :] poly cdef object np_arrays def __init__(self, coeff_arr, tlist, int order, boundary_conditions, **_): tlist = np.array(tlist, dtype=np.float64) coeff_arr = np.array(coeff_arr, dtype=np.complex128) if coeff_arr.ndim != 1: raise ValueError("The array to interpolate must be a 1D array") if coeff_arr.shape != tlist.shape: raise ValueError("tlist must be the same len " "as the array to interpolate") if order < 0: raise ValueError("order must be a positive integer") order = min(order, len(tlist) - 1) if order == 0: coeff_arr = coeff_arr.reshape((1, -1)) elif order == 1: coeff_arr = np.vstack([ np.diff(coeff_arr, append=-1) / np.diff(tlist, append=-1), coeff_arr ]) elif order >= 2: # Use scipy to compute the spline and transform it to polynomes # as used in scipy's PPoly which is easier for us to use. spline = make_interp_spline(tlist, coeff_arr, k=order, bc_type=boundary_conditions) # Scipy can move knots, we add them to tlist tlist = np.sort(np.unique(np.concatenate([spline.t, tlist]))) a = np.arange(spline.k+1) a[0] = 1 fact = np.cumprod(a) coeff_arr = np.concatenate([ spline(tlist, i) / fact[i] for i in range(spline.k, -1, -1) ]).reshape((spline.k+1, -1)) self._prepare(tlist, coeff_arr) def _prepare(self, np_tlist, np_poly, dt=None): self.np_arrays = (np_tlist, np_poly) self.tlist = np_tlist self.poly = np_poly self.order = self.poly.shape[0] - 1 diff = np.diff(self.np_arrays[0]) if dt is not None: self.dt = dt elif len(diff) >= 1 and np.allclose(diff[0], diff): self.dt = diff[0] else: self.dt = 0 @cython.wraparound(False) @cython.boundscheck(False) @cython.cdivision(True) cdef size_t _binary_search(self, double x): # Binary search for the interval # return the indice of the of the biggest element where t <= x cdef size_t low = 0 cdef size_t high = self.tlist.shape[0] cdef size_t middle cdef size_t count = 0 while low+1 != high and count < 64: middle = (low + high)//2 if x < self.tlist[middle]: high = middle else: low = middle # We keep a count to be sure that it never get into an infinit loop # even if tlist has an unexpected format. count += 1 return low @cython.initializedcheck(False) @cython.cdivision(True) cdef double complex _call(self, double t) except *: cdef size_t idx, i cdef double factor cdef double complex out cdef double complex[:] slice if t <= self.tlist[0]: return self.poly[-1, 0] elif t >= self.tlist[-1]: return self.poly[-1, -1] if self.dt: idx = ((t - self.tlist[0]) / self.dt) else: idx = self._binary_search(t) if self.order == 0: out = self.poly[0, idx] else: factor = t - self.tlist[idx] slice = self.poly[:, idx] out = 0. for i in range(self.order+1): out *= factor out += slice[i] return out def __reduce__(self): return (InterCoefficient.restore, (*self.np_arrays, self.dt)) @classmethod def restore(cls, np_tlist, np_poly, dt=None): cdef InterCoefficient out = cls.__new__(cls) out._prepare(np_tlist, np_poly, dt) return out @classmethod def from_PPoly(cls, ppoly, **_): return cls.restore(ppoly.x, np.asarray(ppoly.c, complex)) @classmethod def from_Bspline(cls, spline, **_): tlist = np.unique(spline.t) a = np.arange(spline.k+1) a[0] = 1 fact = np.cumprod(a) + 0j poly = np.concatenate([ spline(tlist, i) / fact[i] for i in range(spline.k, -1, -1) ]).reshape((spline.k+1, -1)).astype(complex, copy=False) return cls.restore(tlist, poly) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return InterCoefficient.restore(*self.np_arrays, self.dt) cdef Coefficient add_inter(InterCoefficient left, InterCoefficient right): """ Add two array coefficient with matching tlist into one.""" if ( left.np_arrays[0].shape == right.np_arrays[0].shape and np.allclose(left.np_arrays[0], right.np_arrays[0], rtol=1e-15, atol=1e-15) and (left.order == right.order) ): return InterCoefficient.restore( left.np_arrays[0], left.np_arrays[1] + right.np_arrays[1], left.dt ) else: # It would be possible to add them by merging tlist. return SumCoefficient(left, right) @cython.auto_pickle(True) cdef class SumCoefficient(Coefficient): """ A :obj:`.Coefficient` built from the sum of two other coefficients. A :obj:`SumCoefficient` is returned as the result of the addition of two coefficients, e.g. :: coefficient("t * t") + coefficient("t") # SumCoefficient """ cdef Coefficient first cdef Coefficient second def __init__(self, Coefficient first, Coefficient second): self.first = first self.second = second cdef complex _call(self, double t) except *: return self.first._call(t) + self.second._call(t) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return SumCoefficient(self.first.copy(), self.second.copy()) def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return SumCoefficient( self.first.replace_arguments(_args, **kwargs), self.second.replace_arguments(_args, **kwargs) ) @cython.auto_pickle(True) cdef class MulCoefficient(Coefficient): """ A :obj:`.Coefficient` built from the product of two other coefficients. A :obj:`MulCoefficient` is returned as the result of the multiplication of two coefficients, e.g. :: coefficient("w * t", args={'w': 1}) * coefficient("t") """ cdef Coefficient first cdef Coefficient second def __init__(self, Coefficient first, Coefficient second): self.first = first self.second = second cdef complex _call(self, double t) except *: return self.first._call(t) * self.second._call(t) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return MulCoefficient(self.first.copy(), self.second.copy()) def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return MulCoefficient( self.first.replace_arguments(_args, **kwargs), self.second.replace_arguments(_args, **kwargs) ) @cython.auto_pickle(True) cdef class ConjCoefficient(Coefficient): """ The conjugate of a :obj:`.Coefficient`. A :obj:`ConjCoefficient` is returned by ``Coefficient.conj()`` and ``qutip.coefficent.conj(Coefficient)``. """ cdef Coefficient base def __init__(self, Coefficient base): self.base = base cdef complex _call(self, double t) except *: return conj(self.base._call(t)) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return ConjCoefficient(self.base.copy()) def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return ConjCoefficient( self.base.replace_arguments(_args, **kwargs) ) @cython.auto_pickle(True) cdef class NormCoefficient(Coefficient): """ The L2 :func:`norm` of a :obj:`.Coefficient`. A shortcut for ``conj(coeff) * coeff``. :obj:`NormCoefficient` is returned by ``qutip.coefficent.norm(Coefficient)``. """ cdef Coefficient base def __init__(self, Coefficient base): self.base = base def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return NormCoefficient( self.base.replace_arguments(_args, **kwargs) ) cdef complex _call(self, double t) except *: return norm(self.base._call(t)) cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return NormCoefficient(self.base.copy()) @cython.auto_pickle(True) cdef class ConstantCoefficient(Coefficient): """ A time-independent coefficient. :obj:`ConstantCoefficient` is returned by ``qutip.coefficent.const(value)``. """ cdef complex value def __init__(self, complex value, **_): self.value = value def replace_arguments(self, _args=None, **kwargs): """ Replace the arguments (``args``) of a coefficient. Returns a new :obj:`.Coefficient` if the coefficient has arguments, or the original coefficient if it does not. Arguments to replace may be supplied either in a dictionary as the first position argument, or passed as keywords, or as a combination of the two. Arguments not replaced retain their previous values. Parameters ---------- _args : dict Dictionary of arguments to replace. **kwargs Arguments to replace. """ return self cdef complex _call(self, double t) except *: return self.value cpdef Coefficient copy(self): """Return a copy of the :obj:`.Coefficient`.""" return self qutip-5.1.1/qutip/core/cy/complex_math.pxd000066400000000000000000000017671474175217300206100ustar00rootroot00000000000000cdef extern from "" namespace "std" nogil: double abs(double complex x) double complex acos(double complex x) double complex acosh(double complex x) double arg(double complex x) double complex asin(double complex x) double complex asinh(double complex x) double complex atan(double complex x) double complex atanh(double complex x) double complex conj(double complex x) double complex cos(double complex x) double complex cosh(double complex x) double complex exp(double complex x) double imag(double complex x) double complex log(double complex x) double complex log10(double complex x) double norm(double complex x) double complex proj(double complex x) double real(double complex x) double complex sin(double complex x) double complex sinh(double complex x) double complex sqrt(double complex x) double complex tan(double complex x) double complex tanh(double complex x) qutip-5.1.1/qutip/core/cy/math.pxd000066400000000000000000000001411474175217300170420ustar00rootroot00000000000000#cython: language_level=3 cdef double erf(double x) cdef double complex zerf(double complex Z) qutip-5.1.1/qutip/core/cy/math.pyx000066400000000000000000000105561474175217300171020ustar00rootroot00000000000000#cython: language_level=3 cimport cython from libc.math cimport (fabs, sinh, cosh, exp, pi, sqrt, cos, sin, copysign) cdef extern from "" namespace "std" nogil: double real(double complex x) double imag(double complex x) @cython.boundscheck(False) @cython.cdivision(True) cdef double erf(double x): """ A Cython version of the erf function from the cdflib in SciPy. """ cdef double c = 0.564189583547756 cdef double a[5] a[:] = [0.771058495001320e-4, -0.133733772997339e-2, 0.323076579225834e-1, 0.479137145607681e-1, 0.128379167095513] cdef double b[3] b[:] = [0.301048631703895e-2, 0.538971687740286e-1, .375795757275549] cdef double p[8] p[:] = [-1.36864857382717e-7, 5.64195517478974e-1, 7.21175825088309, 4.31622272220567e1, 1.52989285046940e2, 3.39320816734344e2, 4.51918953711873e2, 3.00459261020162e2] cdef double q[8] q[:]= [1.0, 1.27827273196294e1, 7.70001529352295e1, 2.77585444743988e2, 6.38980264465631e2, 9.31354094850610e2, 7.90950925327898e2, 3.00459260956983e2] cdef double r[5] r[:] = [2.10144126479064, 2.62370141675169e1, 2.13688200555087e1, 4.65807828718470, 2.82094791773523e-1] cdef double s[4] s[:] = [9.41537750555460e1, 1.87114811799590e2, 9.90191814623914e1, 1.80124575948747e1] cdef double ax = fabs(x) cdef double t, x2, top, bot, erf if ax <= 0.5: t = x*x top = ((((a[0]*t+a[1])*t+a[2])*t+a[3])*t+a[4]) + 1.0 bot = ((b[0]*t+b[1])*t+b[2])*t + 1.0 erf = x * (top/bot) return erf elif ax <= 4.0: x2 = x*x top = ((((((p[0]*ax+p[1])*ax+p[2])*ax+p[3])*ax+p[4])*ax+p[5])*ax+p[6])*ax + p[7] bot = ((((((q[0]*ax+q[1])*ax+q[2])*ax+q[3])*ax+q[4])*ax+q[5])*ax+q[6])*ax + q[7] erf = 0.5 + (0.5-exp(-x2)*top/bot) if x < 0.0: erf = -erf return erf elif ax < 5.8: x2 = x*x t = 1.0/x2 top = (((r[0]*t+r[1])*t+r[2])*t+r[3])*t + r[4] bot = (((s[0]*t+s[1])*t+s[2])*t+s[3])*t + 1.0 erf = (c-top/(x2*bot))/ax erf = 0.5 + (0.5-exp(-x2)*erf) if x < 0.0: erf = -erf return erf else: erf = copysign(1.0, x) return erf # COMPUTATION OF SPECIAL FUNCTIONS # # Shanjie Zhang and Jianming Jin # # Copyrighted but permission granted to use code in programs. # Buy their book "Computation of Special Functions", 1996, John Wiley & Sons, Inc. @cython.cdivision(True) @cython.boundscheck(False) cdef double complex zerf(double complex Z): """ Parameters ---------- Z : double complex Input parameter. X : double Real part of Z. Y : double Imag part of Z. Returns ------- erf(z) : double complex """ cdef double EPS = 1e-12 cdef double X = real(Z) cdef double Y = imag(Z) cdef double X2 = X * X cdef double ER, R, W, C0, ER0, ERR, ERI, CS, SS, ER1, EI1, ER2, W1 cdef size_t K, N if X < 3.5: ER = 1.0 R = 1.0 W = 0.0 for K in range(1, 100): R = R*X2/(K+0.5) ER = ER+R if (fabs(ER-W) < EPS*fabs(ER)): break W = ER C0 = 2.0/sqrt(pi)*X*exp(-X2) ER0 = C0*ER else: ER = 1.0 R=1.0 for K in range(1, 12): R = -R*(K-0.5)/X2 ER = ER+R C0 = exp(-X2)/(X*sqrt(pi)) ER0 = 1.0-C0*ER if Y == 0.0: ERR = ER0 ERI = 0.0 else: CS = cos(2.0*X*Y) SS = sin(2.0*X*Y) ER1 = exp(-X2)*(1.0-CS)/(2.0*pi*X) EI1 = exp(-X2)*SS/(2.0*pi*X) ER2 = 0.0 W1 = 0.0 for N in range(1,100): ER2 = ER2+exp(-.25*N*N)/(N*N+4.0*X2)*(2.0*X-2.0*X*cosh(N*Y)*CS+N*sinh(N*Y)*SS) if (fabs((ER2-W1)/ER2) < EPS): break W1 = ER2 C0 = 2.0*exp(-X2)/pi ERR = ER0+ER1+C0*ER2 EI2 = 0.0 W2 = 0.0 for N in range(1,100): EI2 = EI2+exp(-.25*N*N)/(N*N+4.0*X2)*(2.0*X*cosh(N*Y)*SS+N*sinh(N*Y)*CS) if (fabs((EI2-W2)/EI2) < EPS): break W2 = EI2 ERI = EI1+C0*EI2 return ERR + 1j*ERI qutip-5.1.1/qutip/core/cy/openmp/000077500000000000000000000000001474175217300166765ustar00rootroot00000000000000qutip-5.1.1/qutip/core/cy/openmp/__init__.py000066400000000000000000000000001474175217300207750ustar00rootroot00000000000000qutip-5.1.1/qutip/core/cy/openmp/bench_openmp.py000066400000000000000000000110401474175217300217010ustar00rootroot00000000000000import numpy as np from qutip.settings import settings as qset from timeit import default_timer as timer def _min_timer(function, *args, **kwargs): min_time = 1e6 for kk in range(10000): t0 = timer() function(*args, **kwargs) t1 = timer() min_time = min(min_time, t1-t0) return min_time def system_bench(func, dims): from qutip.random_objects import rand_ket ratio = 0 ratio_old = 0 nnz_old = 0 for N in dims: L = func(N).data vec = rand_ket(L.shape[0], 0.25).full().ravel() nnz = L.nnz out = np.zeros_like(vec) ser = _min_timer(_spmvpy, L.data, L.indices, L.indptr, vec, 1, out) out = np.zeros_like(vec) par = _min_timer(_spmvpy_openmp, L.data, L.indices, L.indptr, vec, 1, out, 2) ratio = ser/par if ratio > 1: break nnz_old = nnz ratio_old = ratio if ratio > 1: rate = (ratio-ratio_old)/(nnz-nnz_old) return int((1.0-ratio_old)/rate+nnz_old) else: return -1 def calculate_openmp_thresh(): # if qset.num_cpus == 1: # return qset.openmp_thresh jc_dims = np.unique(np.logspace(0.45, 1.78, 20, dtype=int)) jc_result = system_bench(_jc_liouvillian, jc_dims) opto_dims = np.unique(np.logspace(0.4, 1.33, 12, dtype=int)) opto_result = system_bench(_opto_liouvillian, opto_dims) spin_dims = np.unique(np.logspace(0.45, 1.17, 10, dtype=int)) spin_result = system_bench(_spin_hamiltonian, spin_dims) # Double result to be conservative thresh = 2*int(max([jc_result, opto_result, spin_result])) if thresh < 0: thresh = np.iinfo(np.int32).max return thresh def _jc_liouvillian(N): from qutip.core import tensor, destroy, qeye, liouvillian wc = 2*np.pi * 1.0 # cavity frequency wa = 2*np.pi * 1.0 # atom frequency g = 2*np.pi * 0.05 # coupling strength kappa = 0.005 # cavity dissipation rate gamma = 0.05 # atom dissipation rate n_th_a = 1 # temperature in frequency units use_rwa = 0 # operators a = tensor(destroy(N), qeye(2)) sm = tensor(qeye(N), destroy(2)) # Hamiltonian H = wc*a.dag()*a + wa*sm.dag()*sm + g*(a.dag()*sm + a*sm.dag()) c_op_list = [] rate = kappa * (1 + n_th_a) if rate > 0.0: c_op_list.append(np.sqrt(rate) * a) rate = kappa * n_th_a if rate > 0.0: c_op_list.append(np.sqrt(rate) * a.dag()) rate = gamma if rate > 0.0: c_op_list.append(np.sqrt(rate) * sm) return liouvillian(H, c_op_list) def _opto_liouvillian(N): from qutip.core import tensor, destroy, qeye, liouvillian Nc = 5 # Number of cavity states Nm = N # Number of mech states kappa = 0.3 # Cavity damping rate E = 0.1 # Driving Amplitude g0 = 2.4*kappa # Coupling strength Qm = 1e4 # Mech quality factor gamma = 1/Qm # Mech damping rate n_th = 1 # Mech bath temperature delta = -0.43 # Detuning a = tensor(destroy(Nc), qeye(Nm)) b = tensor(qeye(Nc), destroy(Nm)) num_b = b.dag()*b num_a = a.dag()*a H = -delta*(num_a)+num_b+g0*(b.dag()+b)*num_a+E*(a.dag()+a) cc = np.sqrt(kappa)*a cm = np.sqrt(gamma*(1.0 + n_th))*b cp = np.sqrt(gamma*n_th)*b.dag() c_ops = [cc, cm, cp] return liouvillian(H, c_ops) def _spin_hamiltonian(N): from qutip.core import tensor, qeye, sigmax, sigmay, sigmaz # array of spin energy splittings and coupling strengths. here we use # uniform parameters, but in general we don't have too h = 2*np.pi * 1.0 * np.ones(N) Jz = 2*np.pi * 0.1 * np.ones(N) Jx = 2*np.pi * 0.1 * np.ones(N) Jy = 2*np.pi * 0.1 * np.ones(N) # dephasing rate si = qeye(2) sx = sigmax() sy = sigmay() sz = sigmaz() sx_list = [] sy_list = [] sz_list = [] for n in range(N): op_list = [si] * N op_list[n] = sx sx_list.append(tensor(op_list)) op_list[n] = sy sy_list.append(tensor(op_list)) op_list[n] = sz sz_list.append(tensor(op_list)) # construct the hamiltonian H = 0 # energy splitting terms for n in range(N): H += - 0.5 * h[n] * sz_list[n] # interaction terms for n in range(N-1): H += - 0.5 * Jx[n] * sx_list[n] * sx_list[n+1] H += - 0.5 * Jy[n] * sy_list[n] * sy_list[n+1] H += - 0.5 * Jz[n] * sz_list[n] * sz_list[n+1] return H qutip-5.1.1/qutip/core/cy/openmp/parfuncs.pxd000066400000000000000000000003261474175217300212350ustar00rootroot00000000000000#cython: language_level=3 cimport numpy as cnp cimport cython cdef void spmvpy_openmp( complex *data, int *ind, int *ptr, complex * vec, complex a, complex * out, unsigned int nrows, unsigned int nthr, ) qutip-5.1.1/qutip/core/cy/openmp/parfuncs.pyx000066400000000000000000000010651474175217300212630ustar00rootroot00000000000000#cython: language_level=3 cdef extern from "src/zspmv_openmp.hpp" nogil: void zspmvpy_openmp(double complex *data, int *ind, int *ptr, double complex *vec, double complex a, double complex *out, int nrows, int nthr) @cython.boundscheck(False) @cython.wraparound(False) cdef inline void spmvpy_openmp(complex * data, int * ind, int * ptr, complex * vec, complex a, complex * out, unsigned int nrows, unsigned int nthr): zspmvpy_openmp(data, ind, ptr, vec, a, out, nrows, nthr) qutip-5.1.1/qutip/core/cy/openmp/src/000077500000000000000000000000001474175217300174655ustar00rootroot00000000000000qutip-5.1.1/qutip/core/cy/openmp/src/zspmv_openmp.cpp000066400000000000000000000142751474175217300227370ustar00rootroot00000000000000#include #include #if defined(__GNUC__) && defined(__SSE3__) // Using GCC or CLANG and SSE3 #include void zspmvpy_openmp(const std::complex * __restrict__ data, const int * __restrict__ ind, const int * __restrict__ ptr, const std::complex * __restrict__ vec, const std::complex a, std::complex * __restrict__ out, const unsigned int nrows, const unsigned int nthr) { size_t row, jj; unsigned int row_start, row_end; __m128d num1, num2, num3, num4; #pragma omp parallel for \ private(row,num1,num2,num3,num4,row_start,row_end,jj) \ shared(data,ind,ptr,out,vec) schedule(static) \ num_threads(nthr) for (row=0; row < nrows; row++) { num4 = _mm_setzero_pd(); row_start = ptr[row]; row_end = ptr[row+1]; for (jj=row_start; jj (data[jj])[0]); num2 = _mm_set_pd(std::imag(vec[ind[jj]]),std::real(vec[ind[jj]])); num3 = _mm_mul_pd(num2, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(data[jj])[1]); num2 = _mm_shuffle_pd(num2, num2, 1); num2 = _mm_mul_pd(num2, num1); num3 = _mm_addsub_pd(num3, num2); num4 = _mm_add_pd(num3, num4); } num1 = _mm_loaddup_pd(&reinterpret_cast(a)[0]); num3 = _mm_mul_pd(num4, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(a)[1]); num4 = _mm_shuffle_pd(num4, num4, 1); num4 = _mm_mul_pd(num4, num1); num3 = _mm_addsub_pd(num3, num4); num2 = _mm_loadu_pd((double *)&out[row]); num3 = _mm_add_pd(num2, num3); _mm_storeu_pd((double *)&out[row], num3); } } #elif defined(__GNUC__) // Using GCC or CLANG but no SSE3 void zspmvpy_openmp(const std::complex * __restrict__ data, const int * __restrict__ ind, const int * __restrict__ ptr, const std::complex * __restrict__ vec, const std::complex a, std::complex * __restrict__ out, const unsigned int nrows, const unsigned int nthr) { size_t row, jj; unsigned int row_start, row_end; std::complex dot; #pragma omp parallel for \ private(row,dot,row_start,row_end,jj) \ shared(data,ind,ptr,out,vec) schedule(static) \ num_threads(nthr) for (row=0; row < nrows; row++) { dot = 0; row_start = ptr[row]; row_end = ptr[row+1]; for (jj=row_start; jj void zspmvpy_openmp(const std::complex * __restrict data, const int * __restrict ind, const int * __restrict ptr, const std::complex * __restrict vec, const std::complex a, std::complex * __restrict out, const int nrows, const unsigned int nthr) { int row, jj; int row_start, row_end; __m128d num1, num2, num3, num4; #pragma omp parallel for \ private(row,num1,num2,num3,num4,row_start,row_end,jj) \ shared(data,ind,ptr,out,vec) schedule(static) \ num_threads(nthr) for (row=0; row < nrows; row++) { num4 = _mm_setzero_pd(); row_start = ptr[row]; row_end = ptr[row+1]; for (jj=row_start; jj (data[jj])[0]); num2 = _mm_set_pd(std::imag(vec[ind[jj]]),std::real(vec[ind[jj]])); num3 = _mm_mul_pd(num2, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(data[jj])[1]); num2 = _mm_shuffle_pd(num2, num2, 1); num2 = _mm_mul_pd(num2, num1); num3 = _mm_addsub_pd(num3, num2); num4 = _mm_add_pd(num3, num4); } num1 = _mm_loaddup_pd(&reinterpret_cast(a)[0]); num3 = _mm_mul_pd(num4, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(a)[1]); num4 = _mm_shuffle_pd(num4, num4, 1); num4 = _mm_mul_pd(num4, num1); num3 = _mm_addsub_pd(num3, num4); num2 = _mm_loadu_pd((double *)&out[row]); num3 = _mm_add_pd(num2, num3); _mm_storeu_pd((double *)&out[row], num3); } } #elif defined(_MSC_VER) // Visual Studio no AVX void zspmvpy_openmp(const std::complex * __restrict data, const int * __restrict ind, const int * __restrict ptr, const std::complex * __restrict vec, const std::complex a, std::complex * __restrict out, const int nrows, const unsigned int nthr) { int row, jj; int row_start, row_end; std::complex dot; #pragma omp parallel for \ private(row,dot,row_start,row_end,jj) \ shared(data,ind,ptr,out,vec) schedule(static) \ num_threads(nthr) for (row=0; row < nrows; row++) { dot = 0; row_start = ptr[row]; row_end = ptr[row+1]; for (jj=row_start; jj * data, const int * ind, const int * ptr, const std::complex * vec, const std::complex a, std::complex * out, const unsigned int nrows, const unsigned int nthr) { size_t row, jj; unsigned int row_start, row_end; std::complex dot; #pragma omp parallel for \ private(row,dot,row_start,row_end,jj) \ shared(data,ind,ptr,out,vec) schedule(static) \ num_threads(nthr) for (row=0; row < nrows; row++) { dot = 0; row_start = ptr[row]; row_end = ptr[row+1]; for (jj=row_start; jj #ifdef __GNUC__ void zspmvpy_openmp(const std::complex * __restrict__ data, const int * __restrict__ ind, const int *__restrict__ ptr, const std::complex * __restrict__ vec, const std::complex a, std::complex * __restrict__ out, const unsigned int nrows, const unsigned int nthr); #elif defined(_MSC_VER) void zspmvpy_openmp(const std::complex * __restrict data, const int * __restrict ind, const int *__restrict ptr, const std::complex * __restrict vec, const std::complex a, std::complex * __restrict out, const int nrows, const unsigned int nthr); #else void zspmvpy_openmp(const std::complex * data, const int * ind, const int * ptr, const std::complex * vec, const std::complex a, std::complex * out, const unsigned int nrows, const unsigned int nthr); #endif qutip-5.1.1/qutip/core/cy/openmp/utilities.py000066400000000000000000000022141474175217300212620ustar00rootroot00000000000000import os from qutip.settings import settings as qset def check_use_openmp(options): """ Check to see if OPENMP should be used in dynamic solvers. """ # TODO: sort this out. return False """ force_omp = False if qset.has_openmp: if options.use_openmp is None: options.use_openmp = True else: force_omp = bool(options.use_openmp) elif (not qset.has_openmp) and options.use_openmp: raise Exception('OPENMP not available.') else: options.use_openmp = False force_omp = False # Disable OPENMP in parallel mode unless explicitly set. if not force_omp and os.environ['QUTIP_IN_PARALLEL'] == 'TRUE': options.use_openmp = False""" def use_openmp(): """ Check for using openmp in general cases outside of dynamics """ return False if qset.has_openmp and os.environ['QUTIP_IN_PARALLEL'] != 'TRUE': return True else: return False def openmp_components(ptr_list): return np.array([False for ptr in ptr_list], dtype=bool) return np.array([ptr[-1] >= qset.openmp_thresh for ptr in ptr_list], dtype=bool) qutip-5.1.1/qutip/core/cy/qobjevo.pxd000066400000000000000000000012701474175217300175620ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data cimport Dense, Data from qutip.core.data.base cimport idxint cdef class QobjEvo: cdef: list elements readonly object _dims readonly (idxint, idxint) shape int _issuper int _isoper readonly dict _feedback_functions readonly dict _solver_only_feedback cpdef Data _call(QobjEvo self, double t) cdef object _prepare(QobjEvo self, object t, Data state=*) cpdef object expect_data(QobjEvo self, object t, Data state) cdef double complex _expect_dense(QobjEvo self, double t, Dense state) except * cpdef Data matmul_data(QobjEvo self, object t, Data state, Data out=*) qutip-5.1.1/qutip/core/cy/qobjevo.pyi000066400000000000000000000056211474175217300175740ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations from qutip.typing import LayerType, ElementType, QobjEvoLike from qutip.core.qobj import Qobj from qutip.core.data import Data from qutip.core.coefficient import Coefficient from numbers import Number from numpy.typing import ArrayLike from typing import Any, overload, Callable class QobjEvo: dims: list isbra: bool isconstant: bool isket: bool isoper: bool isoperbra: bool isoperket: bool issuper: bool num_elements: int shape: tuple[int, int] superrep: str type: str def __init__( self, Q_object: QobjEvoLike, args: dict[str, Any] = None, *, copy: bool = True, compress: bool = True, function_style: str = None, tlist: ArrayLike = None, order: int = 3, boundary_conditions: tuple | str = None, ) -> None: ... @overload def arguments(self, new_args: dict[str, Any]) -> None: ... @overload def arguments(self, **new_args) -> None: ... def compress(self) -> QobjEvo: ... def tidyup(self, atol: Number) -> QobjEvo: ... def copy(self) -> QobjEvo: ... def conj(self) -> QobjEvo: ... def dag(self) -> QobjEvo: ... def trans(self) -> QobjEvo: ... def to(self, data_type: LayerType) -> QobjEvo: ... def linear_map(self, op_mapping: Callable[[Qobj], Qobj]) -> QobjEvo: ... def expect(self, t: Number, state: Qobj, check_real: bool = True) -> Number: ... def expect_data(self, t: Number, state: Data) -> Number: ... def matmul(self, t: Number, state: Qobj) -> Qobj: ... def matmul_data(self, t: Number, state: Data, out: Data = None) -> Data: ... def to_list(self) -> list[ElementType]: ... def __add__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __iadd__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __radd__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __sub__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __isub__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __rsub__(self, other: QobjEvo | Qobj | Number) -> QobjEvo: ... def __and__(self, other: Qobj | QobjEvo) -> QobjEvo: ... def __rand__(self, other: Qobj | QobjEvo) -> QobjEvo: ... def __call__(self, t: float, **new_args) -> Qobj: ... def __matmul__(self, other: Qobj | QobjEvo) -> QobjEvo: ... def __imatmul__(self, other: Qobj | QobjEvo) -> QobjEvo: ... def __rmatmul__(self, other: Qobj | QobjEvo) -> QobjEvo: ... def __mul__(self, other: Number | Coefficient) -> QobjEvo: ... def __imul__(self, other: Number | Coefficient) -> QobjEvo: ... def __rmul__(self, other: Number | Coefficient) -> QobjEvo: ... def __truediv__(self, other : Number) -> QobjEvo: ... def __idiv__(self, other : Number) -> QobjEvo: ... def __neg__(self) -> QobjEvo: ... def __reduce__(self): ... qutip-5.1.1/qutip/core/cy/qobjevo.pyx000066400000000000000000001165421474175217300176200ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False, cdvision=True import numpy as np import numbers import itertools from functools import partial import qutip from .. import Qobj from .. import data as _data from ..dimensions import Dimensions from ..coefficient import coefficient, CompilationOptions from ._element import * from qutip.settings import settings from qutip.core.cy._element cimport _BaseElement from qutip.core.data cimport Dense, Data, dense from qutip.core.data.expect cimport * from qutip.core.data.reshape cimport (column_stack_dense, column_unstack_dense) from qutip.core.cy.coefficient cimport Coefficient from libc.math cimport fabs __all__ = ['QobjEvo'] cdef class QobjEvo: """ A class for representing time-dependent quantum objects, such as quantum operators and states. Importantly, :obj:`.QobjEvo` instances are used to represent such time-dependent quantum objects when working with QuTiP solvers. A :obj:`.QobjEvo` instance may be constructed from one of the following: * a callable ``f(t: double, args: dict) -> Qobj`` that returns the value of the quantum object at time ``t``. * a ``[Qobj, Coefficient]`` pair, where the :obj:`Coefficient` may be any item that :func:`.coefficient` can accept (e.g. a function, a numpy array of coefficient values, a string expression). * a :obj:`.Qobj` (which creates a constant :obj:`.QobjEvo` term). * a list of such callables, pairs or :obj:`.Qobj`\s. * a :obj:`.QobjEvo` (in which case a copy is created, all other arguments are ignored except ``args`` which, if passed, replaces the existing arguments). Parameters ---------- Q_object : callable, list or :obj:`.Qobj` A specification of the time-depedent quantum object. See the paragraph above for a full description and the examples section below for examples. args : dict, optional A dictionary that contains the arguments for the coefficients. Arguments may be omitted if no function or string coefficients that require arguments are present. tlist : array-like, optional A list of times corresponding to the values of the coefficients supplied as numpy arrays. If no coefficients are supplied as numpy arrays, ``tlist`` may be omitted, otherwise it is required. The times in ``tlist`` do not need to be equidistant, but must be sorted. By default, a cubic spline interpolation will be used to interpolate the value of the (numpy array) coefficients at time ``t``. If the coefficients are to be treated as step functions, pass the argument ``order=0`` (see below). order : int, default=3 Order of the spline interpolation that is to be used to interpolate the value of the (numpy array) coefficients at time ``t``. ``0`` use previous or left value. copy : bool, default=True Whether to make a copy of the :obj:`.Qobj` instances supplied in the ``Q_object`` parameter. compress : bool, default=True Whether to compress the :obj:`.QobjEvo` instance terms after the instance has been created. This sums the constant terms in a single term and combines ``[Qobj, coefficient]`` pairs with the same :obj:`.Qobj` into a single pair containing the sum of the coefficients. See :meth:`compress`. function_style : {None, "pythonic", "dict", "auto"} The style of function signature used by callables in ``Q_object``. If style is ``None``, the value of ``qutip.settings.core["function_coefficient_style"]`` is used. Otherwise the supplied value overrides the global setting. boundary_conditions : 2-Tuple, str or None, optional Boundary conditions for spline evaluation. Default value is `None`. Correspond to `bc_type` of scipy.interpolate.make_interp_spline. Refer to Scipy's documentation for further details: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.make_interp_spline.html Attributes ---------- dims : list List of dimensions keeping track of the tensor structure. shape : (int, int) List of dimensions keeping track of the tensor structure. type : str Type of quantum object: 'bra', 'ket', 'oper', 'operator-ket', 'operator-bra', or 'super'. superrep : str Representation used if `type` is 'super'. One of 'super' (Liouville form) or 'choi' (Choi matrix with tr = dimension). Examples -------- A :obj:`.QobjEvo` constructed from a function: .. code-block:: def f(t, args): return qutip.qeye(N) * np.exp(args['w'] * t) QobjEvo(f, args={'w': 1j}) For list based :obj:`.QobjEvo`, the list must consist of :obj:`.Qobj` or ``[Qobj, Coefficient]`` pairs: .. code-block:: QobjEvo([H0, [H1, coeff1], [H2, coeff2]], args=args) The coefficients may be specified either using a :obj:`Coefficient` object or by a function, string, numpy array or any object that can be passed to the :func:`.coefficient` function. See the documentation of :func:`.coefficient` for a full description. An example of a coefficient specified by a function: .. code-block:: def f1_t(t, args): return np.exp(-1j * t * args["w1"]) QobjEvo([[H1, f1_t]], args={"w1": 1.}) And of coefficients specified by string expressions: .. code-block:: H = QobjEvo( [H0, [H1, 'exp(-1j*w1*t)'], [H2, 'cos(w2*t)']], args={"w1": 1., "w2": 2.} ) Coefficients maybe also be expressed as numpy arrays giving a list of the coefficient values: .. code-block:: python tlist = np.logspace(-5, 0, 100) H = QobjEvo( [H0, [H1, np.exp(-1j * tlist)], [H2, np.cos(2. * tlist)]], tlist=tlist ) The coeffients array must have the same len as the tlist. A :obj:`.QobjEvo` may also be built using simple arithmetic operations combining :obj:`.Qobj` with :obj:`Coefficient`, for example: .. code-block:: python coeff = qutip.coefficient("exp(-1j*w1*t)", args={"w1": 1}) qevo = H0 + H1 * coeff """ def __init__(QobjEvo self, Q_object, args=None, *, copy=True, compress=True, function_style=None, tlist=None, order=3, boundary_conditions=None): if isinstance(Q_object, QobjEvo): self._dims = Q_object._dims self.shape = Q_object.shape self.elements = ( Q_object).elements.copy() self._feedback_functions = Q_object._feedback_functions.copy() self._solver_only_feedback = Q_object._solver_only_feedback.copy() if args: self.arguments(args) if compress: self.compress() return self.elements = [] self._dims = None self.shape = (0, 0) self._feedback_functions = {} self._solver_only_feedback = {} args = self._read_args(args or {}) if ( isinstance(Q_object, list) and len(Q_object) == 2 and isinstance(Q_object[0], Qobj) and not isinstance(Q_object[1], (Qobj, list)) ): # The format is [Qobj, coefficient] Q_object = [Q_object] if isinstance(Q_object, list): for op in Q_object: self.elements.append( self._read_element( op, copy=copy, tlist=tlist, args=args, order=order, function_style=function_style, boundary_conditions=boundary_conditions ) ) else: self.elements.append( self._read_element( Q_object, copy=copy, tlist=tlist, args=args, order=order, function_style=function_style, boundary_conditions=boundary_conditions ) ) for key in self._feedback_functions: # During _read_args, the dims could not have been set yet. # To set the dims, for function QobjEvo, they need to be called. # But to be called, the feedback args need to be read... self._feedback_functions[key].check_consistency(self._dims) if compress: self.compress() def __repr__(self): cls = self.__class__.__name__ repr_str = f'{cls}: dims = {self.dims}, shape = {self.shape}, ' repr_str += f'type = {self.type}, superrep = {self.superrep}, ' repr_str += f'isconstant = {self.isconstant}, ' repr_str += f'num_elements = {self.num_elements}' feedback_pairs = [] for key, val in self._feedback_functions.items(): feedback_pairs.append(key + ":" + repr(val)) for key, val in self._solver_only_feedback.items(): feedback_pairs.append(key + ":" + val) if feedback_pairs: repr_str += f', feedback = {feedback_pairs}' return repr_str def _read_element(self, op, copy, tlist, args, order, function_style, boundary_conditions): """ Read a Q_object item and return an element for that item. """ if isinstance(op, Qobj): out = _ConstantElement(op.copy() if copy else op) qobj = op elif isinstance(op, list): out = _EvoElement( op[0].copy() if copy else op[0], coefficient(op[1], tlist=tlist, args=args, order=order, boundary_conditions=boundary_conditions) ) qobj = op[0] elif isinstance(op, _BaseElement): out = op qobj = op.qobj(0) elif callable(op): out = _FuncElement(op, args, style=function_style) qobj = out.qobj(0) if not isinstance(qobj, Qobj): raise TypeError( "Function based time-dependent elements must have the" " signature f(t: double, args: dict) -> Qobj, but" " {!r} returned: {!r}".format(op, qobj) ) else: raise TypeError( "QobjEvo terms should be Qobjs, a list of [Qobj, coefficient]," " or a function f(t: double, args: dict) -> Qobj, but" " received: {!r}".format(op) ) if self._dims is None: self._dims = qobj._dims self.shape = qobj.shape elif self._dims != qobj._dims: raise ValueError( f"QobjEvo term {op!r} has dims {qobj.dims!r} and shape" f" {qobj.shape!r} but previous terms had dims {self.dims!r}" f" and shape {self.shape!r}." ) return out @classmethod def _restore(cls, elements, dims, shape): """Recreate a QobjEvo without using __init__. """ cdef QobjEvo out = cls.__new__(cls) out.elements = elements out._dims = dims out.shape = shape return out def _getstate(self): """ Obtain the state """ # For jax pytree representation # auto_pickle create similar method __getstate__, but since it's # automatically created, it could change depending on cython version # etc., so we create our own. return { "elements": self.elements, "dims": self._dims, "shape": self.shape, } def __call__(self, double t, dict _args=None, **kwargs): """ Get the :obj:`.Qobj` at ``t``. Parameters ---------- t : float Time at which the :obj:`.QobjEvo` is to be evalued. _args : dict [optional] New arguments as a dict. Update args with ``arguments(new_args)``. **kwargs : New arguments as a keywors. Update args with ``arguments(**new_args)``. Notes ----- If both the positional ``_args`` and keywords are passed new values from both will be used. If a key is present with both, the ``_args`` dict value will take priority. """ if _args is not None or kwargs: if _args is not None: kwargs.update(_args) return QobjEvo(self, args=kwargs)(t) t = self._prepare(t, None) if self.isconstant: # For constant QobjEvo's, we sum the contained Qobjs directly in # order to retain the cached values of attributes like .isherm when # possible, rather than calling _call(t) which may lose this cached # information. return sum(element.qobj(t) for element in self.elements) cdef _BaseElement part = self.elements[0] cdef double complex coeff = part.coeff(t) obj = part.qobj(t) cdef Data out = _data.mul(obj.data, coeff) cdef bint isherm = obj._isherm and coeff.imag == 0 for element in self.elements[1:]: part = <_BaseElement> element coeff = part.coeff(t) obj = part.qobj(t) isherm &= obj._isherm and coeff.imag == 0 out = _data.add(out, obj.data, coeff) return Qobj(out, dims=self._dims, copy=False, isherm=isherm or None) cpdef Data _call(QobjEvo self, double t): t = self._prepare(t, None) cdef Data out cdef _BaseElement part = self.elements[0] out = _data.mul(part.data(t), part.coeff(t)) for element in self.elements[1:]: part = <_BaseElement> element out = _data.add( out, part.data(t), part.coeff(t) ) return out cdef object _prepare(QobjEvo self, object t, Data state=None): """ Precomputation before computing getting the element at `t`""" # We keep the function for feedback eventually if self._feedback_functions and state is not None: new_args = { key: func(t, state) for key, func in self._feedback_functions.items() } cache = [] self.elements = [ element.replace_arguments(new_args, cache=cache) for element in self.elements ] return t def copy(QobjEvo self): """Return a copy of this :obj:`.QobjEvo`""" return QobjEvo(self, compress=False) def arguments(QobjEvo self, dict _args=None, **kwargs): """ Update the arguments. Parameters ---------- _args : dict [optional] New arguments as a dict. Update args with ``arguments(new_args)``. **kwargs : New arguments as a keywors. Update args with ``arguments(**new_args)``. Notes ----- If both the positional ``_args`` and keywords are passed new values from both will be used. If a key is present with both, the ``_args`` dict value will take priority. """ if _args is not None: kwargs.update(_args) cache = [] kwargs = self._read_args(kwargs) self.elements = [ element.replace_arguments(kwargs, cache=cache) for element in self.elements ] def _read_args(self, args): """ Filter feedback args from normal args. """ new_args = {} for key, val in args.items(): if isinstance(val, _Feedback): new_args[key] = val.default if self._dims is not None: val.check_consistency(self._dims) if callable(val): self._feedback_functions[key] = val else: self._solver_only_feedback[key] = val.code else: new_args[key] = val if key in self._feedback_functions: del self._feedback_functions[key] if key in self._solver_only_feedback: del self._solver_only_feedback[key] return new_args def _register_feedback(self, solvers_feeds, solver): """ Receive feedback source from solver. Parameters ---------- solvers_feeds : dict[str] When ``feedback={key: solver_specific}`` is used, update arguments with ``args[key] = solvers_feeds[solver_specific]``. solver: str Name of the solver for the error message. """ new_args = {} for key, feed in self._solver_only_feedback.items(): if feed not in solvers_feeds: raise ValueError( f"Desired feedback {key} is not available for the {solver}." ) new_args[key] = solvers_feeds[feed] if new_args: cache = [] self.elements = [ element.replace_arguments(new_args, cache=cache) for element in self.elements ] def _update_feedback(QobjEvo self, QobjEvo other=None): """ Merge feedback from ``op`` into self. """ if other is not None: if not self._feedback_functions and other._feedback_functions: self._feedback_functions = other._feedback_functions.copy() elif other._feedback_functions: self._feedback_functions.update(other._feedback_functions) if not self._solver_only_feedback and other._solver_only_feedback: self._solver_only_feedback = other._solver_only_feedback.copy() elif other._solver_only_feedback: self._solver_only_feedback.update(other._solver_only_feedback) if self._feedback_functions: for key in self._feedback_functions: self._feedback_functions[key].check_consistency(self._dims) ########################################################################### # Math function # ########################################################################### def __add__(left, right): if isinstance(left, QobjEvo): self = left other = right else: self = right other = left if not isinstance(other, (Qobj, QobjEvo, numbers.Number)): return NotImplemented res = self.copy() res += other return res def __radd__(self, other): if not isinstance(other, (Qobj, QobjEvo, numbers.Number)): return NotImplemented res = self.copy() res += other return res def __iadd__(QobjEvo self, other): cdef _BaseElement element if isinstance(other, QobjEvo): if other._dims != self._dims: raise TypeError("incompatible dimensions" + str(self.dims) + ", " + str(other.dims)) for element in ( other).elements: self.elements.append(element) self._update_feedback(other) elif isinstance(other, Qobj): if other._dims != self._dims: raise TypeError("incompatible dimensions" + str(self.dims) + ", " + str(other.dims)) self.elements.append(_ConstantElement(other)) elif ( isinstance(other, numbers.Number) and self._dims[0] == self._dims[1] ): self.elements.append(_ConstantElement(other * qutip.qeye_like(self))) else: return NotImplemented return self def __sub__(left, right): if isinstance(left, QobjEvo): res = left.copy() res += -right return res else: res = -right.copy() res += left return res def __rsub__(self, other): if not isinstance(other, (Qobj, QobjEvo, numbers.Number)): return NotImplemented res = -self res += other return res def __isub__(self, other): if not isinstance(other, (Qobj, QobjEvo, numbers.Number)): return NotImplemented self += (-other) return self def __matmul__(left, right): cdef QobjEvo res if isinstance(left, QobjEvo): return left.copy().__imatmul__(right) elif isinstance(left, Qobj): if left._dims[1] != ( right)._dims[0]: raise TypeError("incompatible dimensions" + str(left.dims[1]) + ", " + str(( right).dims[0])) res = right.copy() res._dims = Dimensions(left._dims[0], right._dims[1]) res.shape = (left.shape[0], right.shape[1]) left = _ConstantElement(left) res.elements = [left @ element for element in res.elements] res._update_feedback() return res else: return NotImplemented def __rmatmul__(QobjEvo self, other): cdef QobjEvo res if isinstance(other, Qobj): if other._dims[1] != self._dims[0]: raise TypeError("incompatible dimensions" + str(other.dims[1]) + ", " + str(self.dims[0])) res = self.copy() res._dims = Dimensions([other._dims[0], res._dims[1]]) res.shape = (other.shape[0], res.shape[1]) other = _ConstantElement(other) res.elements = [other @ element for element in res.elements] res._update_feedback() return res else: return NotImplemented def __imatmul__(QobjEvo self, other): if isinstance(other, (Qobj, QobjEvo)): if self._dims[1] != other._dims[0]: raise TypeError("incompatible dimensions" + str(self.dims[1]) + ", " + str(other.dims[0])) self._dims = Dimensions([self._dims[0], other._dims[1]]) self.shape = (self.shape[0], other.shape[1]) if isinstance(other, Qobj): other = _ConstantElement(other) self.elements = [element @ other for element in self.elements] self._update_feedback() elif isinstance(other, QobjEvo): self.elements = [left @ right for left, right in itertools.product( self.elements, ( other).elements )] self._update_feedback(other) else: return NotImplemented return self def __mul__(left, right): if isinstance(left, QobjEvo): return left.copy().__imul__(right) elif isinstance(left, Qobj): return right.__rmatmul__(left) elif isinstance(left, (numbers.Number, Coefficient)): return right.copy().__imul__(left) else: return NotImplemented def __rmul__(self, other): if isinstance(other, Qobj): return self.__rmatmul__(other) else: res = self.copy() res *= other return res def __imul__(QobjEvo self, other): if isinstance(other, (Qobj, QobjEvo)): self @= other elif isinstance(other, numbers.Number): self.elements = [element * other for element in self.elements] elif isinstance(other, Coefficient): other = _EvoElement(qutip.qeye(self.dims[1]), other) self.elements = [element @ other for element in self.elements] else: return NotImplemented return self def __truediv__(left, right): if isinstance(left, QobjEvo) and isinstance(right, numbers.Number): res = left.copy() res *= 1 / right return res return NotImplemented def __idiv__(self, other): if not isinstance(other, numbers.Number): return NotImplemented self *= 1 / other return self def __neg__(self): res = self.copy() res *= -1 return res ########################################################################### # tensor # ########################################################################### def __and__(left, right): """ Syntax shortcut for tensor: A & B ==> tensor(A, B) """ return qutip.tensor(left, right) ########################################################################### # Unary transformation # ########################################################################### def trans(self): """ Transpose of the quantum object """ cdef QobjEvo res = self.copy() res.elements = [element.linear_map(Qobj.trans) for element in res.elements] res._dims = Dimensions(res._dims[0], res._dims[1]) return res def conj(self): """Get the element-wise conjugation of the quantum object.""" cdef QobjEvo res = self.copy() res.elements = [element.linear_map(Qobj.conj, True) for element in res.elements] return res def dag(self): """Get the Hermitian adjoint of the quantum object.""" cdef QobjEvo res = self.copy() res.elements = [element.linear_map(Qobj.dag, True) for element in res.elements] res._dims = Dimensions(res._dims[0], res._dims[1]) return res def to(self, data_type): """ Convert the underlying data store of all component into the desired storage representation. The different storage representations available are the "data-layer types". By default, these are :obj:`.Dense`, :obj:`.Dia` and :obj:`.CSR`, which respectively construct a dense matrix, diagonal sparse matrixand a compressed sparse row one. The :obj:`.QobjEvo` is transformed inplace. Parameters ---------- data_type : type The data-layer type that the data of this :obj:`.Qobj` should be converted to. Returns ------- None """ return self.linear_map(partial(Qobj.to, data_type=data_type), _skip_check=True) def tidyup(self, atol=1e-12): """Removes small elements from quantum object.""" for element in self.elements: if type(element) is _ConstantElement: element = _ConstantElement(element.qobj(0).tidyup(atol)) elif type(element) is _EvoElement: element = _EvoElement(element.qobj(0).tidyup(atol), element._coefficient) return self def linear_map(self, op_mapping, *, _skip_check=False): """ Apply mapping to each Qobj contribution. Example: ``QobjEvo([sigmax(), coeff]).linear_map(spre)`` gives the same result has ``QobjEvo([spre(sigmax()), coeff])`` Parameters ---------- op_mapping: callable Funtion to apply to each elements. Returns ------- :class:`.QobjEvo` Modified object Notes ----- Does not modify the coefficients, thus ``linear_map(conj)`` would not give the the conjugate of the QobjEvo. It's only valid for linear transformations. """ if not _skip_check: out = op_mapping(self(0)) if not isinstance(out, Qobj): raise TypeError("The op_mapping function must return a Qobj") cdef QobjEvo res = self.copy() res.elements = [element.linear_map(op_mapping) for element in res.elements] res._dims = res.elements[0].qobj(0)._dims res.shape = res.elements[0].qobj(0).shape res._update_feedback() if not _skip_check: if res(0) != out: raise ValueError("The mapping is not linear") return res ########################################################################### # Cleaning and compress # ########################################################################### def _compress_merge_qobj(self, coeff_elements): """Merge element with matching qobj: ``[A, f1], [A, f2] -> [A, f1+f2]`` """ cleaned_elements = [] # Mimic a dict with Qobj not hashable qobjs = [] coeffs = [] for element in coeff_elements: for i, qobj in enumerate(qobjs): if element.qobj(0) == qobj: coeffs[i] = coeffs[i] + element._coefficient break else: qobjs.append(element.qobj(0)) coeffs.append(element._coefficient) for qobj, coeff in zip(qobjs, coeffs): cleaned_elements.append(_EvoElement(qobj, coeff)) return cleaned_elements def compress(self): """ Look for redundance in the :obj:`.QobjEvo` components: Constant parts, (:obj:`.Qobj` without :obj:`Coefficient`) will be summed. Pairs ``[Qobj, Coefficient]`` with the same :obj:`.Qobj` are merged. Example: ``[[sigmax(), f1], [sigmax(), f2]] -> [[sigmax(), f1+f2]]`` The :obj:`.QobjEvo` is transformed inplace. Returns ------- None """ cte_elements = [] coeff_elements = [] func_elements = [] for element in self.elements: if type(element) is _ConstantElement: cte_elements.append(element) elif type(element) is _EvoElement: coeff_elements.append(element) else: func_elements.append(element) cleaned_elements = [] if len(cte_elements) >= 2: # Multiple constant parts cleaned_elements.append(_ConstantElement( sum(element.qobj(0) for element in cte_elements))) else: cleaned_elements += cte_elements coeff_elements = self._compress_merge_qobj(coeff_elements) cleaned_elements += coeff_elements + func_elements self.elements = cleaned_elements def to_list(QobjEvo self): """ Restore the QobjEvo to a list form. Returns ------- list_qevo: list The QobjEvo as a list, element are either :obj:`.Qobj` for constant parts, ``[Qobj, Coefficient]`` for coefficient based term. The original format of the :obj:`Coefficient` is not restored. Lastly if the original :obj:`.QobjEvo` is constructed with a function returning a Qobj, the term is returned as a pair of the original function and args (``dict``). """ out = [] for element in self.elements: if isinstance(element, _ConstantElement): out.append(element.qobj(0)) elif isinstance(element, _EvoElement): coeff = element._coefficient out.append([element.qobj(0), coeff]) elif isinstance(element, _FuncElement): func = element._func args = element._args out.append([func, args]) else: out.append([element, {}]) return out ########################################################################### # properties # ########################################################################### @property def num_elements(self): """Number of parts composing the system""" return len(self.elements) @property def isconstant(self): """Does the system change depending on ``t``""" return not any(type(element) is not _ConstantElement for element in self.elements) @property def isoper(self): """Indicates if the system represents an operator.""" return self._dims.type in ['oper', 'scalar'] @property def issuper(self): """Indicates if the system represents a superoperator.""" return self._dims.type == 'super' @property def dims(self): return self._dims.as_list() @property def type(self): return self._dims.type @property def superrep(self): return self._dims.superrep @property def isbra(self): """Indicates if the system represents a bra state.""" return self._dims.type in ['bra', 'scalar'] @property def isket(self): """Indicates if the system represents a ket state.""" return self._dims.type in ['ket', 'scalar'] @property def isoperket(self): """Indicates if the system represents a operator-ket state.""" return self._dims.type == 'operator-ket' @property def isoperbra(self): """Indicates if the system represents a operator-bra state.""" return self._dims.type == 'operator-bra' @property def dtype(self): """ Type of the data layers of the QobjEvo. When different data layers are used, we return the type of the sum of the parts. """ part_types = [part.dtype for part in self.elements] if ( part_types[0] is not None and all(part == part_types[0] for part in part_types) ): return part_types[0] return self(0).dtype ########################################################################### # operation methods # ########################################################################### def expect(QobjEvo self, object t, state, check_real=True): """ Expectation value of this operator at time ``t`` with the state. Parameters ---------- t : float Time of the operator to apply. state : Qobj right matrix of the product check_real : bool (True) Whether to convert the result to a `real` when the imaginary part is smaller than the real part by a dactor of ``settings.core['rtol']``. Returns ------- expect : float or complex ``state.adjoint() @ self @ state`` if ``state`` is a ket. ``trace(self @ matrix)`` is ``state`` is an operator or operator-ket. """ # TODO: remove reading from `settings` for a typed value when options # support property. cdef float herm_rtol = settings.core['rtol'] if not isinstance(state, Qobj): raise TypeError("A Qobj state is expected") if not (self.isoper or self.issuper): raise ValueError("Must be an operator or super operator to compute" " an expectation value") if not ( (self._dims[1] == state._dims[0]) or (self.issuper and self._dims[1] == state._dims) ): raise ValueError("incompatible dimensions " + str(self.dims) + ", " + str(state.dims)) out = self.expect_data(t, state.data) if ( check_real and (out == 0 or (out.real and fabs(out.imag / out.real) < herm_rtol)) ): return out.real return out cpdef object expect_data(QobjEvo self, object t, Data state): """ Expectation is defined as ``state.adjoint() @ self @ state`` if ``state`` is a vector, or ``state`` is an operator and ``self`` is a superoperator. If ``state`` is an operator and ``self`` is an operator, then expectation is ``trace(self @ matrix)``. """ if type(state) is Dense: return self._expect_dense(t, state) cdef _BaseElement part cdef object out = 0. cdef Data part_data cdef object expect_func t = self._prepare(t, state) if self.issuper: if state.shape[1] != 1: state = _data.column_stack(state) expect_func = _data.expect_super else: expect_func = _data.expect for element in self.elements: part = (<_BaseElement> element) part_data = part.data(t) out += part.coeff(t) * expect_func(part_data, state) return out cdef double complex _expect_dense(QobjEvo self, double t, Dense state) except *: """For Dense state, ``column_stack_dense`` can be done inplace if in fortran format.""" cdef size_t nrow = state.shape[0] cdef _BaseElement part cdef double complex out = 0., coeff cdef Data part_data t = self._prepare(t, state) if self.issuper: if state.shape[1] != 1: state = column_stack_dense(state, inplace=state.fortran) try: for element in self.elements: part = (<_BaseElement> element) coeff = part.coeff(t) part_data = part.data(t) out += coeff * expect_super_data_dense(part_data, state) finally: if state.fortran: # `state` was reshaped inplace, restore it's original shape column_unstack_dense(state, nrow, inplace=state.fortran) else: for element in self.elements: part = (<_BaseElement> element) coeff = part.coeff(t) part_data = part.data(t) out += coeff * expect_data_dense(part_data, state) return out def matmul(self, t, state): """ Product of this operator at time ``t`` to the state. ``self(t) @ state`` Parameters ---------- t : float Time of the operator to apply. state : Qobj right matrix of the product Returns ------- product : Qobj The result product as a Qobj """ if not isinstance(state, Qobj): raise TypeError("A Qobj state is expected") if self._dims[1] != state._dims[0]: raise ValueError("incompatible dimensions " + str(self.dims[1]) + ", " + str(state.dims[0])) return Qobj(self.matmul_data(t, state.data), dims=[self._dims[0], state._dims[1]], copy=False ) cpdef Data matmul_data(QobjEvo self, object t, Data state, Data out=None): """Compute ``out += self(t) @ state``""" cdef _BaseElement part t = self._prepare(t, state) if out is None and type(state) is Dense: out = dense.zeros(self.shape[0], state.shape[1], ( state).fortran) elif out is None: out = _data.zeros[type(state)](self.shape[0], state.shape[1]) for element in self.elements: part = (<_BaseElement> element) out = part.matmul_data_t(t, state, out) return out class _Feedback: default = None def __init__(self): raise NotImplementedError("Use subclass") def check_consistency(self, dims): """ Raise an error when the dims of the e_ops / state don't match. Tell the dims to the feedback for reconstructing the Qobj. """ qutip-5.1.1/qutip/core/data/000077500000000000000000000000001474175217300156765ustar00rootroot00000000000000qutip-5.1.1/qutip/core/data/__init__.pxd000066400000000000000000000007451474175217300201600ustar00rootroot00000000000000#cython: language_level=3 # Package-level relative imports in Cython (0.29.17) are temperamental. from qutip.core.data cimport dense, csr from qutip.core.data.base cimport Data, idxint from qutip.core.data.dense cimport Dense from qutip.core.data.csr cimport CSR from qutip.core.data.dia cimport Dia from qutip.core.data.add cimport * from qutip.core.data.adjoint cimport * from qutip.core.data.kron cimport * from qutip.core.data.matmul cimport * from qutip.core.data.mul cimport * qutip-5.1.1/qutip/core/data/__init__.py000066400000000000000000000032271474175217300200130ustar00rootroot00000000000000# First-class type imports from . import dense, csr from .dense import Dense from .csr import CSR from .dia import Dia from .base import Data from .add import * from .adjoint import * from .constant import * from .eigen import * from .expect import * from .expm import * from .inner import * from .kron import * from .linalg import * from .matmul import * from .make import * from .mul import * from .pow import * from .project import * from .properties import * from .ptrace import * from .reshape import * from .tidyup import * from .trace import * from .solve import * from .extract import * # For operations with mulitple related versions, we just import the module. from . import norm, permute # Set up the data conversions that are known by us. All types covered by # conversions will be made available for use in the dispatcher functions. from .convert import to, create to.add_conversions([ (Dense, CSR, dense.from_csr, 1), (CSR, Dense, csr.from_dense, 1.4), (Dia, Dense, dia.from_dense, 1.4), (Dense, Dia, dense.from_dia, 1.2), (Dia, CSR, dia.from_csr, 1), (CSR, Dia, csr.from_dia, 1), ]) to.register_aliases(['csr', 'CSR'], CSR) to.register_aliases(['Dense', 'dense'], Dense) to.register_aliases(['DIA', 'Dia', 'dia', 'diag'], Dia) from . import _creator_utils import numpy as np create.add_creators([ (_creator_utils.is_data, _creator_utils.data_copy, 100), (_creator_utils.isspmatrix_csr, CSR, 80), (_creator_utils.isspmatrix_dia, Dia, 80), (_creator_utils.is_nparray, Dense, 80), (_creator_utils.issparse, CSR, 20), (_creator_utils.true, Dense, -np.inf), ]) del _creator_utils del np from .dispatch import Dispatcher qutip-5.1.1/qutip/core/data/_creator_utils.py000066400000000000000000000013621474175217300212700ustar00rootroot00000000000000""" Define functions to use as Data creator for `create` in `convert.py`. """ from scipy.sparse import isspmatrix_csr, issparse, isspmatrix_dia import numpy as np from .csr import CSR from .base import Data from .dense import Dense __all__ = [ 'data_copy', 'is_data', 'is_nparray', 'isspmatrix_csr', 'isspmatrix_dia', 'issparse' ] def is_data(arg): return isinstance(arg, Data) def is_nparray(arg): return isinstance(arg, np.ndarray) def true(arg): return True def data_copy(arg, shape, copy=True): if shape is not None and shape != arg.shape: raise ValueError("".join([ "shapes do not match: ", str(shape), " and ", str(arg.shape), ])) return arg.copy() if copy else arg qutip-5.1.1/qutip/core/data/add.pxd000066400000000000000000000011561474175217300171460ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia cdef void add_dense_eq_order_inplace(Dense left, Dense right, double complex scale) cpdef CSR add_csr(CSR left, CSR right, double complex scale=*) cpdef Dense add_dense(Dense left, Dense right, double complex scale=*) cpdef Dia add_dia(Dia left, Dia right, double complex scale=*) cpdef Dense iadd_dense(Dense left, Dense right, double complex scale=*) cpdef CSR sub_csr(CSR left, CSR right) cpdef Dense sub_dense(Dense left, Dense right) cpdef Dia sub_dia(Dia left, Dia right) qutip-5.1.1/qutip/core/data/add.pyx000066400000000000000000000277331474175217300172040ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False cimport cython import numpy as np cimport numpy as cnp from scipy.linalg cimport cython_blas as blas from qutip.settings import settings from qutip.core.data.base cimport idxint, Data from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia from qutip.core.data.tidyup cimport tidyup_dia from qutip.core.data.csr cimport ( CSR, Accumulator, acc_alloc, acc_free, acc_scatter, acc_gather, acc_reset, ) from qutip.core.data cimport csr, dense, dia cnp.import_array() __all__ = [ 'add', 'add_csr', 'add_dense', 'iadd_dense', 'add_dia', 'sub', 'sub_csr', 'sub_dense', 'sub_dia', ] cdef int _ONE=1 cdef int _check_shape(Data left, Data right) except -1 nogil: if left.shape[0] != right.shape[0] or left.shape[1] != right.shape[1]: raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) return 0 cdef idxint _add_csr(Accumulator *acc, CSR a, CSR b, CSR c, double tol) nogil: """ Perform the operation c := a + b for CSR matrices, where `a` and `b` are guaranteed to be the correct shape, and `c` already has enough space allocated (at least nnz(a)+nnz(b)). Return the true value of nnz(c). """ cdef idxint row, ptr_a, ptr_b, ptr_a_max, ptr_b_max, nnz=0, col_a, col_b cdef idxint ncols = a.shape[1] c.row_index[0] = nnz ptr_a_max = ptr_b_max = 0 for row in range(a.shape[0]): ptr_a = ptr_a_max ptr_a_max = a.row_index[row + 1] ptr_b = ptr_b_max ptr_b_max = b.row_index[row + 1] col_a = a.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 col_b = b.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 # We use this method of going through the row to give the Accumulator # the best chance of receiving the scatters in a sorted order. We # could also safely iterate through a completely then b, which would be # more cache efficient, but would quite often require a sort within the # gather, making the algorithimic complexity worse. while ptr_a < ptr_a_max or ptr_b < ptr_b_max: if col_a < col_b: acc_scatter(acc, a.data[ptr_a], col_a) ptr_a += 1 col_a = a.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 else: acc_scatter(acc, b.data[ptr_b], col_b) ptr_b += 1 col_b = b.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 # There's no need to test col_a == col_b because the Accumulator # already tests that in all scatters anyway. nnz += acc_gather(acc, c.data + nnz, c.col_index + nnz, tol) acc_reset(acc) c.row_index[row + 1] = nnz return nnz cdef idxint _add_csr_scale(Accumulator *acc, CSR a, CSR b, CSR c, double complex scale, double tol) nogil: """ Perform the operation c := a + scale*b for CSR matrices, where `a` and `b` are guaranteed to be the correct shape, and `c` already has enough space allocated (at least nnz(a)+nnz(b)). Return the true value of nnz(c). """ cdef idxint row, ptr_a, ptr_b, ptr_a_max, ptr_b_max, nnz=0, col_a, col_b cdef idxint ncols = a.shape[1] c.row_index[0] = nnz ptr_a_max = ptr_b_max = 0 for row in range(a.shape[0]): ptr_a = ptr_a_max ptr_a_max = a.row_index[row + 1] ptr_b = ptr_b_max ptr_b_max = b.row_index[row + 1] col_a = a.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 col_b = b.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 while ptr_a < ptr_a_max or ptr_b < ptr_b_max: if col_a < col_b: acc_scatter(acc, a.data[ptr_a], col_a) ptr_a += 1 col_a = a.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 else: acc_scatter(acc, scale * b.data[ptr_b], col_b) ptr_b += 1 col_b = b.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 nnz += acc_gather(acc, c.data + nnz, c.col_index + nnz, tol) acc_reset(acc) c.row_index[row + 1] = nnz return nnz cpdef CSR add_csr(CSR left, CSR right, double complex scale=1): """ Matrix addition of `left` and `right` for CSR inputs and output. If given, `right` is multiplied by `scale`, so the full operation is ``out := left + scale*right`` The two matrices must be of exactly the same shape. Parameters ---------- left : CSR Matrix to be added. right : CSR Matrix to be added. If `scale` is given, this matrix will be multiplied by `scale` before addition. scale : optional double complex (1) The scalar value to multiply `right` by before addition. Returns ------- out : CSR The result `left + scale*right`. """ _check_shape(left, right) cdef idxint left_nnz = csr.nnz(left) cdef idxint right_nnz = csr.nnz(right) cdef idxint worst_nnz = left_nnz + right_nnz cdef idxint i cdef CSR out cdef Accumulator acc cdef double tol = 0 if settings.core['auto_tidyup']: tol = settings.core['auto_tidyup_atol'] # Fast paths for zero matrices. if right_nnz == 0 or scale == 0: return left.copy() if left_nnz == 0: out = right.copy() # Fast path if the multiplication is a no-op. if scale != 1: for i in range(right_nnz): out.data[i] *= scale return out # Main path. out = csr.empty(left.shape[0], left.shape[1], worst_nnz) acc = acc_alloc(left.shape[1]) if scale == 1: _add_csr(&acc, left, right, out, tol) else: _add_csr_scale(&acc, left, right, out, scale, tol) acc_free(&acc) return out cdef void add_dense_eq_order_inplace(Dense left, Dense right, double complex scale): cdef int size = left.shape[0] * left.shape[1] with nogil: blas.zaxpy(&size, &scale, right.data, &_ONE, left.data, &_ONE) cdef Dense _add_dense_eq_order(Dense left, Dense right, double complex scale): cdef Dense out = left.copy() cdef int size = left.shape[0] * left.shape[1] with nogil: blas.zaxpy(&size, &scale, right.data, &_ONE, out.data, &_ONE) return out cpdef Dense add_dense(Dense left, Dense right, double complex scale=1): _check_shape(left, right) if not (left.fortran ^ right.fortran): return _add_dense_eq_order(left, right, scale) cdef Dense out = left.copy() cdef size_t nrows=left.shape[0], ncols=left.shape[1], idx # We always iterate through `left` and `out` in memory-layout order. cdef int dim1, dim2 dim1, dim2 = (nrows, ncols) if left.fortran else (ncols, nrows) with nogil: for idx in range(dim2): blas.zaxpy(&dim1, &scale, right.data + idx, &dim2, out.data + idx*dim1, &_ONE) return out cpdef Dense iadd_dense(Dense left, Dense right, double complex scale=1): _check_shape(left, right) cdef int size = left.shape[0] * left.shape[1] cdef int dim1, dim2 cdef size_t nrows=left.shape[0], ncols=left.shape[1], idx dim1, dim2 = (nrows, ncols) if left.fortran else (ncols, nrows) with nogil: if not (left.fortran ^ right.fortran): blas.zaxpy(&size, &scale, right.data, &_ONE, left.data, &_ONE) else: for idx in range(dim2): blas.zaxpy(&dim1, &scale, right.data + idx, &dim2, left.data + idx*dim1, &_ONE) return left cpdef Dia add_dia(Dia left, Dia right, double complex scale=1): _check_shape(left, right) cdef idxint diag_left=0, diag_right=0, out_diag=0, i cdef double complex *ptr_out, cdef double complex *ptr_left cdef double complex *ptr_right cdef bint sorted=True cdef Dia out = dia.empty(left.shape[0], left.shape[1], left.num_diag + right.num_diag) cdef int length, size=left.shape[1] ptr_out = out.data ptr_left = left.data ptr_right = right.data with nogil: while diag_left < left.num_diag and diag_right < right.num_diag: if left.offsets[diag_left] == right.offsets[diag_right]: out.offsets[out_diag] = left.offsets[diag_left] blas.zcopy(&size, ptr_left, &_ONE, ptr_out, &_ONE) blas.zaxpy(&size, &scale, ptr_right, &_ONE, ptr_out, &_ONE) ptr_left += size diag_left += 1 ptr_right += size diag_right += 1 elif left.offsets[diag_left] <= right.offsets[diag_right]: out.offsets[out_diag] = left.offsets[diag_left] blas.zcopy(&size, ptr_left, &_ONE, ptr_out, &_ONE) ptr_left += size diag_left += 1 else: out.offsets[out_diag] = right.offsets[diag_right] blas.zcopy(&size, ptr_right, &_ONE, ptr_out, &_ONE) if scale != 1: blas.zscal(&size, &scale, ptr_out, &_ONE) ptr_right += size diag_right += 1 if out_diag != 0 and out.offsets[out_diag-1] >= out.offsets[out_diag]: sorted=False ptr_out += size out_diag += 1 if diag_left < left.num_diag: for i in range(left.num_diag - diag_left): out.offsets[out_diag] = left.offsets[diag_left + i] if out_diag != 0 and out.offsets[out_diag-1] >= out.offsets[out_diag]: sorted=False out_diag += 1 length = size * (left.num_diag - diag_left) blas.zcopy(&length, ptr_left, &_ONE, ptr_out, &_ONE) if diag_right < right.num_diag: for i in range(right.num_diag - diag_right): out.offsets[out_diag] = right.offsets[diag_right + i] if out_diag != 0 and out.offsets[out_diag-1] >= out.offsets[out_diag]: sorted=False out_diag += 1 length = size * (right.num_diag - diag_right) blas.zcopy(&length, ptr_right, &_ONE, ptr_out, &_ONE) if scale != 1: blas.zscal(&length, &scale, ptr_out, &_ONE) out.num_diag = out_diag if not sorted: dia.clean_dia(out, True) if settings.core['auto_tidyup']: tidyup_dia(out, settings.core['auto_tidyup_atol'], True) return out cpdef CSR sub_csr(CSR left, CSR right): return add_csr(left, right, -1) cpdef Dense sub_dense(Dense left, Dense right): return add_dense(left, right, -1) cpdef Dia sub_dia(Dia left, Dia right): return add_dia(left, right, -1) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect add = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('scale', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=1), ]), name='add', module=__name__, inputs=('left', 'right'), out=True, ) add.__doc__ =\ """ Perform the operation left + scale*right where `left` and `right` are matrices, and `scale` is an optional complex scalar. """ add.add_specialisations([ (Dense, Dense, Dense, add_dense), (CSR, CSR, CSR, add_csr), (Dia, Dia, Dia, add_dia), ], _defer=True) sub = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), ]), name='sub', module=__name__, inputs=('left', 'right'), out=True, ) sub.__doc__ =\ """ Perform the operation left - right where `left` and `right` are matrices. """ sub.add_specialisations([ (Dense, Dense, Dense, sub_dense), (CSR, CSR, CSR, sub_csr), (Dia, Dia, Dia, sub_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/adjoint.pxd000066400000000000000000000007221474175217300200440ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia cpdef CSR adjoint_csr(CSR matrix) cpdef CSR transpose_csr(CSR matrix) cpdef CSR conj_csr(CSR matrix) cpdef Dense adjoint_dense(Dense matrix) cpdef Dense transpose_dense(Dense matrix) cpdef Dense conj_dense(Dense matrix) cpdef Dia adjoint_dia(Dia matrix) cpdef Dia transpose_dia(Dia matrix) cpdef Dia conj_dia(Dia matrix) qutip-5.1.1/qutip/core/data/adjoint.pyx000066400000000000000000000161101474175217300200670ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memset cimport cython from qutip.core.data.base cimport idxint from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia from qutip.core.data cimport csr, dense, dia # Import std::conj as `_conj` to avoid clashing with our 'conj' dispatcher. cdef extern from "" namespace "std" nogil: double complex _conj "conj"(double complex x) __all__ = [ 'adjoint', 'adjoint_csr', 'adjoint_dense', 'adjoint_dia', 'conj', 'conj_csr', 'conj_dense', 'conj_dia', 'transpose', 'transpose_csr', 'transpose_dense', 'transpose_dia', ] cpdef CSR transpose_csr(CSR matrix): """Transpose the CSR matrix, and return a new object.""" cdef CSR out = csr.empty(matrix.shape[1], matrix.shape[0], csr.nnz(matrix)) cdef idxint row, col, ptr, ptr_out cdef idxint rows_in=matrix.shape[0], rows_out=matrix.shape[1] with nogil: memset(&out.row_index[0], 0, (rows_out + 1) * sizeof(idxint)) for row in range(rows_in): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] + 1 out.row_index[col] += 1 for row in range(rows_out): out.row_index[row + 1] += out.row_index[row] for row in range(rows_in): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] ptr_out = out.row_index[col] out.data[ptr_out] = matrix.data[ptr] out.col_index[ptr_out] = row out.row_index[col] = ptr_out + 1 for row in range(rows_out, 0, -1): out.row_index[row] = out.row_index[row - 1] out.row_index[0] = 0 return out cpdef CSR adjoint_csr(CSR matrix): """Conjugate-transpose the CSR matrix, and return a new object.""" cdef idxint nnz_ = csr.nnz(matrix) cdef CSR out = csr.empty(matrix.shape[1], matrix.shape[0], nnz_) cdef idxint row, col, ptr, ptr_out cdef idxint rows_in=matrix.shape[0], rows_out=matrix.shape[1] with nogil: memset(&out.row_index[0], 0, (rows_out + 1) * sizeof(idxint)) for row in range(rows_in): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] + 1 out.row_index[col] += 1 for row in range(rows_out): out.row_index[row + 1] += out.row_index[row] for row in range(rows_in): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] ptr_out = out.row_index[col] out.data[ptr_out] = _conj(matrix.data[ptr]) out.col_index[ptr_out] = row out.row_index[col] = ptr_out + 1 for row in range(rows_out, 0, -1): out.row_index[row] = out.row_index[row - 1] out.row_index[0] = 0 return out cpdef CSR conj_csr(CSR matrix): """Conjugate the CSR matrix, and return a new object.""" cdef CSR out = csr.copy_structure(matrix) cdef idxint ptr with nogil: for ptr in range(csr.nnz(matrix)): out.data[ptr] = _conj(matrix.data[ptr]) return out cpdef Dense adjoint_dense(Dense matrix): cdef Dense out = dense.empty_like(matrix, fortran=not matrix.fortran) out.shape = (out.shape[1], out.shape[0]) with nogil: for ptr in range(matrix.shape[0] * matrix.shape[1]): out.data[ptr] = _conj(matrix.data[ptr]) return out cpdef Dense transpose_dense(Dense matrix): cdef Dense out = matrix.copy() out.shape = (out.shape[1], out.shape[0]) out.fortran = not out.fortran return out cpdef Dense conj_dense(Dense matrix): cdef Dense out = dense.empty_like(matrix) cdef size_t ptr with nogil: for ptr in range(matrix.shape[0] * matrix.shape[1]): out.data[ptr] = _conj(matrix.data[ptr]) return out cpdef Dia adjoint_dia(Dia matrix): cdef Dia out = dia.empty(matrix.shape[1], matrix.shape[0], matrix.num_diag) cdef size_t i, new_i, cdef idxint new_offset, j with nogil: out.num_diag = matrix.num_diag for i in range(matrix.num_diag): new_i = matrix.num_diag - i - 1 new_offset = out.offsets[new_i] = -matrix.offsets[i] for j in range(out.shape[1]): if (j < new_offset) or (j - new_offset >= matrix.shape[1]): out.data[new_i * out.shape[1] + j] = 0. else: out.data[new_i * out.shape[1] + j] = _conj(matrix.data[i * matrix.shape[1] + j - new_offset]) return out cpdef Dia transpose_dia(Dia matrix): cdef Dia out = dia.empty(matrix.shape[1], matrix.shape[0], matrix.num_diag) cdef size_t i, new_i, cdef idxint new_offset, j with nogil: out.num_diag = matrix.num_diag for i in range(matrix.num_diag): new_i = matrix.num_diag - i - 1 new_offset = out.offsets[new_i] = -matrix.offsets[i] for j in range(out.shape[1]): if (j < new_offset) or (j - new_offset >= matrix.shape[1]): out.data[new_i * out.shape[1] + j] = 0. else: out.data[new_i * out.shape[1] + j] = matrix.data[i * matrix.shape[1] + j - new_offset] return out cpdef Dia conj_dia(Dia matrix): cdef Dia out = dia.empty_like(matrix) cdef size_t i, j with nogil: out.num_diag = matrix.num_diag for i in range(matrix.num_diag): out.offsets[i] = matrix.offsets[i] for j in range(matrix.shape[1]): out.data[i * matrix.shape[1] + j] = _conj(matrix.data[i * matrix.shape[1] + j]) return out from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect adjoint = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='adjoint', module=__name__, inputs=('matrix',), out=True, ) adjoint.__doc__ = """Hermitian adjoint (matrix conjugate transpose).""" adjoint.add_specialisations([ (Dense, Dense, adjoint_dense), (CSR, CSR, adjoint_csr), (Dia, Dia, adjoint_dia), ], _defer=True) transpose = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='transpose', module=__name__, inputs=('matrix',), out=True, ) transpose.__doc__ = """Transpose of a matrix.""" transpose.add_specialisations([ (Dense, Dense, transpose_dense), (CSR, CSR, transpose_csr), (Dia, Dia, transpose_dia), ], _defer=True) conj = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='conj', module=__name__, inputs=('matrix',), out=True, ) conj.__doc__ = """Element-wise conjugation of a matrix.""" conj.add_specialisations([ (Dense, Dense, conj_dense), (CSR, CSR, conj_csr), (Dia, Dia, conj_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/base.pxd000066400000000000000000000007011474175217300173230ustar00rootroot00000000000000#cython: language_level=3 cdef extern from "src/intdtype.h": # cython is smart enough to understand this int can be 32 or 64 bits. ctypedef int idxint cdef int _idxint_size cdef int idxint_DTYPE cdef class Data: cdef readonly (idxint, idxint) shape cpdef object to_array(self) cpdef double complex trace(self) cpdef Data adjoint(self) cpdef Data conj(self) cpdef Data transpose(self) cpdef Data copy(self) qutip-5.1.1/qutip/core/data/base.pyx000066400000000000000000000046271474175217300173630ustar00rootroot00000000000000#cython: language_level=3 #cython: c_api_binop_methods=True import numpy as np cimport numpy as cnp import qutip.core.data as _data from qutip.settings import settings __all__ = [ 'idxint_size', 'idxint_dtype', 'Data', 'EfficiencyWarning', ] if _idxint_size == 32: idxint_dtype = np.int32 idxint_DTYPE = cnp.NPY_INT32 else: idxint_dtype = np.int64 idxint_DTYPE = cnp.NPY_INT64 idxint_size = _idxint_size # As this is an abstract base class with C entry points, we have to explicitly # stub out methods since we can't mark them as abstract. cdef class Data: def __init__(self, shape): self.shape = shape cpdef object to_array(self): raise NotImplementedError cpdef double complex trace(self): return NotImplementedError cpdef Data adjoint(self): raise NotImplementedError cpdef Data conj(self): raise NotImplementedError cpdef Data transpose(self): raise NotImplementedError cpdef Data copy(self): raise NotImplementedError def __add__(left, right): if isinstance(left, Data) and isinstance(right, Data): return _data.add(left, right) return NotImplemented def __sub__(left, right): if isinstance(left, Data) and isinstance(right, Data): return _data.sub(left, right) return NotImplemented def __matmul__(left, right): if isinstance(left, Data) and isinstance(right, Data): return _data.matmul(left, right) return NotImplemented def __mul__(left, right): data, number = (left, right) if isinstance(left, Data) else (right, left) try: return _data.mul(data, number) except TypeError: return NotImplemented def __truediv__(left, right): data, number = (left, right) if isinstance(left, Data) else (right, left) try: return _data.mul(data, 1/number) except TypeError: return NotImplemented def __neg__(self): return _data.neg(self) def __eq__(left, right): if not (isinstance(left, Data) and isinstance(right, Data)): return NotImplemented if ( left.shape[0] == right.shape[0] and left.shape[1] == right.shape[1] ): return _data.iszero(_data.sub(left, right), settings.core['atol']) return False class EfficiencyWarning(Warning): pass qutip-5.1.1/qutip/core/data/constant.py000066400000000000000000000073371474175217300201130ustar00rootroot00000000000000# This module exists to supply a couple of very standard constant matrices # which are used in the data layer, and within `Qobj` itself. Other matrices # (e.g. `create`) should not be here, but should be defined within the # higher-level components of QuTiP instead. from . import csr, dense, dia from .csr import CSR from .dia import Dia from .dense import Dense from .base import Data from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect __all__ = ['zeros', 'identity', 'zeros_like', 'identity_like', 'zeros_like_dense', 'identity_like_dense', 'zeros_like_data', 'identity_like_data'] zeros = _Dispatcher( _inspect.Signature([ _inspect.Parameter('rows', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('cols', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='zeros', module=__name__, inputs=(), out=True, ) zeros.__doc__ =\ """ Create matrix representation of 0 with the given dimensions. Depending on the selected output type, this may or may not actually contained explicit values; sparse matrices will typically contain nothing (which is their representation of 0), and dense matrices will still be filled. Parameters ---------- rows, cols : int The number of rows and columns in the output matrix. """ zeros.add_specialisations([ (CSR, csr.zeros), (Dia, dia.zeros), (Dense, dense.zeros), ], _defer=True) identity = _Dispatcher( _inspect.Signature([ _inspect.Parameter('dimension', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('scale', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=1), ]), name='identity', module=__name__, inputs=(), out=True, ) identity.__doc__ =\ """ Create a square identity matrix of the given dimension. Optionally, the `scale` can be given, where all the diagonal elements will be that instead of 1. Parameters ---------- dimension : int The dimension of the square output identity matrix. scale : complex, optional The element which should be placed on the diagonal. """ identity.add_specialisations([ (CSR, csr.identity), (Dia, dia.identity), (Dense, dense.identity), ], _defer=True) def zeros_like_data(data, /): """ Create an zeros matrix of the same type and shape. """ return zeros[type(data)](*data.shape) def zeros_like_dense(data, /): """ Create an zeros matrix of the same type and shape. """ return dense.zeros(*data.shape, fortran=data.fortran) def identity_like_data(data, /): """ Create an identity matrix of the same type and shape. """ if not data.shape[0] == data.shape[1]: raise ValueError( "Can't create an identity matrix like a non square matrix." ) return identity[type(data)](data.shape[0]) def identity_like_dense(data, /): """ Create an identity matrix of the same type and shape. """ if not data.shape[0] == data.shape[1]: raise ValueError( "Can't create an identity matrix like a non square matrix." ) return dense.identity(data.shape[0], fortran=data.fortran) identity_like = _Dispatcher( identity_like_data, name='identity_like', module=__name__, inputs=("data",), out=False, ) identity_like.add_specialisations([ (Data, identity_like_data), (Dense, identity_like_dense), ], _defer=True) zeros_like = _Dispatcher( zeros_like_data, name='zeros_like', module=__name__, inputs=("data",), out=False, ) zeros_like.add_specialisations([ (Data, zeros_like_data), (Dense, zeros_like_dense), ], _defer=True) del _Dispatcher, _inspect qutip-5.1.1/qutip/core/data/convert.pyx000066400000000000000000000445641474175217300201350ustar00rootroot00000000000000#cython: language_level=3 """ The conversion machinery between different data-layer types, and creation routines from arbitrary data. The classes `_to` and `_create` are not intended to be exported names, but are the backing machinery of the functions `data.to` and `data.create`, which are built up as the last objects in the `__init__.py` initialisation of the `data` module. """ # This module is compiled by Cython because it's the core of the entire # dispatch table, and having it compiled to a C extension saves about 1Âľs per # call. This is not much at all, and there's very little which benefits from # Cython compiliation, but such core functionality is called millions of times # even in a simple interactive QuTiP session, and it all adds up. import numbers import numpy as np from scipy.sparse import dok_matrix, csgraph cimport cython from qutip.core.data.base cimport Data __all__ = ['to', 'create'] class _Epsilon: """ Constant for an small weight non-null weight. Use to set `Data` specialisation just over direct specialisation. """ def __repr__(self): return "EPSILON" def __eq__(self, other): if isinstance(other, _Epsilon): return True return NotImplemented def __add__(self, other): if isinstance(other, _Epsilon): return self return other def __radd__(self, other): if isinstance(other, _Epsilon): return self return other def __lt__(self, other): """ positive number > _Epsilon > 0 """ if isinstance(other, _Epsilon): return False return other > 0. def __gt__(self, other): if isinstance(other, _Epsilon): return False return other <= 0. EPSILON = _Epsilon() def _raise_if_unconnected(dtype_list, weights): unconnected = {} for i, type_ in enumerate(dtype_list): missing = [dtype_list[j].__name__ for j, weight in enumerate(weights[:, i]) if weight == np.inf] if missing: unconnected[type_.__name__] = missing if unconnected: message = "Conversion graph not connected. Cannot reach:\n * " message += "\n * ".join(to + " from (" + ", ".join(froms) + ")" for to, froms in unconnected.items()) raise NotImplementedError(message) cdef class _converter: """Callable which converts objects of type `x.from_` to type `x.to`.""" cdef list functions cdef Py_ssize_t n_functions cdef readonly type to cdef readonly type from_ def __init__(self, functions, to_type, from_type): self.functions = list(functions) self.n_functions = len(self.functions) self.to = to_type self.from_ = from_type @cython.boundscheck(False) @cython.wraparound(False) def __call__(self, arg): if not isinstance(arg, self.from_): raise TypeError(str(arg) + " is not of type " + str(self.from_)) cdef Py_ssize_t i for i in range(self.n_functions): arg = self.functions[i](arg) return arg def __repr__(self): return ("") def identity_converter(arg): return arg cdef class _partial_converter: """Convert from any known data-layer type into the type `x.to`.""" cdef object converter cdef readonly type to def __init__(self, converter, to_type): self.converter = converter self.to = to_type def __call__(self, arg): try: return self.converter[self.to, type(arg)](arg) except KeyError: raise TypeError("unknown type of input: " + str(arg)) from None def __repr__(self): return "" # While `_to` and `_create` are defined as objects here, they are actually # exported by `data.__init__.py` as singleton function objects of their # respective types (without the leading underscore). cdef class _to: """ Convert data into a different type. This object is the knowledge source for every allowable data-layer type in QuTiP, and provides the conversions between all of them. The base use is to call this object as a function with signature (type, data) -> converted_data where `type` is a type object (such as `data.CSR`, or that obtained by calling `type(matrix)`) and `data` is data in a data-layer type. If you want to create a data-layer type from non-data-layer data, use `create` instead. You can get individual converters by using the key-lookup syntax. For example, the item to[CSR, Dense] is a callable which accepts arguments of type `Dense` and returns the equivalent item of type `CSR`. You can also get a generic converter to a particular data type if only one type is specified, so to[Dense] is a callable which accepts all known (at the time of the lookup) data-layer types, and converts them to `Dense`. See the `Efficiency notes` section below for more detail. Internally, the conversion process may go through several steps if new data-layer types have been defined with few conversions specified between them and the pre-existing converters. The first-class QuTiP data types `Dense` and `CSR` will typically have the best connectivity. Adding new types ---------------- You can add new data-layer types by calling the `add_conversions` method of this object, and then rebuilding all of the mathematical dispatchers. See the docstring of that method for more information. Efficiency notes ---------------- From an efficiency perspective, there is very little benefit to using the key-lookup syntax. Internally, `to(to_type, data)` effectively calls `to[to_type, type(data)]`, so storing the object elides the creation of a single tuple and a dict lookup, but the cost of this is generally less than 500ns. Using the one-argument lookup (e.g. `to[Dense]`) is no more efficient than the general call at all, but can be used in cases where a single callable is required and is more efficient than `functools.partial`. """ cdef readonly set dtypes cdef readonly list dispatchers cdef dict _direct_convert cdef dict _convert cdef readonly dict weight cdef readonly dict _str2type def __init__(self): self._direct_convert = {} self._convert = {} self.dtypes = set() self.weight = {} self.dispatchers = [] self._str2type = {} def add_conversions(self, converters): """ Add conversion functions between different data types. This is an advanced function, and is only intended for the QuTiP user who wants to add a new underlying data type to QuTiP. Any new data type must have at least one converter function given to produce the new data type from an existing data type, and at least one which produces an existing data type from the new one. You need not specify any more than this, although for efficiency reasons, you may want to specify direct conversions for all types you expect the new type to interact with frequently. Parameters ---------- converters : iterable of (to_type, from_type, converter, [weight]) An iterable of 3- or 4-tuples describing all the new conversions. Each element can individually be a 3- or 4-tuple; they do not need to be all one or the other. Elements ........ to_type : type The data-layer type that is output by the converter. from_type : type The data-layer type to be input to the converter. converter : callable (Data -> Data) The converter function. This should take a single argument (the input data-layer function) and output a data-layer object of `to_type`. The converter may assume without error checking that its input will always be of `to_type`. It is safe to specify the same conversion function for multiple inputs so long as the function handles them all safely, but it must always return a single output type. weight : positive real, optional (1) The weight associated with this conversion. This must be > 0, and defaults to `1` if not supplied (which is fixed to be the cost of conversion to `Dense` from `CSR`). It is generally safe just to leave this blank; it is always at best an approximation. The currently defined weights are accessible in the `weights` attribute of this object. Weight of ~0.001 are should be used in case when no conversion is needed or ``converter = lambda mat : mat``. """ for arg in converters: if len(arg) == 3: to_type, from_type, converter = arg weight = 1 elif len(arg) == 4: to_type, from_type, converter, weight = arg else: raise TypeError("unknown converter specification: " + str(arg)) if not isinstance(to_type, type): raise TypeError(repr(to_type) + " is not a type object") if not isinstance(from_type, type): raise TypeError(repr(from_type) + " is not a type object") if not isinstance(weight, numbers.Real) or weight <= 0: raise TypeError("weight " + repr(weight) + " is not valid") self.dtypes.add(from_type) self.dtypes.add(to_type) self._direct_convert[(to_type, from_type)] = (converter, weight) # Two-way mapping to convert between the type of a dtype and an integer # enumeration value for it. order, index = [], {} for i, dtype in enumerate(self.dtypes): order.append(dtype) index[dtype] = i # Treat the conversion problem as a shortest-path graph problem. We # build up the graph description as a matrix, then solve the # all-pairs-shortest-path problem. We forbid negative weights and # there are unlikely to be many data types, so the choice of algorithm # is unimportant (Dijkstra's, Floyd--Warshall, Bellman--Ford, etc). graph = dok_matrix((len(order), len(order))) for (to_type, from_type), (_, weight) in self._direct_convert.items(): graph[index[from_type], index[to_type]] = weight weights, predecessors =\ csgraph.floyd_warshall(graph.tocsr(), return_predecessors=True) _raise_if_unconnected(order, weights) # Build the whole shortest path conversion lookup. We directly store # all complete shortest paths, even though this is not the most memory # efficient, because we expect that there will generally be a small # number of available data types, and we care more about minimising the # number of lookups required. self.weight = {} self._convert = {} for i, from_t in enumerate(order): for j, to_t in enumerate(order): convert = [] weight = 0 cur_t = to_t pred_i = predecessors[i, j] while pred_i >= 0: pred_t = order[pred_i] _convert, _weight = self._direct_convert[(cur_t, pred_t)] convert.append(_convert) weight += _weight cur_t = pred_t pred_i = predecessors[i, pred_i] self.weight[(to_t, from_t)] = weight self._convert[(to_t, from_t)] =\ _converter(convert[::-1], to_t, from_t) for dtype in self.dtypes: self.weight[(dtype, Data)] = 1. self.weight[(Data, dtype)] = EPSILON self._convert[(dtype, Data)] = _partial_converter(self, dtype) self._convert[(Data, dtype)] = identity_converter for dispatcher in self.dispatchers: dispatcher.rebuild_lookup() def register_aliases(self, aliases, layer_type): """ Register a user frendly name for a data-layer type to be recognized by the :meth:`parse` method. Parameters ---------- aliases : str or list of str Name of list of names to be understood to represent the layer_type. layer_type : type Data-layer type, must have been registered with :meth:`add_conversions` first. """ if layer_type not in self.dtypes: raise ValueError( "Type is not a data-layer type: " + repr(layer_type)) if isinstance(aliases, str): aliases = [aliases] for alias in aliases: if type(alias) is not str: raise TypeError("The alias must be a str : " + repr(alias)) self._str2type[alias] = layer_type def parse(self, dtype): """ Return a data-layer type object given its name or the type itself. Parameters ---------- dtype : type, str Either the name of a data-layer type or a type itself. Returns ------- type A data-layer type. Raises ------ TypeError If ``dtype`` is neither a string nor a type. ValueError If ``dtype`` is a name, but no data-layer type of that name is registered, or if ``dtype`` is a type, but not a known data-layer type. """ if type(dtype) is type: if dtype not in self.dtypes and dtype is not Data: raise ValueError( "Type is not a data-layer type: " + repr(dtype)) return dtype elif type(dtype) is str: try: return self._str2type[dtype] except KeyError: raise ValueError( "Type name is not known to the data-layer: " + repr(dtype) ) from None raise TypeError( "Invalid dtype is neither a type nor a type name: " + repr(dtype)) @cython.boundscheck(False) @cython.wraparound(False) def __getitem__(self, arg): if type(arg) is not tuple: arg = (arg,) if not arg or len(arg) > 2: raise KeyError(arg) to_t = self.parse(arg[0]) if len(arg) == 1: return _partial_converter(self, to_t) from_t = self.parse(arg[1]) return self._convert[to_t, from_t] def __call__(self, to_type, data): to_type = self.parse(to_type) from_type = self.parse(type(data)) if to_type == from_type: return data return self._convert[to_type, from_type](data) cdef class _create: cdef readonly list _creators def __init__(self): self._creators = [] def add_creators(self, creators): """ Add creation functions to make a data-layer object from an arbitrary Python object. Parameters ---------- creators : iterable of (condition, creator, [priority]) An iterable of 2- or 3-tuples describing the new data layer creation functions. Each element can individually be a 2- or 3-tuple; they do not need to be all one or the other. Elements ........ condition : callable (object) -> bool Function determining if the given object can be converted to a data-layer type using this creator. creator function: callable (object, shape, copy=True) -> Data The creator function. It should take an object and a shape and return a data-layer type instance. The object may be any object for which the condition function returned ``True`` when tested. The ``object`` and ``shape`` parameters are passed positionally, and the ``copy`` parameter is passed by keyword. priority : real, optional (0) The priority associated with this creator. Higher priority conditions will be tested first and the first valid creator (i.e. for which ``condition(object) == True``) will handle the creation. Notes ----- Default creators are added with the following priorities: * Objects that are instances of data-layer types are converted using ``.copy`` with priority 100. * Objects that have a direct equivalent such as ``numpy.ndarray`` or ``scipy.sparse.csr_matrix`` are converted with priority 80. * Objects for which ``scipy.sparse.issparse`` is ``True`` are converted using an internal CSR converter with priority 20. * If no condition are meet, ``numpy.array`` is used to try convert the input to an array (priority -inf). """ for condition, creator, *priority in creators: if not callable(condition): raise TypeError(repr(condition) + " is not a callable") if not callable(create): raise TypeError(repr(create) + " is not a callable") if len(priority) >= 2: raise ValueError("Too many values to unpack for a creator, " + "expected 2 or 3, got "+ str(2+len(priority))) priority = float(priority[0] if priority else 0) self._creators.append((condition, creator, priority)) self._creators.sort(key=lambda creator: creator[2], reverse=True) def __call__(self, arg, shape=None, copy=True): """ Build a :class:`.Data` object from arg. Parameters ---------- arg : object Object to be converted to `qutip.data.Data`. Anything that can be converted to a numpy array are valid input. shape : tuple, optional The shape of the output as (``rows``, ``columns``). """ for condition, create, _ in self._creators: if condition(arg): return create(arg, shape, copy=copy) raise TypeError(f"arg `{repr(arg)}` cannot be converted to " "qutip data format") to = _to() create = _create() qutip-5.1.1/qutip/core/data/csr.pxd000066400000000000000000000143021474175217300172020ustar00rootroot00000000000000#cython: language_level=3 from cpython cimport mem from libcpp.algorithm cimport sort from libc.math cimport fabs cdef extern from *: void *PyMem_Calloc(size_t n, size_t elsize) import numpy as np cimport numpy as cnp from qutip.core.data cimport base from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia cdef class CSR(base.Data): cdef double complex *data cdef base.idxint *col_index cdef base.idxint *row_index cdef size_t size cdef object _scipy cdef bint _deallocate cpdef CSR copy(CSR self) cpdef object as_scipy(CSR self, bint full=*) cpdef CSR sort_indices(CSR self) cpdef double complex trace(CSR self) cpdef CSR adjoint(CSR self) cpdef CSR conj(CSR self) cpdef CSR transpose(CSR self) cdef struct Accumulator: # Provides the scatter/gather accumulator pattern for populating CSR/CSC # matrices row-by-row (or column-by-column for CSC) where entries may need # to be accumulated (summed) from several locations which may not be # sorted. # # See usage in `csr.from_coo_pointers` and `add_csr`; generally, add values # to the accumulator for this row by calling `scatter`, then fill the row # in the output by calling `gather`. Prepare the accumulator to receive # the next row by calling `reset`. double complex *values size_t *modified base.idxint *nonzero size_t _cur_row, nnz, size bint _sorted cdef inline Accumulator acc_alloc(size_t size): """ Initialise this accumulator. `size` should be the number of columns in the matrix (for CSR) or the number of rows (for CSC). """ cdef Accumulator acc acc.values = mem.PyMem_Malloc(size * sizeof(double complex)) acc.modified = PyMem_Calloc(size, sizeof(size_t)) acc.nonzero = mem.PyMem_Malloc(size * sizeof(base.idxint)) if acc.values == NULL or acc.modified == NULL or acc.nonzero == NULL: raise MemoryError acc.size = size acc.nnz = 0 # The value of _cur_row doesn't actually need to match the true row in # the output, it just needs to be a unique number so that we can use it # as a sentinel in `modified` to tell if there's a value in the current # column. acc._cur_row = 1 acc._sorted = True return acc cdef inline void acc_scatter(Accumulator *acc, double complex value, base.idxint position) noexcept nogil: """ Add a value to the accumulator for this row, in column `position`. The value is added on to any value already scattered into this position. """ # We have to branch on modified[position] anyway (to know whether to add an # entry in nonzero), so we _actually_ reset `values` here. This has the # potential to save operations too, if the same column is never touched # again. if acc.modified[position] == acc._cur_row: acc.values[position] += value else: acc.values[position] = value acc.modified[position] = acc._cur_row acc.nonzero[acc.nnz] = position acc._sorted &= acc.nnz == 0 or acc.nonzero[acc.nnz - 1] < position acc.nnz += 1 cdef inline base.idxint acc_gather(Accumulator *acc, double complex *values, base.idxint *indices, double tol=0) noexcept nogil: """ Copy all the accumulated values into this row into the output pointers. This will always output its values in sorted order. The pointers should point to the first free space for data to be copied into. This method will copy in _at most_ `self.nnz` elements into the pointers, but may copy in slightly fewer if some of them are now (explicit) zeros. `self.nnz` is updated after each `self.scatter()` operation, and is reset by `self.reset()`. Return the actual number of elements copied in. """ cdef size_t i, nnz=0, position cdef double complex value if not acc._sorted: sort(acc.nonzero, acc.nonzero + acc.nnz) acc._sorted = True for i in range(acc.nnz): position = acc.nonzero[i] value = acc.values[position] if fabs(value.real) < tol: value.real = 0 if fabs(value.imag) < tol: value.imag = 0 if value != 0: values[nnz] = value indices[nnz] = position nnz += 1 return nnz cdef inline void acc_reset(Accumulator *acc) noexcept nogil: """Prepare the accumulator to accept the next row of input.""" # We actually don't need to do anything to reset other than to change # our sentinel values; the sentinel `_cur_row` makes it easy to detect # whether a value was set in this current row (and if not, `scatter` # resets it when it's used), while `nnz` acc.nnz = 0 acc._sorted = True acc._cur_row += 1 cdef inline void acc_free(Accumulator *acc): mem.PyMem_Free(acc.values) mem.PyMem_Free(acc.modified) mem.PyMem_Free(acc.nonzero) # Internal structure for sorting pairs of elements. Not actually meant to be # used in external code. cdef struct _data_col: double complex data base.idxint col cdef class Sorter: cdef size_t size cdef base.idxint **argsort cdef _data_col *sort cdef void inplace(Sorter self, CSR matrix, base.idxint ptr, size_t size) nogil cdef void copy(Sorter self, double complex *dest_data, base.idxint *dest_cols, double complex *src_data, base.idxint *src_cols, size_t size) nogil cpdef CSR fast_from_scipy(object sci) cpdef CSR copy_structure(CSR matrix) cpdef CSR sorted(CSR matrix) cpdef base.idxint nnz(CSR matrix) nogil cpdef CSR empty(base.idxint rows, base.idxint cols, base.idxint size) cpdef CSR empty_like(CSR other) cpdef CSR zeros(base.idxint rows, base.idxint cols) cpdef CSR identity(base.idxint dimension, double complex scale=*) cpdef CSR from_dense(Dense matrix) cdef CSR from_coo_pointers(base.idxint *rows, base.idxint *cols, double complex *data, base.idxint n_rows, base.idxint n_cols, base.idxint nnz, double tol=*) cpdef CSR from_dia(Dia matrix) cpdef CSR _from_csr_blocks(base.idxint[:] block_rows, base.idxint[:] block_cols, CSR[:] block_ops, base.idxint n_blocks, base.idxint block_size) qutip-5.1.1/qutip/core/data/csr.pyx000066400000000000000000001222531474175217300172340ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memset, memcpy from libcpp cimport bool from libcpp.algorithm cimport sort cimport cython from cpython cimport mem import numbers import warnings import builtins import numpy as np cimport numpy as cnp import scipy.sparse from scipy.sparse import csr_matrix as scipy_csr_matrix from functools import partial from packaging.version import parse as parse_version if parse_version(scipy.version.version) >= parse_version("1.14.0"): from scipy.sparse._data import _data_matrix as scipy_data_matrix # From scipy 1.14.0, a check that the input is not scalar was added for # sparse arrays. scipy_data_matrix = partial(scipy_data_matrix, arg1=(0,)) elif parse_version(scipy.version.version) >= parse_version("1.8.0"): # The file data was renamed to _data from scipy 1.8.0 from scipy.sparse._data import _data_matrix as scipy_data_matrix else: from scipy.sparse.data import _data_matrix as scipy_data_matrix from scipy.linalg cimport cython_blas as blas from qutip.core.data cimport base, Dense, Dia from qutip.core.data.adjoint cimport adjoint_csr, transpose_csr, conj_csr from qutip.core.data.trace cimport trace_csr from qutip.core.data.tidyup cimport tidyup_csr from .base import idxint_dtype from qutip.settings import settings cnp.import_array() cdef extern from *: void PyArray_ENABLEFLAGS(cnp.ndarray arr, int flags) void *PyDataMem_NEW(size_t size) void PyDataMem_FREE(void *ptr) # Very little should be exported on star-import, because most stuff will have # naming collisions with other type modules. __all__ = ['CSR'] cdef int _ONE = 1 cdef object _csr_matrix(data, indices, indptr, shape): """ Factory method of scipy csr_matrix: we skip all the index type-checking because this takes tens of microseconds, and we already know we're in a sensible format. """ cdef object out = scipy_csr_matrix.__new__(scipy_csr_matrix) # `_data_matrix` is the first object in the inheritance chain which # doesn't have a really slow __init__. scipy_data_matrix.__init__(out) out.data = data out.indices = indices out.indptr = indptr out._shape = shape return out cdef class CSR(base.Data): """ Data type for quantum objects storing its data in compressed sparse row (CSR) format. This is similar to the `scipy` type `scipy.sparse.csr_matrix`, but significantly faster on many operations. You can retrieve a `scipy.sparse.csr_matrix` which views onto the same data using the `as_scipy()` method. """ def __cinit__(self, *args, **kwargs): # By default, we want CSR to deallocate its memory (we depend on Cython # to ensure we don't deallocate a NULL pointer), and we only flip this # when we create a scipy backing. Since creating the scipy backing # depends on knowing the shape, which happens _after_ data # initialisation and may throw an exception, it is better to have a # single flag that is set as soon as the pointers are assigned. self._deallocate = True def __init__(self, arg=None, shape=None, copy=True, bint tidyup=False): # This is the Python __init__ method, so we do not care that it is not # super-fast C access. Typically Cython code will not call this, but # will use a factory method in this module or at worst, call # CSR.__new__ and manually set everything. We must be very careful in # this function that the deallocation is set up correctly if any # exceptions occur. cdef size_t ptr cdef base.idxint col cdef object data, col_index, row_index if isinstance(arg, scipy.sparse.spmatrix): arg = arg.tocsr() if shape is not None and shape != arg.shape: raise ValueError("".join([ "shapes do not match: ", str(shape), " and ", str(arg.shape), ])) shape = arg.shape arg = (arg.data, arg.indices, arg.indptr) if not isinstance(arg, tuple): raise TypeError("arg must be a scipy matrix or tuple") if len(arg) != 3: raise ValueError("arg must be a (data, col_index, row_index) tuple") if np.lib.NumpyVersion(np.__version__) < '2.0.0b1': # np2 accept None which act as np1's False copy = builtins.bool(copy) data = np.array(arg[0], dtype=np.complex128, copy=copy, order='C') col_index = np.array(arg[1], dtype=idxint_dtype, copy=copy, order='C') row_index = np.array(arg[2], dtype=idxint_dtype, copy=copy, order='C') # This flag must be set at the same time as data, col_index and # row_index are assigned. These assignments cannot raise an exception # in user code due to the above three lines, but further code may. self._deallocate = False self.data = cnp.PyArray_GETPTR1(data, 0) self.col_index = cnp.PyArray_GETPTR1(col_index, 0) self.row_index = cnp.PyArray_GETPTR1(row_index, 0) self.size = (cnp.PyArray_SIZE(data) if cnp.PyArray_SIZE(data) < cnp.PyArray_SIZE(col_index) else cnp.PyArray_SIZE(col_index)) if shape is None: warnings.warn("instantiating CSR matrix of unknown shape") # row_index contains an extra element which is nnz. We assume the # smallest matrix which can hold all these values by iterating # through the columns. This is slow and probably inaccurate, since # there could be columns containing zero (hence the warning). self.shape[0] = cnp.PyArray_DIMS(row_index)[0] - 1 col = 1 for ptr in range(self.size): col = self.col_index[ptr] if self.col_index[ptr] > col else col self.shape[1] = col else: if not isinstance(shape, tuple): raise TypeError("shape must be a 2-tuple of positive ints") if not (len(shape) == 2 and isinstance(shape[0], int) and isinstance(shape[1], int) and shape[0] > 0 and shape[1] > 0): raise ValueError("shape must be a 2-tuple of positive ints") self.shape = shape # Store a reference to the backing scipy matrix so it doesn't get # deallocated before us. self._scipy = _csr_matrix(data, col_index, row_index, self.shape) if tidyup: tidyup_csr(self, settings.core['auto_tidyup_atol'], True) def __reduce__(self): return (fast_from_scipy, (self.as_scipy(),)) cpdef CSR copy(self): """ Return a complete (deep) copy of this object. If the type currently has a scipy backing, such as that produced by `as_scipy`, this will not be copied. The backing is a view onto our data, and a straight copy of this view would be incorrect. We do not create a new view at copy time, since the user may only access this through a creation method, and creating it ahead of time would incur an unnecessary speed penalty for users who do not need it (including low-level C code). """ cdef base.idxint nnz_ = nnz(self) cdef CSR out = empty_like(self) memcpy(out.data, self.data, nnz_*sizeof(double complex)) memcpy(out.col_index, self.col_index, nnz_*sizeof(base.idxint)) memcpy(out.row_index, self.row_index, (self.shape[0] + 1)*sizeof(base.idxint)) return out cpdef object to_array(self): """ Get a copy of this data as a full 2D, C-contiguous NumPy array. This is not a view onto the data, and changes to new array will not affect the original data structure. """ cdef cnp.npy_intp *dims = [self.shape[0], self.shape[1]] cdef object out = cnp.PyArray_ZEROS(2, dims, cnp.NPY_COMPLEX128, 0) cdef double complex [:, ::1] buffer = out cdef size_t row, ptr for row in range(self.shape[0]): for ptr in range(self.row_index[row], self.row_index[row + 1]): buffer[row, self.col_index[ptr]] = self.data[ptr] return out cpdef object as_scipy(self, bint full=False): """ Get a view onto this object as a `scipy.sparse.csr_matrix`. The underlying data structures are exposed, such that modifications to the `data`, `indices` and `indptr` buffers in the resulting object will modify this object too. If `full` is False (the default), the output array is squeezed so that the SciPy array sees only the filled elements. If `full` is True, SciPy will see the full underlying buffers, which may include uninitialised elements. Setting `full=True` is intended for Python-space factory methods. In all other use cases, `full=False` is much less error prone. """ # We store a reference to the scipy matrix not only for caching this # relatively expensive method, but also because we transferred # ownership of our data to the numpy arrays, and we can't allow them to # be collected while we're alive. if self._scipy is not None: return self._scipy cdef cnp.npy_intp length = self.size if full else nnz(self) data = cnp.PyArray_SimpleNewFromData(1, [length], cnp.NPY_COMPLEX128, self.data) indices = cnp.PyArray_SimpleNewFromData(1, [length], base.idxint_DTYPE, self.col_index) indptr = cnp.PyArray_SimpleNewFromData(1, [self.shape[0] + 1], base.idxint_DTYPE, self.row_index) PyArray_ENABLEFLAGS(data, cnp.NPY_ARRAY_OWNDATA) PyArray_ENABLEFLAGS(indices, cnp.NPY_ARRAY_OWNDATA) PyArray_ENABLEFLAGS(indptr, cnp.NPY_ARRAY_OWNDATA) self._deallocate = False self._scipy = _csr_matrix(data, indices, indptr, self.shape) return self._scipy cpdef CSR sort_indices(self): cdef Sorter sort cdef base.idxint ptr cdef size_t row, diff, size=0 for row in range(self.shape[0]): diff = self.row_index[row + 1] - self.row_index[row] size = diff if diff > size else size sort = Sorter(size) for row in range(self.shape[0]): ptr = self.row_index[row] diff = self.row_index[row + 1] - ptr sort.inplace(self, ptr, diff) return self cpdef double complex trace(self): return trace_csr(self) cpdef CSR adjoint(self): return adjoint_csr(self) cpdef CSR conj(self): return conj_csr(self) cpdef CSR transpose(self): return transpose_csr(self) def __repr__(self): return "".join([ "CSR(shape=", str(self.shape), ", nnz=", str(nnz(self)), ")", ]) def __str__(self): return self.__repr__() def __dealloc__(self): # If we have a reference to a scipy type, then we've passed ownership # of the data to numpy, so we let it handle refcounting and we don't # need to deallocate anything ourselves. if not self._deallocate: return if self.data != NULL: PyDataMem_FREE(self.data) if self.col_index != NULL: PyDataMem_FREE(self.col_index) if self.row_index != NULL: PyDataMem_FREE(self.row_index) cpdef CSR fast_from_scipy(object sci): """ Fast path construction from scipy.sparse.csr_matrix. This does _no_ type checking on any of the inputs, and should consequently be considered very unsafe. This is primarily for use in the unpickling operation. """ cdef CSR out = CSR.__new__(CSR) out.shape = sci.shape out._deallocate = False out._scipy = sci out.data = cnp.PyArray_GETPTR1(sci.data, 0) out.col_index = cnp.PyArray_GETPTR1(sci.indices, 0) out.row_index = cnp.PyArray_GETPTR1(sci.indptr, 0) out.size = cnp.PyArray_SIZE(sci.data) return out cpdef CSR copy_structure(CSR matrix): """ Return a copy of the input matrix with identical `col_index` and `row_index` matrices, and an allocated, but empty, `data`. The returned pointers are all separately allocated, but contain the same information. This is intended for unary functions on CSR types that maintain the exact structure, but modify each non-zero data element without change their location. """ cdef CSR out = empty_like(matrix) memcpy(out.col_index, matrix.col_index, nnz(matrix) * sizeof(base.idxint)) memcpy(out.row_index, matrix.row_index, (matrix.shape[0] + 1)*sizeof(base.idxint)) return out cpdef inline base.idxint nnz(CSR matrix) noexcept nogil: """Get the number of non-zero elements of a CSR matrix.""" return matrix.row_index[matrix.shape[0]] cdef bool _sorter_cmp_ptr(base.idxint *i, base.idxint *j) nogil: return i[0] < j[0] cdef bool _sorter_cmp_struct(_data_col x, _data_col y) nogil: return x.col < y.col ctypedef fused _swap_data: double complex base.idxint cdef inline void _sorter_swap(_swap_data *a, _swap_data *b) noexcept nogil: a[0], b[0] = b[0], a[0] cdef class Sorter: # Look on my works, ye mighty, and despair! # # This class has hard-coded sorts for up to three elements, for both # copying and in-place varieties. Everything above that we delegate to a # proper sorting algorithm. def __init__(self, size_t size): self.size = size cdef void inplace(self, CSR matrix, base.idxint ptr, size_t size) nogil: cdef size_t n cdef base.idxint col0, col1, col2 # Fast paths for tridiagonal matrices. These fast paths minimise the # number of comparisons and swaps made. if size < 2: return if size == 2: if matrix.col_index[ptr] > matrix.col_index[ptr + 1]: _sorter_swap(matrix.col_index + ptr, matrix.col_index + ptr+1) _sorter_swap(matrix.data + ptr, matrix.data + ptr+1) return if size == 3: # Faster to store rather than re-dereference, and if someone # changes the data underneath us, we've got larger problems anyway. col0 = matrix.col_index[ptr] col1 = matrix.col_index[ptr + 1] col2 = matrix.col_index[ptr + 2] if col0 < col1: if col1 > col2: _sorter_swap(matrix.col_index + ptr+1, matrix.col_index + ptr+2) _sorter_swap(matrix.data + ptr+1, matrix.data + ptr+2) if col0 > col2: _sorter_swap(matrix.col_index + ptr, matrix.col_index + ptr+1) _sorter_swap(matrix.data + ptr, matrix.data + ptr+1) elif col1 < col2: _sorter_swap(matrix.col_index + ptr, matrix.col_index + ptr+1) _sorter_swap(matrix.data + ptr, matrix.data + ptr+1) if col0 > col2: _sorter_swap(matrix.col_index + ptr+1, matrix.col_index + ptr+2) _sorter_swap(matrix.data + ptr+1, matrix.data + ptr+2) else: _sorter_swap(matrix.col_index + ptr, matrix.col_index + ptr+2) _sorter_swap(matrix.data + ptr, matrix.data + ptr+2) return # Now we actually have to do the sort properly. It's easiest just to # copy the data into a temporary structure. if size > self.size or self.sort == NULL: # realloc(NULL, size) is equivalent to malloc(size), so there's no # problem if cols and argsort weren't allocated before. self.size = size if size > self.size else self.size with gil: self.sort = <_data_col *> mem.PyMem_Realloc(self.sort, self.size * sizeof(_data_col)) for n in range(size): self.sort[n].data = matrix.data[ptr + n] self.sort[n].col = matrix.col_index[ptr + n] sort(self.sort, self.sort + size, &_sorter_cmp_struct) for n in range(size): matrix.data[ptr + n] = self.sort[n].data matrix.col_index[ptr + n] = self.sort[n].col cdef void copy(self, double complex *dest_data, base.idxint *dest_cols, double complex *src_data, base.idxint *src_cols, size_t size) nogil: cdef size_t n, ptr # Fast paths for small sizes. Not pretty, but it speeds things up a # lot for up to triadiaongal systems (which are pretty common). if size == 0: return if size == 1: dest_cols[0] = src_cols[0] dest_data[0] = src_data[0] return if size == 2: if src_cols[0] < src_cols[1]: dest_cols[0] = src_cols[0] dest_data[0] = src_data[0] dest_cols[1] = src_cols[1] dest_data[1] = src_data[1] else: dest_cols[1] = src_cols[0] dest_data[1] = src_data[0] dest_cols[0] = src_cols[1] dest_data[0] = src_data[1] return if size == 3: if src_cols[0] < src_cols[1]: if src_cols[0] < src_cols[2]: dest_cols[0] = src_cols[0] dest_data[0] = src_data[0] if src_cols[1] < src_cols[2]: dest_cols[1] = src_cols[1] dest_data[1] = src_data[1] dest_cols[2] = src_cols[2] dest_data[2] = src_data[2] else: dest_cols[2] = src_cols[1] dest_data[2] = src_data[1] dest_cols[1] = src_cols[2] dest_data[1] = src_data[2] else: dest_cols[1] = src_cols[0] dest_data[1] = src_data[0] dest_cols[2] = src_cols[1] dest_data[2] = src_data[1] dest_cols[0] = src_cols[2] dest_data[0] = src_data[2] elif src_cols[0] < src_cols[2]: dest_cols[1] = src_cols[0] dest_data[1] = src_data[0] dest_cols[0] = src_cols[1] dest_data[0] = src_data[1] dest_cols[2] = src_cols[2] dest_data[2] = src_data[2] else: dest_cols[2] = src_cols[0] dest_data[2] = src_data[0] if src_cols[1] < src_cols[2]: dest_cols[0] = src_cols[1] dest_data[0] = src_data[1] dest_cols[1] = src_cols[2] dest_data[1] = src_data[2] else: dest_cols[1] = src_cols[1] dest_data[1] = src_data[1] dest_cols[0] = src_cols[2] dest_data[0] = src_data[2] return # Now we're left with the full case, and we have to sort properly. if size > self.size or self.argsort == NULL: # realloc(NULL, size) is equivalent to malloc(size), so there's no # problem if cols and argsort weren't allocated before. self.size = size if size > self.size else self.size with gil: self.argsort = ( mem.PyMem_Realloc(self.argsort, self.size * sizeof(base.idxint *)) ) # We do the argsort with two levels of indirection to minimise memory # allocation and copying requirements when this function is being used # to assemble a CSR matrix under an operation which may change the # order of the columns (e.g. permute). First the user makes the # columns accessible in some contiguous memory (or if they're not # changing them, they can just use the CSR buffers). We put pointers # to each of those columns in the array which actually gets sorted # using a comparison function which dereferences the pointers and # compares the result. After the sort, `argsort` will be the pointers # sorted according to the new column, and we know that the "lowest" # pointer in there has the value `src_cols`, so we can do pointer # arithmetic to know which element we should take. # # This is about 30-40% faster than allocating space for structs of # (double complex, idxint), copying in the data and column, sorting and # copying into the new arrays. Allocating the structs actually # allocates more space than the pointer method (double complex is # very likely to be 2x the size of a pointer, _and_ the struct may need # extra padding to be aligned), so it's probably actually worse for # cache locality. Despite the sort relying on pointer dereference in # this case, it's actually got very good cache locality. for n in range(size): self.argsort[n] = src_cols + n sort(self.argsort, self.argsort + size, &_sorter_cmp_ptr) for n in range(size): ptr = self.argsort[n] - src_cols dest_cols[n] = src_cols[ptr] dest_data[n] = src_data[ptr] def __dealloc__(self): if self.argsort != NULL: mem.PyMem_Free(self.argsort) if self.sort != NULL: mem.PyMem_Free(self.sort) cpdef CSR sorted(CSR matrix): cdef CSR out = empty_like(matrix) cdef Sorter sort cdef base.idxint ptr cdef size_t row, diff, size=0 memcpy(out.row_index, matrix.row_index, (matrix.shape[0] + 1) * sizeof(base.idxint)) for row in range(matrix.shape[0]): diff = matrix.row_index[row + 1] - matrix.row_index[row] size = diff if diff > size else size sort = Sorter(size) for row in range(matrix.shape[0]): ptr = matrix.row_index[row] diff = matrix.row_index[row + 1] - ptr sort.copy(out.data + ptr, out.col_index + ptr, matrix.data + ptr, matrix.col_index + ptr, diff) return out cpdef CSR empty(base.idxint rows, base.idxint cols, base.idxint size): """ Allocate an empty CSR matrix of the given shape, with space for `size` elements in the `data` and `col_index` arrays. This does not initialise any of the memory returned, but sets the last element of `row_index` to 0 to indicate that there are 0 non-zero elements. """ if size < 0: raise ValueError("size must be a positive integer.") # Python doesn't like allocating nothing. if size == 0: size += 1 cdef CSR out = CSR.__new__(CSR) cdef base.idxint row_size = rows + 1 out.shape = (rows, cols) out.size = size out.data =\ PyDataMem_NEW(size * sizeof(double complex)) out.col_index =\ PyDataMem_NEW(size * sizeof(base.idxint)) out.row_index =\ PyDataMem_NEW(row_size * sizeof(base.idxint)) if not out.data: raise MemoryError( f"Failed to allocate the `data` of a ({rows}, {cols}) " f"CSR array of {size} max elements." ) if not out.col_index: raise MemoryError( f"Failed to allocate the `col_index` of a ({rows}, {cols}) " f"CSR array of {size} max elements." ) if not out.row_index: raise MemoryError( f"Failed to allocate the `row_index` of a ({rows}, {cols}) " f"CSR array of {size} max elements." ) # Set the number of non-zero elements to 0. out.row_index[rows] = 0 return out cpdef CSR empty_like(CSR other): return empty(other.shape[0], other.shape[1], nnz(other)) cpdef CSR zeros(base.idxint rows, base.idxint cols): """ Allocate the zero matrix with a given shape. There will not be any room in the `data` and `col_index` buffers to add new elements. """ # We always allocate matrices with at least one element to ensure that we # actually _are_ asking for memory (Python doesn't like allocating nothing) cdef CSR out = empty(rows, cols, 1) out.data[0] = out.col_index[0] = 0 memset(out.row_index, 0, (rows + 1) * sizeof(base.idxint)) return out cpdef CSR identity(base.idxint dimension, double complex scale=1): """ Return a square matrix of the specified dimension, with a constant along the diagonal. By default this will be the identity matrix, but if `scale` is passed, then the result will be `scale` times the identity. """ cdef CSR out = empty(dimension, dimension, dimension) cdef base.idxint i for i in range(dimension): out.data[i] = scale out.col_index[i] = i out.row_index[i] = i out.row_index[dimension] = dimension return out cpdef CSR from_dense(Dense matrix): # Assume worst-case scenario for non-zero. cdef CSR out = empty(matrix.shape[0], matrix.shape[1], matrix.shape[0]*matrix.shape[1]) cdef size_t row, col, ptr_in, ptr_out=0, row_stride, col_stride row_stride = 1 if matrix.fortran else matrix.shape[1] col_stride = matrix.shape[0] if matrix.fortran else 1 out.row_index[0] = 0 for row in range(matrix.shape[0]): ptr_in = row_stride * row for col in range(matrix.shape[1]): if matrix.data[ptr_in] != 0: out.data[ptr_out] = matrix.data[ptr_in] out.col_index[ptr_out] = col ptr_out += 1 ptr_in += col_stride out.row_index[row + 1] = ptr_out return out cdef CSR from_coo_pointers( base.idxint *rows, base.idxint *cols, double complex *data, base.idxint n_rows, base.idxint n_cols, base.idxint nnz, double tol=0 ): # Note that COO pointers may not be sorted in row-major order, and that # they may contain duplicate entries which should be implicitly summed. cdef Accumulator acc = acc_alloc(n_cols) cdef CSR out = empty(n_rows, n_cols, nnz) cdef double complex *data_tmp cdef base.idxint *cols_tmp cdef base.idxint row cdef size_t ptr_in, ptr_out, ptr_prev data_tmp = mem.PyMem_Malloc(nnz * sizeof(double complex)) cols_tmp = mem.PyMem_Malloc(nnz * sizeof(base.idxint)) if data_tmp == NULL or cols_tmp == NULL: raise MemoryError( f"Failed to allocate the memory needed for a ({n_rows}, {n_cols}) " f"CSR array with {nnz} elements." ) with nogil: memset(out.row_index, 0, (n_rows + 1) * sizeof(base.idxint)) for ptr_in in range(nnz): out.row_index[rows[ptr_in] + 1] += 1 for ptr_out in range(n_rows): out.row_index[ptr_out + 1] += out.row_index[ptr_out] # out.row_index is currently in the normal output form, but we're # temporarily going to modify it to keep track of how many values we've # placed in each row as we iterate through. At every state, # out.row_index[row] will contain a pointer to the next location that # an element should be placed in this row. for ptr_in in range(nnz): row = rows[ptr_in] ptr_out = out.row_index[row] cols_tmp[ptr_out] = cols[ptr_in] data_tmp[ptr_out] = data[ptr_in] out.row_index[row] += 1 # Apply the scatter/gather pattern to find the actual number of # non-zero elements we're writing into each row (since there's a sum, # there may be some zeros of duplicates). Remember we also need to # shift the row_index array back to what it was before as well. ptr_out = 0 ptr_prev = 0 for row in range(n_rows): for ptr_in in range(ptr_prev, out.row_index[row]): acc_scatter(&acc, data_tmp[ptr_in], cols_tmp[ptr_in]) ptr_prev = out.row_index[row] out.row_index[row] = ptr_out ptr_out += acc_gather(&acc, out.data + ptr_out, out.col_index + ptr_out, tol) acc_reset(&acc) out.row_index[n_rows] = ptr_out mem.PyMem_Free(data_tmp) mem.PyMem_Free(cols_tmp) acc_free(&acc) return out cpdef CSR from_dia(Dia matrix): cdef base.idxint col, diag, i, ptr=0 cdef base.idxint nrows=matrix.shape[0], ncols=matrix.shape[1] cdef base.idxint nnz = matrix.num_diag * min(matrix.shape) cdef double complex[:] data = np.zeros(nnz, dtype=complex) cdef base.idxint[:] cols = np.zeros(nnz, dtype=idxint_dtype) cdef base.idxint[:] rows = np.zeros(nnz, dtype=idxint_dtype) for i in range(matrix.num_diag): diag = matrix.offsets[i] for col in range(ncols): if col - diag < 0 or col - diag >= nrows: continue data[ptr] = matrix.data[i * ncols + col] rows[ptr] = col - diag cols[ptr] = col ptr += 1 return from_coo_pointers(&rows[0], &cols[0], &data[0], matrix.shape[0], matrix.shape[1], nnz) cdef inline base.idxint _diagonal_length( base.idxint offset, base.idxint n_rows, base.idxint n_cols, ) nogil: if offset > 0: return n_rows if offset <= n_cols - n_rows else n_cols - offset return n_cols if offset > n_cols - n_rows else n_rows + offset cdef CSR diag( double complex[:] diagonal, base.idxint offset, base.idxint n_rows, base.idxint n_cols, ): """ Construct a CSR matrix with a single non-zero diagonal. Parameters ---------- diagonal : indexable of double complex The entries (including zeros) that should be placed on the diagonal in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal. offsets : idxint The index of the diagonals. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. n_rows, n_cols : idxint The shape of the output. The result does not need to be square, but the diagonal must be of the correct length to fit in. """ if n_rows < 0 or n_cols < 0: raise ValueError("shape must be positive") cdef base.idxint nnz = len(diagonal) cdef base.idxint n_diag = _diagonal_length(offset, n_rows, n_cols) if nnz != n_diag: raise ValueError("incorrect number of diagonal elements") cdef CSR out = empty(n_rows, n_cols, nnz) cdef base.idxint start_row = 0 if offset >= 0 else -offset cdef base.idxint col = 0 if offset <= 0 else offset memset(out.row_index, 0, (start_row + 1) * sizeof(base.idxint)) nnz = 0 for row in range(start_row + 1, start_row + n_diag + 1): out.col_index[nnz] = col out.data[nnz] = diagonal[nnz] col += 1 nnz += 1 out.row_index[row] = nnz for row in range(start_row + n_diag + 1, n_rows + 1): out.row_index[row] = nnz return out cdef CSR diags_( list diagonals, base.idxint[:] offsets, base.idxint n_rows, base.idxint n_cols, ): """ Construct a CSR matrix from a list of diagonals and their offsets. The offsets are assumed to be in sorted order. This is the C-only interface to csr.diags, and inputs are not sanity checked (use the Python interface for that). Parameters ---------- diagonals : list of indexable of double complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal (not checked). offsets : idxint[:] The indices of the diagonals. These should be sorted and without duplicates. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. n_rows, n_cols : idxint The shape of the output. The result does not need to be square, but the diagonals must be of the correct length to fit in. """ cdef size_t n_diagonals = len(diagonals) if n_diagonals == 0: return zeros(n_rows, n_cols) cdef base.idxint k, row, start_row, offset, nnz=0, cdef base.idxint min_k=n_diagonals, max_k=n_diagonals cdef double complex value for k in range(n_diagonals): offset = offsets[k] if offset >= 0 and min_k > k: min_k = k nnz += _diagonal_length(offset, n_rows, n_cols) cdef CSR out = empty(n_rows, n_cols, nnz) nnz = 0 out.row_index[0] = 0 for row in range(n_rows): if min_k > 0: offset = offsets[min_k - 1] start_row = 0 if offset >= 0 else -offset if start_row == row: min_k -= 1 if max_k > 0: offset = offsets[max_k - 1] start_row = 0 if offset >= 0 else -offset if start_row + _diagonal_length(offset, n_rows, n_cols) - 1 < row: max_k -= 1 for k in range(min_k, max_k): offset = offsets[k] value = diagonals[k][row if offset >= 0 else row + offset] if value == 0: continue out.data[nnz] = value out.col_index[nnz] = row + offset nnz += 1 out.row_index[row + 1] = nnz return out @cython.wraparound(True) def diags(diagonals, offsets=None, shape=None): """ Construct a CSR matrix from diagonals and their offsets. Using this function in single-argument form produces a square matrix with the given values on the main diagonal. With lists of diagonals and offsets, the matrix will be the smallest possible square matrix if shape is not given, but in all cases the diagonals must fit exactly with no extra or missing elements. Duplicated diagonals will be summed together in the output. Parameters ---------- diagonals : sequence of array_like of complex or array_like of complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal and no more. offsets : sequence of integer or integer, optional The indices of the diagonals. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. shape : tuple, optional The shape of the output as (``rows``, ``columns``). The result does not need to be square, but the diagonals must be of the correct length to fit in exactly. """ cdef base.idxint n_rows, n_cols, offset try: diagonals = list(diagonals) if diagonals and np.isscalar(diagonals[0]): # Catch the case where we're being called as (for example) # diags([1, 2, 3], 0) # with a single diagonal and offset. diagonals = [diagonals] except TypeError: raise TypeError("diagonals must be a list of arrays of complex") from None if offsets is None: if len(diagonals) == 0: offsets = [] elif len(diagonals) == 1: offsets = [0] else: raise TypeError("offsets must be supplied if passing more than one diagonal") offsets = np.atleast_1d(offsets) if offsets.ndim > 1: raise ValueError("offsets must be a 1D array of integers") if len(diagonals) != len(offsets): raise ValueError("number of diagonals does not match number of offsets") if len(diagonals) == 0: if shape is None: raise ValueError("cannot construct matrix with no diagonals without a shape") else: n_rows, n_cols = shape return zeros(n_rows, n_cols) order = np.argsort(offsets) diagonals_ = [] offsets_ = [] prev, cur = None, None for i in order: cur = offsets[i] if cur == prev: diagonals_[-1] += np.asarray(diagonals[i], dtype=np.complex128) else: offsets_.append(cur) diagonals_.append(np.asarray(diagonals[i], dtype=np.complex128)) prev = cur if shape is None: n_rows = n_cols = abs(offsets_[0]) + len(diagonals_[0]) else: try: n_rows, n_cols = shape except (TypeError, ValueError): raise TypeError("shape must be a 2-tuple of positive integers") if n_rows < 0 or n_cols < 0: raise ValueError("shape must be a 2-tuple of positive integers") for i in range(len(diagonals_)): offset = offsets_[i] if len(diagonals_[i]) != _diagonal_length(offset, n_rows, n_cols): raise ValueError("given diagonals do not have the correct lengths") if n_rows == 0 and n_cols == 0: raise ValueError("can't produce a 0x0 matrix") if len(offsets) == 1: # Fast path for a single diagonal. return diag(diagonals_[0], offsets_[0], n_rows, n_cols) return diags_( diagonals_, np.array(offsets_, dtype=idxint_dtype), n_rows, n_cols, ) cpdef CSR _from_csr_blocks( base.idxint[:] block_rows, base.idxint[:] block_cols, CSR[:] block_ops, base.idxint n_blocks, base.idxint block_size ): """ Construct a CSR from non-overlapping blocks. Each operator in ``block_ops`` should be a square CSR operator with shape ``(block_size, block_size)``. The output operator consists of ``n_blocks`` by ``n_blocks`` blocks and thus has shape ``(n_blocks * block_size, n_blocks * block_size)``. None of the operators should overlap (i.e. the list of block row and column pairs should be unique). Parameters ---------- block_rows : sequence of base.idxint integers The block row for each operator. The block row should be in ``range(0, n_blocks)``. block_cols : sequence of base.idxint integers The block column for each operator. The block column should be in ``range(0, n_blocks)``. block_ops : sequence of CSR matrixes The operators corresponding to the rows and columns in ``block_rows`` and ``block_cols``. n_blocks : base.idxint Number of blocks. The shape of the final matrix is (n_blocks * block, n_blocks * block). block_size : base.idxint Size of each block. The shape of matrices in ``block_ops`` is ``(block_size, block_size)``. """ cdef CSR op cdef base.idxint shape = n_blocks * block_size cdef base.idxint nnz_ = 0 cdef base.idxint n_ops = len(block_ops) cdef base.idxint i, j cdef base.idxint row_idx, col_idx # check arrays are the same length if len(block_rows) != n_ops or len(block_cols) != n_ops: raise ValueError( "The arrays block_rows, block_cols and block_ops should have" " the same length." ) if n_ops == 0: return zeros(shape, shape) # check op shapes and calculate nnz for op in block_ops: nnz_ += nnz(op) if op.shape[0] != block_size or op.shape[1] != block_size: raise ValueError( "Block operators (block_ops) do not have the correct shape." ) # check ops are ordered by (row, column) row_idx = block_rows[0] col_idx = block_cols[0] for i in range(1, n_ops): if ( block_rows[i] < row_idx or (block_rows[i] == row_idx and block_cols[i] <= col_idx) ): raise ValueError( "The arrays block_rows and block_cols must be sorted" " by (row, column)." ) row_idx = block_rows[i] col_idx = block_cols[i] if nnz_ == 0: return zeros(shape, shape) cdef CSR out = empty(shape, shape, nnz_) cdef base.idxint op_idx = 0 cdef base.idxint prev_op_idx = 0 cdef base.idxint end = 0 cdef base.idxint row_pos, col_pos cdef base.idxint op_row, op_row_start, op_row_end, op_row_len out.row_index[0] = 0 for row_idx in range(n_blocks): prev_op_idx = op_idx while op_idx < n_ops: if block_rows[op_idx] != row_idx: break op_idx += 1 row_pos = row_idx * block_size for op_row in range(block_size): for i in range(prev_op_idx, op_idx): op = block_ops[i] if nnz(op) == 0: # empty CSR matrices have uninitialized row_index entries. # it's unclear whether users should ever see such matrixes # but we support them here anyway. continue col_idx = block_cols[i] col_pos = col_idx * block_size op_row_start = op.row_index[op_row] op_row_end = op.row_index[op_row + 1] op_row_len = op_row_end - op_row_start for j in range(op_row_len): out.col_index[end + j] = op.col_index[op_row_start + j] + col_pos out.data[end + j] = op.data[op_row_start + j] end += op_row_len out.row_index[row_pos + op_row + 1] = end return out qutip-5.1.1/qutip/core/data/dense.pxd000066400000000000000000000022241474175217300175110ustar00rootroot00000000000000#cython: language_level=3 cimport numpy as cnp from . cimport base from qutip.core.data.csr cimport CSR from qutip.core.data.dia cimport Dia cdef class Dense(base.Data): cdef double complex *data cdef readonly bint fortran cdef object _np cdef bint _deallocate cdef void _fix_flags(Dense self, object array, bint make_owner=*) cpdef Dense reorder(Dense self, int fortran=*) cpdef Dense copy(Dense self) cpdef object as_ndarray(Dense self) cpdef object to_array(Dense self) cpdef double complex trace(Dense self) cpdef Dense adjoint(Dense self) cpdef Dense conj(Dense self) cpdef Dense transpose(Dense self) cpdef Dense fast_from_numpy(object array) cdef Dense wrap(double complex *ptr, base.idxint rows, base.idxint cols, bint fortran=*) cpdef Dense empty(base.idxint rows, base.idxint cols, bint fortran=*) cpdef Dense empty_like(Dense other, int fortran=*) cpdef Dense zeros(base.idxint rows, base.idxint cols, bint fortran=*) cpdef Dense identity(base.idxint dimension, double complex scale=*, bint fortran=*) cpdef Dense from_csr(CSR matrix, bint fortran=*) cpdef Dense from_dia(Dia matrix) qutip-5.1.1/qutip/core/data/dense.pyx000066400000000000000000000412621474175217300175430ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memcpy cimport cython import numbers import builtins import numpy as np cimport numpy as cnp from scipy.linalg cimport cython_blas as blas from .base import EfficiencyWarning from qutip.core.data cimport base, CSR, Dia from qutip.core.data.adjoint cimport adjoint_dense, transpose_dense, conj_dense from qutip.core.data.trace cimport trace_dense cnp.import_array() cdef int _ONE = 1 cdef extern from *: void PyArray_ENABLEFLAGS(cnp.ndarray arr, int flags) void PyArray_CLEARFLAGS(cnp.ndarray arr, int flags) void *PyDataMem_NEW(size_t size) void *PyDataMem_NEW_ZEROED(size_t size, size_t elsize) void PyDataMem_FREE(void *ptr) @cython.overflowcheck(True) cdef size_t _mul_mem_checked(size_t a, size_t b, size_t c=0): if c != 0: return a * b * c return a * b # Creation functions like 'identity' and 'from_csr' aren't exported in __all__ # to avoid naming clashes with other type modules. __all__ = [ 'Dense', 'OrderEfficiencyWarning', ] class OrderEfficiencyWarning(EfficiencyWarning): pass is_numpy1 = np.lib.NumpyVersion(np.__version__) < '2.0.0b1' cdef class Dense(base.Data): def __init__(self, data, shape=None, copy=True): if is_numpy1: # np2 accept None which act as np1's False copy = builtins.bool(copy) base = np.array(data, dtype=np.complex128, order='K', copy=copy) # Ensure that the array is contiguous. # Non contiguous array with copy=False would otherwise slip through if not (cnp.PyArray_IS_C_CONTIGUOUS(base) or cnp.PyArray_IS_F_CONTIGUOUS(base)): base = base.copy() if shape is None: shape = base.shape if len(shape) == 0: shape = (1, 1) # Promote to a ket by default if passed 1D data. if len(shape) == 1: shape = (shape[0], 1) if not ( len(shape) == 2 and isinstance(shape[0], numbers.Integral) and isinstance(shape[1], numbers.Integral) and shape[0] > 0 and shape[1] > 0 ): raise ValueError("shape must be a 2-tuple of positive ints, but is " + repr(shape)) if shape[0] * shape[1] != base.size: raise ValueError("".join([ "invalid shape ", str(shape), " for input data with size ", str(base.size) ])) self._np = base.reshape(shape, order='A') self._deallocate = False self.data = cnp.PyArray_GETPTR2(self._np, 0, 0) self.fortran = cnp.PyArray_IS_F_CONTIGUOUS(self._np) self.shape = (shape[0], shape[1]) def __reduce__(self): return (fast_from_numpy, (self.as_ndarray(),)) def __repr__(self): return "".join([ "Dense(shape=", str(self.shape), ", fortran=", str(self.fortran), ")", ]) def __str__(self): return self.__repr__() cpdef Dense reorder(self, int fortran=-1): cdef bint fortran_ if fortran < 0: fortran_ = not self.fortran else: fortran_ = fortran if bool(fortran_) == bool(self.fortran): return self.copy() cdef Dense out = empty_like(self, fortran_) cdef size_t idx_self=0, idx_out, idx_out_start, stride, splits stride = self.shape[1] if self.fortran else self.shape[0] splits = self.shape[0] if self.fortran else self.shape[1] for idx_out_start in range(stride): idx_out = idx_out_start for _ in range(splits): out.data[idx_out] = self.data[idx_self] idx_self += 1 idx_out += stride return out cpdef Dense copy(self): """ Return a complete (deep) copy of this object. If the type currently has a numpy backing, such as that produced by `as_ndarray`, this will not be copied. The backing is a view onto our data, and a straight copy of this view would be incorrect. We do not create a new view at copy time, since the user may only access this through a creation method, and creating it ahead of time would incur an unnecessary speed penalty for users who do not need it (including low-level C code). """ cdef Dense out = Dense.__new__(Dense) cdef size_t size = ( _mul_mem_checked(self.shape[0], self.shape[1], sizeof(double complex)) ) cdef double complex *ptr = PyDataMem_NEW(size) if not ptr: raise MemoryError( "Could not allocate memory to copy a " f"({self.shape[0]}, {self.shape[1]}) Dense matrix." ) memcpy(ptr, self.data, size) out.shape = self.shape out.data = ptr out.fortran = self.fortran out._deallocate = True return out cdef void _fix_flags(self, object array, bint make_owner=False): cdef int enable = cnp.NPY_ARRAY_OWNDATA if make_owner else 0 cdef int disable = 0 cdef cnp.npy_intp *dims = cnp.PyArray_DIMS(array) cdef cnp.npy_intp *strides = cnp.PyArray_STRIDES(array) # Not necessary when creating a new array because this will already # have been done, but needed for as_ndarray() if we have been mutated. dims[0] = self.shape[0] dims[1] = self.shape[1] if self.shape[0] == 1 or self.shape[1] == 1: enable |= cnp.NPY_ARRAY_F_CONTIGUOUS | cnp.NPY_ARRAY_C_CONTIGUOUS strides[0] = self.shape[1] * sizeof(double complex) strides[1] = sizeof(double complex) elif self.fortran: enable |= cnp.NPY_ARRAY_F_CONTIGUOUS disable |= cnp.NPY_ARRAY_C_CONTIGUOUS strides[0] = sizeof(double complex) strides[1] = self.shape[0] * sizeof(double complex) else: enable |= cnp.NPY_ARRAY_C_CONTIGUOUS disable |= cnp.NPY_ARRAY_F_CONTIGUOUS strides[0] = self.shape[1] * sizeof(double complex) strides[1] = sizeof(double complex) PyArray_ENABLEFLAGS(array, enable) PyArray_CLEARFLAGS(array, disable) cpdef object to_array(self): """ Get a copy of this data as a full 2D, contiguous NumPy array. This may be Fortran or C-ordered, but will be contiguous in one of the dimensions. This is not a view onto the data, and changes to new array will not affect the original data structure. """ cdef size_t size = ( _mul_mem_checked(self.shape[0], self.shape[1], sizeof(double complex)) ) cdef double complex *ptr = PyDataMem_NEW(size) if not ptr: raise MemoryError( "Could not allocate memory to convert to a numpy array a " f"({self.shape[0]}, {self.shape[1]}) Dense matrix." ) memcpy(ptr, self.data, size) cdef object out =\ cnp.PyArray_SimpleNewFromData(2, [self.shape[0], self.shape[1]], cnp.NPY_COMPLEX128, ptr) self._fix_flags(out, make_owner=True) return out cpdef object as_ndarray(self): """ Get a view onto this object as a `numpy.ndarray`. The underlying data structure is exposed, such that modifications to the array will modify this object too. The array may be uninitialised, depending on how the Dense type was created. The output will be contiguous and of dtype 'complex128', but may be C- or Fortran-ordered. """ if self._np is not None: # We have to do this every time in case someone has changed our # ordering or shape inplace. self._fix_flags(self._np, make_owner=False) return self._np self._np =\ cnp.PyArray_SimpleNewFromData( 2, [self.shape[0], self.shape[1]], cnp.NPY_COMPLEX128, self.data ) self._fix_flags(self._np, make_owner=self._deallocate) self._deallocate = False return self._np cpdef double complex trace(self): return trace_dense(self) cpdef Dense adjoint(self): return adjoint_dense(self) cpdef Dense conj(self): return conj_dense(self) cpdef Dense transpose(self): return transpose_dense(self) def __dealloc__(self): if self._deallocate and self.data != NULL: PyDataMem_FREE(self.data) cpdef Dense fast_from_numpy(object array): """ Fast path construction from numpy ndarray. This does _no_ type checking on the input, and should consequently be considered very unsafe. This is primarily for use in the unpickling operation. """ cdef Dense out = Dense.__new__(Dense) if array.ndim == 1: out.shape = (array.shape[0], 1) array = array[:, None] else: out.shape = (array.shape[0], array.shape[1]) out._deallocate = False out._np = array out.data = cnp.PyArray_GETPTR2(array, 0, 0) out.fortran = cnp.PyArray_IS_F_CONTIGUOUS(array) return out cdef Dense wrap(double complex *data, base.idxint rows, base.idxint cols, bint fortran=False): cdef Dense out = Dense.__new__(Dense) out.data = data out._deallocate = False out.fortran = fortran or cols == 1 or rows == 1 out.shape = (rows, cols) return out cpdef Dense empty(base.idxint rows, base.idxint cols, bint fortran=True): """ Return a new Dense type of the given shape, with the data allocated but uninitialised. """ cdef Dense out = Dense.__new__(Dense) out.shape = (rows, cols) out.data = PyDataMem_NEW( _mul_mem_checked(rows, cols, sizeof(double complex)) ) if not out.data: raise MemoryError( "Could not allocate memory to create an empty " f"({rows}, {cols}) Dense matrix." ) out._deallocate = True out.fortran = fortran return out cpdef Dense empty_like(Dense other, int fortran=-1): cdef bint fortran_ if fortran < 0: fortran_ = other.fortran else: fortran_ = fortran return empty(other.shape[0], other.shape[1], fortran=fortran_) cpdef Dense zeros(base.idxint rows, base.idxint cols, bint fortran=True): """Return the zero matrix with the given shape.""" cdef Dense out = Dense.__new__(Dense) out.shape = (rows, cols) out.data =\ PyDataMem_NEW_ZEROED( _mul_mem_checked(rows, cols), sizeof(double complex) ) if not out.data: raise MemoryError( "Could not allocate memory to create a zero " f"({rows}, {cols}) Dense matrix." ) out.fortran = fortran out._deallocate = True return out cpdef Dense identity(base.idxint dimension, double complex scale=1, bint fortran=True): """ Return a square matrix of the specified dimension, with a constant along the diagonal. By default this will be the identity matrix, but if `scale` is passed, then the result will be `scale` times the identity. """ cdef size_t row cdef Dense out = zeros(dimension, dimension, fortran=fortran) for row in range(dimension): out.data[row*dimension + row] = scale return out cpdef Dense from_csr(CSR matrix, bint fortran=False): cdef Dense out = Dense.__new__(Dense) out.shape = matrix.shape out.data = ( PyDataMem_NEW_ZEROED( _mul_mem_checked(out.shape[0], out.shape[1]), sizeof(double complex) ) ) if not out.data: raise MemoryError( "Could not allocate memory to create a " f"({out.shape[0]}, {out.shape[1]}) Dense matrix from a CSR." ) out.fortran = fortran out._deallocate = True cdef size_t row, ptr_in, ptr_out, row_stride, col_stride row_stride = 1 if fortran else out.shape[1] col_stride = out.shape[0] if fortran else 1 ptr_out = 0 for row in range(out.shape[0]): for ptr_in in range(matrix.row_index[row], matrix.row_index[row + 1]): out.data[ptr_out + matrix.col_index[ptr_in]*col_stride] = matrix.data[ptr_in] ptr_out += row_stride return out cpdef Dense from_dia(Dia matrix): return Dense(matrix.to_array(), copy=False) cdef inline base.idxint _diagonal_length( base.idxint offset, base.idxint n_rows, base.idxint n_cols, ) nogil: if offset > 0: return n_rows if offset <= n_cols - n_rows else n_cols - offset return n_cols if offset > n_cols - n_rows else n_rows + offset @cython.wraparound(True) def diags(diagonals, offsets=None, shape=None): """ Construct a matrix from diagonals and their offsets. Using this function in single-argument form produces a square matrix with the given values on the main diagonal. With lists of diagonals and offsets, the matrix will be the smallest possible square matrix if shape is not given, but in all cases the diagonals must fit exactly with no extra or missing elements. Duplicated diagonals will be summed together in the output. Parameters ---------- diagonals : sequence of array_like of complex or array_like of complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal and no more. offsets : sequence of integer or integer, optional The indices of the diagonals. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. shape : tuple, optional The shape of the output as (``rows``, ``columns``). The result does not need to be square, but the diagonals must be of the correct length to fit in exactly. """ cdef base.idxint n_rows, n_cols, offset try: diagonals = list(diagonals) if diagonals and np.isscalar(diagonals[0]): # Catch the case where we're being called as (for example) # diags([1, 2, 3], 0) # with a single diagonal and offset. diagonals = [diagonals] except TypeError: raise TypeError("diagonals must be a list of arrays of complex") from None if offsets is None: if len(diagonals) == 0: offsets = [] elif len(diagonals) == 1: offsets = [0] else: raise TypeError("offsets must be supplied if passing more than one diagonal") offsets = np.atleast_1d(offsets) if offsets.ndim > 1: raise ValueError("offsets must be a 1D array of integers") if len(diagonals) != len(offsets): raise ValueError("number of diagonals does not match number of offsets") if len(diagonals) == 0: if shape is None: raise ValueError("cannot construct matrix with no diagonals without a shape") else: n_rows, n_cols = shape return zeros(n_rows, n_cols) order = np.argsort(offsets) diagonals_ = [] offsets_ = [] prev, cur = None, None for i in order: cur = offsets[i] if cur == prev: diagonals_[-1] += np.asarray(diagonals[i], dtype=np.complex128) else: offsets_.append(cur) diagonals_.append(np.asarray(diagonals[i], dtype=np.complex128)) prev = cur if shape is None: n_rows = n_cols = abs(offsets_[0]) + len(diagonals_[0]) else: try: n_rows, n_cols = shape except (TypeError, ValueError): raise TypeError("shape must be a 2-tuple of positive integers") if n_rows < 0 or n_cols < 0: raise ValueError("shape must be a 2-tuple of positive integers") for i in range(len(diagonals_)): offset = offsets_[i] if len(diagonals_[i]) != _diagonal_length(offset, n_rows, n_cols): raise ValueError("given diagonals do not have the correct lengths") if n_rows == 0 and n_cols == 0: raise ValueError("can't produce a 0x0 matrix") out = zeros(n_rows, n_cols, fortran=True) cdef size_t diag_idx, idx, n_diagonals = len(diagonals_) for diag_idx in range(n_diagonals): offset = offsets_[diag_idx] if offset <= 0: for idx in range(_diagonal_length(offset, n_rows, n_cols)): out.data[idx*(n_rows+1) - offset] = diagonals_[diag_idx][idx] else: for idx in range(_diagonal_length(offset, n_rows, n_cols)): out.data[idx*(n_rows+1) + offset*n_rows] = diagonals_[diag_idx][idx] return out qutip-5.1.1/qutip/core/data/dia.pxd000066400000000000000000000021451474175217300171520ustar00rootroot00000000000000#cython: language_level=3 # from cpython cimport mem # from libcpp.algorithm cimport sort # from libc.math cimport fabs # cdef extern from *: # void *PyMem_Calloc(size_t n, size_t elsize) # import numpy as np # cimport numpy as cnp from qutip.core.data cimport base from qutip.core.data.dense cimport Dense from qutip.core.data.csr cimport CSR cdef class Dia(base.Data): cdef double complex *data cdef base.idxint *offsets cdef readonly size_t num_diag, _max_diag cdef object _scipy cdef bint _deallocate cpdef Dia copy(Dia self) cpdef object as_scipy(Dia self, bint full=*) cpdef double complex trace(Dia self) cpdef Dia adjoint(Dia self) cpdef Dia conj(Dia self) cpdef Dia transpose(Dia self) cpdef Dia fast_from_scipy(object sci) cpdef Dia empty(base.idxint rows, base.idxint cols, base.idxint num_diag) cpdef Dia empty_like(Dia other) cpdef Dia zeros(base.idxint rows, base.idxint cols) cpdef Dia identity(base.idxint dimension, double complex scale=*) cpdef Dia from_dense(Dense matrix) cpdef Dia from_csr(CSR matrix) cpdef Dia clean_dia(Dia matrix, bint inplace=*) qutip-5.1.1/qutip/core/data/dia.pyx000066400000000000000000000521141474175217300172000ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memset, memcpy from libcpp cimport bool from libcpp.algorithm cimport sort from libc.math cimport fabs cimport cython from cpython cimport mem import numbers import warnings import builtins import numpy as np cimport numpy as cnp import scipy.sparse from scipy.sparse import dia_matrix as scipy_dia_matrix from packaging.version import parse as parse_version from functools import partial if parse_version(scipy.version.version) >= parse_version("1.14.0"): from scipy.sparse._data import _data_matrix as scipy_data_matrix # From scipy 1.14.0, a check that the input is not scalar was added for # sparse arrays. scipy_data_matrix = partial(scipy_data_matrix, arg1=(0,)) elif parse_version(scipy.version.version) >= parse_version("1.8.0"): # The file data was renamed to _data from scipy 1.8.0 from scipy.sparse._data import _data_matrix as scipy_data_matrix else: from scipy.sparse.data import _data_matrix as scipy_data_matrix from scipy.linalg cimport cython_blas as blas from qutip.core.data cimport base, Dense, CSR from qutip.core.data.adjoint import adjoint_dia, transpose_dia, conj_dia from qutip.core.data.trace import trace_dia from qutip.core.data.tidyup import tidyup_dia from .base import idxint_dtype from qutip.settings import settings cnp.import_array() cdef extern from *: void PyArray_ENABLEFLAGS(cnp.ndarray arr, int flags) void *PyDataMem_NEW(size_t size) void PyDataMem_FREE(void *ptr) __all__ = ['Dia'] cdef object _dia_matrix(data, offsets, shape): """ Factory method of scipy diag_matrix: we skip all the index type-checking because this takes tens of microseconds, and we already know we're in a sensible format. """ cdef object out = scipy_dia_matrix.__new__(scipy_dia_matrix) # `_data_matrix` is the first object in the inheritance chain which # doesn't have a really slow __init__. scipy_data_matrix.__init__(out) out.data = data out.offsets = offsets out._shape = shape return out cdef tuple _count_element(complex[:] line, size_t length): cdef size_t pre = 0, post = length while pre < length and line[pre] == 0.: pre += 1 while post and line[post-1] == 0.: post -= 1 return (post, length - pre) cdef class Dia(base.Data): def __cinit__(self, *args, **kwargs): self._deallocate = True def __init__(self, arg=None, shape=None, copy=True, bint tidyup=False): cdef size_t ptr cdef base.idxint col cdef object data, offsets if isinstance(arg, scipy.sparse.spmatrix): arg = arg.todia() if shape is not None and shape != arg.shape: raise ValueError("".join([ "shapes do not match: ", str(shape), " and ", str(arg.shape), ])) shape = arg.shape arg = (arg.data, arg.offsets) if not isinstance(arg, tuple): raise TypeError("arg must be a scipy matrix or tuple") if len(arg) != 2: raise ValueError("arg must be a (data, offsets) tuple") if np.lib.NumpyVersion(np.__version__) < '2.0.0b1': # np2 accept None which act as np1's False copy = builtins.bool(copy) data = np.array(arg[0], dtype=np.complex128, copy=copy, order='C') offsets = np.array(arg[1], dtype=idxint_dtype, copy=copy, order='C') self.num_diag = offsets.shape[0] self._max_diag = self.num_diag if shape is None: warnings.warn("instantiating Dia matrix of unknown shape") nrows = 0 ncols = 0 for i in range(self.num_diag): pre, post = _count_element(data[i], data.shape[1]) if offsets[i] >= 0: row = post col = post + offsets[i] else: row = pre - offsets[i] col = pre nrows = nrows if nrows > row else row ncols = ncols if ncols > col else col self.shape = (nrows, ncols) else: if not isinstance(shape, tuple): raise TypeError("shape must be a 2-tuple of positive ints") if not (len(shape) == 2 and isinstance(shape[0], numbers.Integral) and isinstance(shape[1], numbers.Integral) and shape[0] > 0 and shape[1] > 0): raise ValueError("shape must be a 2-tuple of positive ints") self.shape = shape # Scipy support ``data`` with diag of any length. They can be sorter if # the last columns are empty or have extra unused columns at the end. if data.shape[0] != 0 and data.shape[1] != self.shape[1]: new_data = np.zeros((self.num_diag, self.shape[1]), dtype=np.complex128, order='C') copy_length = min(data.shape[1], self.shape[1]) new_data[:, :copy_length] = data[:, :copy_length] data = new_data self._deallocate = False self.data = cnp.PyArray_GETPTR1(data, 0) self.offsets = cnp.PyArray_GETPTR1(offsets, 0) self._scipy = _dia_matrix(data, offsets, self.shape) if tidyup: tidyup_dia(self, settings.core['auto_tidyup_atol'], True) def __reduce__(self): return (fast_from_scipy, (self.as_scipy(),)) cpdef Dia copy(self): """ Return a complete (deep) copy of this object. If the type currently has a scipy backing, such as that produced by `as_scipy`, this will not be copied. The backing is a view onto our data, and a straight copy of this view would be incorrect. We do not create a new view at copy time, since the user may only access this through a creation method, and creating it ahead of time would incur an unnecessary speed penalty for users who do not need it (including low-level C code). """ cdef Dia out = empty_like(self) out.num_diag = self.num_diag memcpy(out.data, self.data, self.num_diag * self.shape[1] * sizeof(double complex)) memcpy(out.offsets, self.offsets, self.num_diag * sizeof(base.idxint)) return out cpdef object to_array(self): """ Get a copy of this data as a full 2D, C-contiguous NumPy array. This is not a view onto the data, and changes to new array will not affect the original data structure. """ cdef cnp.npy_intp *dims = [self.shape[0], self.shape[1]] cdef object out = cnp.PyArray_ZEROS(2, dims, cnp.NPY_COMPLEX128, 0) cdef size_t col, i, nrows = self.shape[0] cdef base.idxint diag for i in range(self.num_diag): diag = self.offsets[i] for col in range(self.shape[1]): if col - diag < 0 or col - diag >= nrows: continue out[(col-diag), col] = self.data[i * self.shape[1] + col] return out cpdef object as_scipy(self, bint full=False): """ Get a view onto this object as a `scipy.sparse.dia_matrix`. The underlying data structures are exposed, such that modifications to the `data` and `offsets` buffers in the resulting object will modify this object too. """ # We store a reference to the scipy matrix not only for caching this # relatively expensive method, but also because we transferred # ownership of our data to the numpy arrays, and we can't allow them to # be collected while we're alive. if self._scipy is not None: return self._scipy cdef cnp.npy_intp num_diag = self.num_diag if not full else self._max_diag cdef cnp.npy_intp size = self.shape[1] data = cnp.PyArray_SimpleNewFromData(2, [num_diag, size], cnp.NPY_COMPLEX128, self.data) offsets = cnp.PyArray_SimpleNewFromData(1, [num_diag], base.idxint_DTYPE, self.offsets) PyArray_ENABLEFLAGS(data, cnp.NPY_ARRAY_OWNDATA) PyArray_ENABLEFLAGS(offsets, cnp.NPY_ARRAY_OWNDATA) self._deallocate = False self._scipy = _dia_matrix(data, offsets, self.shape) return self._scipy cpdef double complex trace(self): return trace_dia(self) cpdef Dia adjoint(self): return adjoint_dia(self) cpdef Dia conj(self): return conj_dia(self) cpdef Dia transpose(self): return transpose_dia(self) def __repr__(self): return "".join([ "Dia(shape=", str(self.shape), ", num_diag=", str(self.num_diag), ")", ]) def __str__(self): return self.__repr__() def __dealloc__(self): # If we have a reference to a scipy type, then we've passed ownership # of the data to numpy, so we let it handle refcounting and we don't # need to deallocate anything ourselves. if not self._deallocate: return if self.data != NULL: PyDataMem_FREE(self.data) if self.offsets != NULL: PyDataMem_FREE(self.offsets) cpdef Dia fast_from_scipy(object sci): """ Fast path construction from scipy.sparse.csr_matrix. This does _no_ type checking on any of the inputs, and should consequently be considered very unsafe. This is primarily for use in the unpickling operation. """ cdef Dia out = Dia.__new__(Dia) out.shape = sci.shape out._deallocate = False out._scipy = sci out.data = cnp.PyArray_GETPTR1(sci.data, 0) out.offsets = cnp.PyArray_GETPTR1(sci.offsets, 0) out.num_diag = sci.offsets.shape[0] out._max_diag = sci.offsets.shape[0] return out cpdef Dia empty(base.idxint rows, base.idxint cols, base.idxint num_diag): """ Allocate an empty Dia matrix of the given shape, ``with num_diag`` diagonals. This does not initialise any of the memory returned. """ if num_diag < 0: raise ValueError("num_diag must be a positive integer.") cdef Dia out = Dia.__new__(Dia) out.shape = (rows, cols) out.num_diag = 0 # Python doesn't like allocating nothing. if num_diag == 0: num_diag += 1 out._max_diag = num_diag out.data =\ PyDataMem_NEW(cols * num_diag * sizeof(double complex)) out.offsets =\ PyDataMem_NEW(num_diag * sizeof(base.idxint)) if not out.data: raise MemoryError( f"Failed to allocate the `data` of a ({rows}, {cols}) " f"Dia array of {num_diag} diagonals." ) if not out.offsets: raise MemoryError( f"Failed to allocate the `offsets` of a ({rows}, {cols}) " f"Dia array of {num_diag} diagonals." ) return out cpdef Dia empty_like(Dia other): return empty(other.shape[0], other.shape[1], other.num_diag) cpdef Dia zeros(base.idxint rows, base.idxint cols): """ Allocate the zero matrix with a given shape. There will not be any room in the `data` and `col_index` buffers to add new elements. """ # We always allocate matrices with at least one element to ensure that we # actually _are_ asking for memory (Python doesn't like allocating nothing) cdef Dia out = empty(rows, cols, 0) memset(out.data, 0, out.shape[1] * sizeof(double complex)) out.offsets[0] = 0 return out cpdef Dia identity(base.idxint dimension, double complex scale=1): """ Return a square matrix of the specified dimension, with a constant along the diagonal. By default this will be the identity matrix, but if `scale` is passed, then the result will be `scale` times the identity. """ cdef Dia out = empty(dimension, dimension, 1) for i in range(dimension): out.data[i] = scale out.offsets[0] = 0 out.num_diag = 1 return out @cython.boundscheck(True) cpdef Dia from_dense(Dense matrix): cdef Dia out = empty(matrix.shape[0], matrix.shape[1], matrix.shape[0] + matrix.shape[1] - 1) memset(out.data, 0, out._max_diag * out.shape[1] * sizeof(double complex)) cdef size_t diag_, ptr_in, ptr_out=0, stride cdef row, col out.num_diag = matrix.shape[0] + matrix.shape[1] - 1 for i in range(matrix.shape[0] + matrix.shape[1] - 1): out.offsets[i] = i -matrix.shape[0] + 1 strideR = 1 if matrix.fortran else matrix.shape[1] strideC = 1 if not matrix.fortran else matrix.shape[0] for row in range(matrix.shape[0]): for col in range(matrix.shape[1]): out.data[(col - row + matrix.shape[0] - 1) * out.shape[1] + col] = matrix.data[row * strideR + col * strideC] if settings.core["auto_tidyup"]: tidyup_dia(out, settings.core["auto_tidyup_atol"], True) return out cpdef Dia from_csr(CSR matrix): out_diag = set() for row in range(matrix.shape[0]): for ptr in range(matrix.row_index[row], matrix.row_index[row+1]): out_diag.add(matrix.col_index[ptr] - row) data = np.zeros((len(out_diag), matrix.shape[1]), dtype=complex) diags = np.sort(np.fromiter(out_diag, idxint_dtype, len(out_diag))) for row in range(matrix.shape[0]): for ptr in range(matrix.row_index[row], matrix.row_index[row+1]): diag = matrix.col_index[ptr] - row idx = np.searchsorted(diags, diag) data[idx, matrix.col_index[ptr]] = matrix.data[ptr] return Dia((data, diags), shape=matrix.shape, copy=False) cpdef Dia clean_dia(Dia matrix, bint inplace=False): """ Sort and sum duplicates of offsets. Set out of bound values to zeros. """ cdef Dia out = matrix if inplace else matrix.copy() cdef base.idxint diag=0, new_diag=0, start, end, col cdef double complex zONE=1. cdef bint has_duplicate cdef int length=out.shape[1], ONE=1 if out.num_diag == 0: return out # We sort using insertion sort on the offsets, summing data of duplicated. # This does not scale well with large number of diagonal for new_diag in range(out.num_diag): smallest_offsets = out.offsets[new_diag] smallest_diag = new_diag comp_diag = new_diag + 1 has_duplicate = False for comp_diag in range(new_diag + 1, out.num_diag): if out.offsets[comp_diag] < smallest_offsets: smallest_offsets = out.offsets[comp_diag] smallest_diag = comp_diag has_duplicate = False elif out.offsets[comp_diag] == smallest_offsets: blas.zaxpy( &length, &zONE, &out.data[comp_diag * out.shape[1]], &ONE, &out.data[smallest_diag * out.shape[1]], &ONE ) out.offsets[comp_diag] = out.shape[1] if smallest_offsets == out.shape[1]: new_diag -= 1 break if new_diag == smallest_diag: continue blas.zswap(&length, &out.data[new_diag * out.shape[1]], &ONE, &out.data[smallest_diag * out.shape[1]], &ONE) out.offsets[smallest_diag] = out.offsets[new_diag] out.offsets[new_diag] = smallest_offsets out.num_diag = new_diag + 1 for diag in range(out.num_diag): start = max(0, out.offsets[diag]) end = min(out.shape[1], out.shape[0] + out.offsets[diag]) for col in range(start): out.data[diag * out.shape[1] + col] = 0. for col in range(end, out.shape[1]): out.data[diag * out.shape[1] + col] = 0. if out._scipy is not None: out._scipy.data = out._scipy.data[:out.num_diag] out._scipy.offsets = out._scipy.offsets[:out.num_diag] return out cdef inline base.idxint _diagonal_length( base.idxint offset, base.idxint n_rows, base.idxint n_cols, ) nogil: if offset > 0: return n_rows if offset <= n_cols - n_rows else n_cols - offset return n_cols if offset > n_cols - n_rows else n_rows + offset cdef Dia diags_( list diagonals, base.idxint[:] offsets, base.idxint n_rows, base.idxint n_cols, ): """ Construct a Dia matrix from a list of diagonals and their offsets. The offsets are assumed to be in sorted order. This is the C-only interface to diag.diags, and inputs are not sanity checked (use the Python interface for that). Parameters ---------- diagonals : list of indexable of double complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal (not checked). offsets : idxint[:] The indices of the diagonals. These should be sorted and without duplicates. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. n_rows, n_cols : idxint The shape of the output. The result does not need to be square, but the diagonals must be of the correct length to fit in. """ cdef base.idxint i out = empty(n_rows, n_cols, len(offsets)) out.num_diag = len(offsets) for i in range(len(offsets)): out.offsets[i] = offsets[i] offset = max(offsets[i], 0) for col in range(len(diagonals[i])): out.data[i * out.shape[1] + col + offset] = diagonals[i][col] return out @cython.wraparound(True) def diags(diagonals, offsets=None, shape=None): """ Construct a Dia matrix from diagonals and their offsets. Using this function in single-argument form produces a square matrix with the given values on the main diagonal. With lists of diagonals and offsets, the matrix will be the smallest possible square matrix if shape is not given, but in all cases the diagonals must fit exactly with no extra or missing elements. Duplicated diagonals will be summed together in the output. Parameters ---------- diagonals : sequence of array_like of complex or array_like of complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal and no more. offsets : sequence of integer or integer, optional The indices of the diagonals. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. shape : tuple, optional The shape of the output as (``rows``, ``columns``). The result does not need to be square, but the diagonals must be of the correct length to fit in exactly. """ cdef base.idxint n_rows, n_cols, offset try: diagonals = list(diagonals) if diagonals and np.isscalar(diagonals[0]): # Catch the case where we're being called as (for example) # diags([1, 2, 3], 0) # with a single diagonal and offset. diagonals = [diagonals] except TypeError: raise TypeError("diagonals must be a list of arrays of complex") from None if offsets is None: if len(diagonals) == 0: offsets = [] elif len(diagonals) == 1: offsets = [0] else: raise TypeError("offsets must be supplied if passing more than one diagonal") offsets = np.atleast_1d(offsets) if offsets.ndim > 1: raise ValueError("offsets must be a 1D array of integers") if len(diagonals) != len(offsets): raise ValueError("number of diagonals does not match number of offsets") if len(diagonals) == 0: if shape is None: raise ValueError("cannot construct matrix with no diagonals without a shape") else: n_rows, n_cols = shape return zeros(n_rows, n_cols) order = np.argsort(offsets) diagonals_ = [] offsets_ = [] prev, cur = None, None for i in order: cur = offsets[i] if cur == prev: diagonals_[-1] += np.asarray(diagonals[i], dtype=np.complex128) else: offsets_.append(cur) diagonals_.append(np.asarray(diagonals[i], dtype=np.complex128)) prev = cur if shape is None: n_rows = n_cols = abs(offsets_[0]) + len(diagonals_[0]) else: try: n_rows, n_cols = shape except (TypeError, ValueError): raise TypeError("shape must be a 2-tuple of positive integers") if n_rows < 0 or n_cols < 0: raise ValueError("shape must be a 2-tuple of positive integers") for i in range(len(diagonals_)): offset = offsets_[i] if len(diagonals_[i]) != _diagonal_length(offset, n_rows, n_cols): raise ValueError("given diagonals do not have the correct lengths") if n_rows == 0 and n_cols == 0: raise ValueError("can't produce a 0x0 matrix") return diags_( diagonals_, np.array(offsets_, dtype=idxint_dtype), n_rows, n_cols, ) qutip-5.1.1/qutip/core/data/dispatch.pyx000066400000000000000000000376521474175217300202540ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False import functools import inspect import itertools import warnings from .convert import to as _to from .convert import EPSILON cimport cython from libc cimport math from libcpp cimport bool from qutip.core.data.base cimport Data __all__ = ['Dispatcher'] cdef double _conversion_weight(tuple froms, tuple tos, dict weight_map, bint out) except -1: """ Find the total weight of conversion if the types in `froms` are converted element-wise to the types in `tos`. `weight_map` is a mapping of `(to_type, from_type): real`; it should almost certainly be `data.to.weight`. Specialisations that support any types input should use ``Data``. """ cdef double weight = 0.0 cdef Py_ssize_t i, n=len(froms) if len(tos) != n: raise ValueError( "number of arguments not equal: " + str(n) + " and " + str(len(tos)) ) if out: n = n - 1 weight = weight + weight_map[froms[n], tos[n]] for i in range(n): weight = weight + weight_map[tos[i], froms[i]] return weight cdef class _constructed_specialisation: """ Callable object providing the specialisation of a data-layer operation for a particular set of types (`self.types`). This may or may not involve conversion of the input types and the output to match a known specialisation; if it has no conversions, `self.direct` will be `True`, otherwise it will be `False`. See `self.__signature__` or `self.__text_signature__` for the call signature of this object. """ cdef readonly bint _output cdef object _call cdef readonly Py_ssize_t _n_inputs, _n_dispatch cdef readonly tuple types cdef readonly tuple _converters cdef readonly str _short_name cdef public str __doc__ cdef public str __name__ # cdef public str __module__ cdef public object __signature__ cdef readonly str __text_signature__ def __init__(self, base, Dispatcher dispatcher, types, converters, out): self.__doc__ = inspect.getdoc(dispatcher) self._short_name = dispatcher.__name__ self.__name__ = ( self._short_name + "_" + "_".join([x.__name__ for x in types]) ) # self.__module__ = dispatcher.__module__ self.__signature__ = dispatcher.__signature__ self.__text_signature__ = dispatcher.__text_signature__ self._output = out self._call = base self.types = types self._converters = converters self._n_dispatch = len(converters) self._n_inputs = len(converters) - out @cython.wraparound(False) def __call__(self, *args, **kwargs): cdef int i cdef list _args = list(args) for i in range(self._n_inputs): _args[i] = self._converters[i](args[i]) out = self._call(*_args, **kwargs) if self._output: out = self._converters[self._n_dispatch - 1](out) return out def __repr__(self): if len(self.types) == 1: spec = self.types[0].__name__ else: spec = "(" + ", ".join(x.__name__ for x in self.types) + ")" return "".join([ "" ]) cdef class Dispatcher: """ Dispatcher for a data-layer operation. This object can be called with the signature shown in `self.__signature__` or `self.__text_signature__`, where the arguments listed in `self.inputs` can be any data-layer types (i.e. ones that have valid conversions in `data.to`). You can define additional specialisations for this dispatcher by calling its `add_specialisations` method. New data types must be added to `data.to` before they can be added as specialisations to a dispatcher. You can get a callable object representing a single set of dispatcher types by using the key-lookup syntax Dispatcher[type1, type2, ...] where `type1`, `type2`, etc are the dispatched arguments (with the output type on the end, if this is a dispatcher over the output type. """ cdef readonly dict _specialisations cdef readonly Py_ssize_t _n_dispatch, _n_inputs cdef readonly dict _lookup cdef readonly set _dtypes cdef readonly bint _pass_on_dtype cdef readonly tuple inputs cdef readonly bint output cdef public str __doc__ cdef public str __name__ # cdef public str __module__ cdef public object __signature__ cdef readonly str __text_signature__ def __init__(self, signature_source, inputs, bint out=False, str name=None, str module=None): """ Create a new data layer dispatching operator. Parameters ---------- signature_source : callable or inspect.Signature An object from which the call signature of operation can be determined. You can pass any callable defined in Python space, and the signature will be extracted. Note that the callable will not be added as a specialisation by this; you will still have to call `add_specialisations`. If you cannot provide a callable with an extractable signature (e.g. Cython extension methods), you can instead directly provide an instance of `inspect.Signature`, which will be used instead. inputs : iterable of str The parameters which should be dispatched over. These must be positional arguments, and must feature in the signature provided. out : bool, optional (False) Whether to dispatch on the output of the function. Defaults to `False`. name : str, optional If given, the `__name__` parameter of the dispatcher is set to this. If not given and `signature_source` is _not_ an instance of `inspect.Signature`, then we will attempt to read `__name__` from there instead. module : str, optional If given, the `__module__` parameter of the dispatcher is set to this. If not given and `signature_source` is _not_ an instance of `inspect.Signature`, then we will attempt to read `__module__` from there instead. .. note:: Commented for now because of a bug in cython 3 (cython#5472) """ if isinstance(inputs, str): inputs = (inputs,) inputs = tuple(inputs) if inputs == () and out is False: warnings.warn( "No parameters to dispatch on." " Maybe you meant to specify 'inputs' or 'out'?" ) self.inputs = inputs if isinstance(signature_source, inspect.Signature): self.__signature__ = signature_source else: self.__signature__ = inspect.signature(signature_source) for input in self.inputs: if ( self.__signature__._parameters[input].kind != inspect.Parameter.POSITIONAL_ONLY ): raise ValueError("inputs parameters must be positional only.") if list(self.__signature__._parameters).index(input) >= len(inputs): raise ValueError("inputs must be the first positional parameters.") if name is not None: self.__name__ = name elif not isinstance(signature_source, inspect.Signature): self.__name__ = signature_source.__name__ else: self.__name__ = 'dispatcher' # if module is not None: # self.__module__ = module # elif not isinstance(signature_source, inspect.Signature): # self.__module__ = signature_source.__module__ self.__text_signature__ = self.__name__ + str(self.__signature__) if not isinstance(signature_source, inspect.Signature): self.__doc__ = inspect.getdoc(signature_source) self.output = out self._specialisations = {} self._lookup = {} self._n_inputs = len(self.inputs) self._n_dispatch = len(self.inputs) + self.output self._pass_on_dtype = 'dtype' in self.__signature__.parameters # Add ourselves to the list of dispatchers to be updated. _to.dispatchers.append(self) def add_specialisations(self, specialisations, _defer=False): """ Add specialisations for particular combinations of data types to this operation. The data types must already be known in `data.to` before you try to provide them here. All data types defined in `data.to` will automatically work with this dispatcher, but will involve inefficient conversions to and from other types unless you define a closer specialisation using this method. The lookup table will automatically be rebuilt after this method is called. Specialisations defined more than once will use the most recent version; you can use this to override currently known specialisations if desired. Parameters ---------- specialisations : iterable of tuples An iterable where each element specifies a new specialisation for this operation. Each element of the iterable should be a tuple, whose items are the types (instances of `type`) which this specialisation takes in each of the slots defined by `Dispatcher.inputs`, and the output type if this is a dispatcher over output types. The last element should be the callable itself. The callable must have exactly the same signature as `Dispatcher.__signature__`; it is not enough that it takes all the same keyword arguments, but they must come in the same order as well (this is a speed optimisation for the dispatching operation). For example, if this is a dispatcher with the signature add(left, right, scale=1) which also dispatches over its output, and we have specialisations add_1(left: CSR, right: Dense, scale=1) -> Dense add_2(left: Dense, right: CSC, scale=1) -> CSR then to add this, `specialisations` should look like [ (CSR, Dense, Dense, add_1), (Dense, CSC, CSR, add_2), ] Type annotations present in the specialisation objects are ignored. _defer : bool, optional (False) Only intended for internal library use during initialisation. If `True`, then the input types are not checked, and the full lookup table is not built until a manual call to `Dispatcher.rebuild_lookup()` is made. If you are getting errors, remember that you should add the data type conversions to `data.to` before you try to add specialisations. """ for arg in specialisations: arg = tuple(arg) if len(arg) != self._n_dispatch + 1: raise ValueError( "specialisation " + str(arg) + " has wrong number of parameters: needed types for " + str(self.inputs) + (", an output type" if self.output else "") + " and a callable" ) for i in range(self._n_dispatch): if ( not _defer and arg[i] not in _to.dtypes and arg[i] is not Data ): raise ValueError(str(arg[i]) + " is not a known data type") if not callable(arg[self._n_dispatch]): raise TypeError(str(arg[-1]) + " is not callable") self._specialisations[arg[:-1]] = arg[-1] if not _defer: self.rebuild_lookup() cdef object _find_specialization(self, tuple in_types, bint output): # The complexity of building the table here is very poor, but it's a # cost we pay very infrequently, and until it's proved to be a # bottle-neck in real code, we stick with the simple algorithm. cdef double weight, cur cdef tuple types, out_types, displayed_type cdef object function cdef int n_dispatch weight = math.INFINITY types = None function = None n_dispatch = len(in_types) for out_types, out_function in self._specialisations.items(): cur = _conversion_weight( in_types, out_types[:n_dispatch], _to.weight, out=output) if cur < weight: weight = cur types = out_types function = out_function if cur == math.INFINITY: raise ValueError("No valid specialisations found") if weight in [EPSILON, 0.] and not (output and types[-1] is Data): self._lookup[in_types] = function else: if output: converters = tuple( [_to[pair] for pair in zip(types[:-1], in_types[:-1])] + [_to[in_types[-1], types[-1]]] ) else: converters = tuple(_to[pair] for pair in zip(types, in_types)) displayed_type = in_types if len(in_types) < len(types): displayed_type = displayed_type + (types[-1],) self._lookup[in_types] =\ _constructed_specialisation(function, self, displayed_type, converters, output) def rebuild_lookup(self): """ Manually trigger a rebuild of the lookup table for this dispatcher. This is called automatically when new data types are added to `data.to`, or when specialisations are added to this object with `Dispatcher.add_specialisations`. You most likely do not need to call this function yourself. """ if not self._specialisations: return self._dtypes = _to.dtypes.copy() for in_types in itertools.product(self._dtypes, repeat=self._n_dispatch): self._find_specialization(in_types, self.output) # Now build the lookup table in the case that we dispatch on the output # type as well, but the user has called us without specifying it. # TODO: option to control default output type choice if unspecified? if self.output: for in_types in itertools.product(self._dtypes, repeat=self._n_dispatch-1): self._find_specialization(in_types, False) def __getitem__(self, types): """ Get the particular specialisation for the given types. The output is a callable object which requires that the dispatched arguments match those specified in `types`. """ if type(types) is not tuple: types = (types,) types = tuple(_to.parse(arg) for arg in types) try: return self._lookup[types] except KeyError: raise TypeError("specialisation not known for types: " + str(types)) from None def __repr__(self): return "" def __call__(self, *args, dtype=None, **kwargs): cdef list dispatch = [] cdef int i if self._pass_on_dtype: kwargs['dtype'] = dtype if not (self._pass_on_dtype or self.output) and dtype is not None: raise TypeError("unknown argument 'dtype'") if len(args) < self._n_inputs: raise TypeError( "All dispatched data input must be passed " "as positional arguments." ) for i in range(self._n_inputs): dispatch.append(type(args[i])) if self.output and dtype is not None: dtype = _to.parse(dtype) dispatch.append(dtype) try: function = self._lookup[tuple(dispatch)] except KeyError: raise TypeError("unknown types to dispatch on: " + str(dispatch)) from None return function(*args, **kwargs) qutip-5.1.1/qutip/core/data/eigen.py000066400000000000000000000362561474175217300173530ustar00rootroot00000000000000import numpy as np import scipy.linalg import scipy.sparse as sp import scipy.sparse.linalg from itertools import combinations from .dense import Dense, from_csr from .csr import CSR, nnz from .properties import isherm as _isherm from qutip.settings import settings __all__ = [ 'eigs', 'eigs_csr', 'eigs_dense', 'svd', 'svd_csr', 'svd_dense', ] def _orthogonalize(vec, other): cross = np.sum(np.conj(other) * vec) vec -= cross * other norm = np.sum(np.conj(vec) * vec)**0.5 vec /= norm if settings.eigh_unsafe: def eigh(mat, eigvals=None): val, vec = scipy.linalg.eig(mat) val = np.real(val) idx = np.argsort(val) val = val[idx] vec = vec[:, idx] if eigvals: val = val[eigvals[0]:eigvals[1]+1] vec = vec[:, eigvals[0]:eigvals[1]+1] same_eigv = 0 for i in range(1, len(val)): if abs(val[i] - val[i-1]) < 1e-12: same_eigv += 1 for j in range(same_eigv): _orthogonalize(vec[:, i], vec[:, i-j-1]) else: same_eigv = 0 return val, vec def eigvalsh(a, eigvals=None): val = scipy.linalg.eigvals(a) val = np.sort(np.real(val)) if eigvals: return val[eigvals[0]:eigvals[1]+1] return val else: eigh = scipy.linalg.eigh eigvalsh = scipy.linalg.eigvalsh def _eigs_dense(data, isherm, vecs, eigvals, num_large, num_small): """ Internal functions for computing eigenvalues and eigenstates for a dense matrix. """ N = data.shape[0] kwargs = {} if eigvals != 0 and isherm: kwargs['subset_by_index'] = ( [0, num_small-1] if num_small else [N-num_large, N-1] ) if vecs: driver = eigh if isherm else scipy.linalg.eig evals, evecs = driver(data, **kwargs) else: driver = eigvalsh if isherm else scipy.linalg.eigvals evals = driver(data, **kwargs) evecs = None _zipped = list(zip(evals, range(len(evals)))) _zipped.sort() evals, perm = list(zip(*_zipped)) if vecs: evecs = np.array([evecs[:, k] for k in perm]).T if not isherm and eigvals > 0: if vecs: if num_small > 0: evals, evecs = evals[:num_small], evecs[:, :num_small] elif num_large > 0: evals = evals[(N - num_large):] evecs = evecs[:, (N - num_large):] else: if num_small > 0: evals = evals[:num_small] elif num_large > 0: evals = evals[(N - num_large):] return np.array(evals), evecs def _eigs_csr(data, isherm, vecs, eigvals, num_large, num_small, tol, maxiter): """ Internal functions for computing eigenvalues and eigenstates for a sparse matrix. """ N = data.shape[0] big_vals = np.array([]) small_vals = np.array([]) evecs = None remove_one = 0 # 0: remove none, 1: remove smallest, -1: remove largest if eigvals == (N - 1): # calculate all eigenvalues and remove one at output if using sparse # 1: remove the smallest, -1, remove the largest remove_one = 1 if (num_small > 0) else -1 eigvals = 0 num_small = num_large = N // 2 num_small += N % 2 if vecs: if isherm: if num_large > 0: big_vals, big_vecs = sp.linalg.eigsh(data, k=num_large, which='LA', tol=tol, maxiter=maxiter) if num_small > 0: small_vals, small_vecs = sp.linalg.eigsh( data, k=num_small, which='SA', tol=tol, maxiter=maxiter) else: if num_large > 0: big_vals, big_vecs = sp.linalg.eigs(data, k=num_large, which='LR', tol=tol, maxiter=maxiter) if num_small > 0: small_vals, small_vecs = sp.linalg.eigs( data, k=num_small, which='SR', tol=tol, maxiter=maxiter) if num_large != 0 and num_small != 0: evecs = np.hstack([small_vecs, big_vecs]) elif num_large != 0 and num_small == 0: evecs = big_vecs elif num_large == 0 and num_small != 0: evecs = small_vecs else: if isherm: if num_large > 0: big_vals = sp.linalg.eigsh( data, k=num_large, which='LA', return_eigenvectors=False, tol=tol, maxiter=maxiter) if num_small > 0: small_vals = sp.linalg.eigsh( data, k=num_small, which='SA', return_eigenvectors=False, tol=tol, maxiter=maxiter) else: if num_large > 0: big_vals = sp.linalg.eigs( data, k=num_large, which='LR', return_eigenvectors=False, tol=tol, maxiter=maxiter) if num_small > 0: small_vals = sp.linalg.eigs( data, k=num_small, which='SR', return_eigenvectors=False, tol=tol, maxiter=maxiter) evals = np.hstack((small_vals, big_vals)) if isherm: evals = np.real(evals) _zipped = list(zip(evals, range(len(evals)))) _zipped.sort() evals, perm = list(zip(*_zipped)) if vecs: evecs = np.array([evecs[:, k] for k in perm]).T # remove last element if requesting N-1 eigs and using sparse if remove_one == 1: evals = evals[:-1] if vecs: evecs = evecs[:, :-1] elif remove_one == -1: evals = evals[1:] if vecs: evecs = evecs[:, 1:] return np.array(evals), evecs def _eigs_check_shape(data): if data.shape[0] != data.shape[1]: raise TypeError("Can only diagonalize square matrices") def _eigs_fix_eigvals(data, eigvals, sort): N = data.shape[0] if eigvals == N: eigvals = 0 if eigvals > N: raise ValueError("Number of requested eigen vals/vecs must be <= N.") if sort not in ('low', 'high'): raise ValueError("'sort' must be 'low' or 'high'") # set number of large and small eigenvals/vecs if eigvals == 0: # user wants all eigs (default) num_small = num_large = N // 2 num_small += N % 2 else: # if user wants only a few eigen vals/vecs num_small, num_large = (eigvals, 0) if sort == 'low' else (0, eigvals) return eigvals, num_large, num_small def eigs_csr(data, /, isherm=None, vecs=True, sort='low', eigvals=0, tol=0, maxiter=100000): """ Return eigenvalues and eigenvectors for a CSR matrix. This specialisation may take some extra keyword arguments in addition to the full documentation specified in :func:`.eigs`. This method is typically slower and less accurate than the dense eigenvalue solver; you probably want that, unless memory concerns deem it impossible. Extra keyword arguments ----------------------- tol : float (0) Tolerance for sparse eigensolver. Sufficiently small tolerances (such as 0) cause the solver to use machine precision. maxiter : int (100_000) Max number of iterations used by sparse eigensolver. """ if not isinstance(data, CSR): raise TypeError("expected data in CSR format but got " + str(type(data))) if data.shape[0] < 4: # For small matrix, the sparse solver can't compute all eigenvalues. return eigs_dense(from_csr(data), isherm, vecs, sort, eigvals) _eigs_check_shape(data) eigvals, num_large, num_small = _eigs_fix_eigvals(data, eigvals, sort) if nnz(data) == 0: # With change in ARPACK used with scipy 1.15, zeros matrix input raise # an error. evals = np.zeros(num_large + num_small) evecs = np.zeros((num_large + num_small, data.shape[0]), dtype=complex) for i in range(num_large + num_small): evecs[i, i] = 1.+0j return (evals, Dense(evecs, copy=False)) if vecs else evals # eigsh call eigs for complex matrix. Using the Hermitian version only cast # the eigen values to real values. isherm = isherm if isherm is not None else False evals, evecs = _eigs_csr(data.as_scipy(), isherm, vecs, eigvals, num_large, num_small, tol, maxiter) if vecs and isherm: i = 0 degen_tol = (2 * tol or 1e-15 * data.shape[0]) while i < len(evals): num_degen = np.sum(np.abs(evals[i:] - evals[i]) < degen_tol) # orthogonalize vectors 1 .. k with respect to the first, then # 2 .. k with respect to the second, and so on. Relies on both the # order of each pair and the ordering of pairs returned by # combinations. for k, l in combinations(range(num_degen), 2): _orthogonalize(evecs[:, i+l], evecs[:, i+k]) i += num_degen if sort == 'high': # Flip arrays around. if vecs: evecs = np.fliplr(evecs) evals = evals[::-1] return (evals, Dense(evecs, copy=False)) if vecs else evals def eigs_dense(data, /, isherm=None, vecs=True, sort='low', eigvals=0): """ Return eigenvalues and eigenvectors for a Dense matrix. Takes no special keyword arguments; see the primary documentation in :func:`.eigs`. """ if not isinstance(data, Dense): raise TypeError("expected data in Dense format but got " + str(type(data))) _eigs_check_shape(data) eigvals, num_large, num_small = _eigs_fix_eigvals(data, eigvals, sort) isherm = isherm if isherm is not None else _isherm(data) evals, evecs = _eigs_dense(data.as_ndarray(), isherm, vecs, eigvals, num_large, num_small) if sort == 'high': # Flip arrays around. if vecs: evecs = np.fliplr(evecs) evals = evals[::-1] return (evals, Dense(evecs, copy=False)) if vecs else evals from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect # We use eigs_dense as the signature source, since in this case it has the # complete signature that we allow, so we don't need to manually set it. eigs = _Dispatcher(eigs_dense, name='eigs', inputs=('data',), out=False) eigs.__doc__ =\ """ Return eigenvalues and (optionally) eigenvectors for a data-layer object. Some particular specialisations of this function may take additional keyword arguments (such as the CSR solver). See their particular docstrings for details on those. Parameters ---------- data : Data Input matrix isherm : bool, optional Indicate whether the matrix is Hermitian or not. There are special Hermitian eigenvalue and -vector solvers for this case, which will take care of orthonormalisation and ensuring better accuracy. If this is not specified either way, it will be calculated from the data. vecs : bool, optional (True) Whether the eigenvectors should be returned as well. sort : {'low', 'high'}, optional Sort the output of the eigenvalues and -vectors ordered by the relevant size of the real part of the eigenvalue from 'low' to high or from 'high' to low. If not all of the eigenvalues are requested, this influences which eigenvalues will be found. eigvals : int, optional Number of eigenvalues and -vectors to return. If `0`, then returns all. Returns ------- eigenvalues : np.ndarray The requested eigenvalues, sorted in the expected order. The dtype is `np.complex128`, unless `isherm=True`, in which case it will be `np.float64`. eigenvectors : Data Only if `vecs=True`. An array of the eigenvectors corresponding to the order of the eigenvalues. """ eigs.add_specialisations([ (CSR, eigs_csr), (Dense, eigs_dense), ], _defer=True) def svd_csr(data, vecs=True, k=6, **kw): """ Singular Value Decomposition: ``data = U @ S @ Vh`` Where ``S`` is diagonal. Parameters ---------- data : Data Input matrix vecs : bool, optional (True) Whether the singular vectors (``U``, ``Vh``) should be returned. k : int, optional (6) Number of state to compute, default is ``6`` to match scipy's default. **kw : dict Options to pass to ``scipy.sparse.linalg.svds``. Returns ------- U : Dense Left singular vectors as columns. Only returned if ``vecs == True``. shape = (data.shape[0], k) S : np.ndarray The ``k``'s largest singular values. Vh : Dense Right singular vectors as rows. Only returned if ``vecs == True``. shape = (k, data.shape[1]) .. note:: svds cannot compute all states at once. While it could find the largest and smallest in 2 calls, it has issues converging with when solving for the smallest (finding the 5 smallest in a 50x50 matrix can fail with default options). It should be used when not all states are needed. """ out = scipy.sparse.linalg.svds( data.as_scipy(), k, return_singular_vectors=vecs, **kw ) if vecs: u, s, vh = out return Dense(u, copy=False), s, Dense(vh, copy=False) return out def svd_dense(data, vecs=True, **kw): """ Singular Value Decomposition: ``data = U @ S @ Vh`` Where ``S`` is diagonal. Parameters ---------- data : Data Input matrix vecs : bool, optional (True) Whether the singular vectors (``U``, ``Vh``) should be returned. **kw : dict Options to pass to ``scipy.linalg.svd``. Returns ------- U : Dense Left singular vectors as columns. Only returned if ``vecs == True``. S : np.ndarray Singular values. Vh : Dense Right singular vectors as rows. Only returned if ``vecs == True``. """ out = scipy.linalg.svd( data.to_array(), compute_uv=vecs, **kw ) if vecs: u, s, vh = out return Dense(u, copy=False), s, Dense(vh, copy=False) return out svd = _Dispatcher( _inspect.Signature([ _inspect.Parameter('data', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('vecs', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='svd', module=__name__, inputs=('data',), out=False) svd.__doc__ =\ """ Singular Value Decomposition: ``data = U @ S @ Vh`` Where ``S`` is diagonal. Parameters ---------- data : Data Input matrix vecs : bool, optional (True) Whether the singular vectors (``U``, ``Vh``) should be returned. Returns ------- U : Dense Left singular vectors as columns. Only returned if ``vecs == True``. S : np.ndarray Singular values. Vh : Dense Right singular vectors as rows. Only returned if ``vecs == True``. """ # Dense implementation return all states, but sparse implementation compute # only a few states. So only the dense version is registered. svd.add_specialisations([ (Dense, svd_dense), ], _defer=True) del _Dispatcher del _inspect qutip-5.1.1/qutip/core/data/expect.pxd000066400000000000000000000017271474175217300177120ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from qutip.core.data cimport CSR, Dense, Data, Dia cpdef double complex expect_csr(CSR op, CSR state) except * cpdef double complex expect_super_csr(CSR op, CSR state) except * cpdef double complex expect_csr_dense(CSR op, Dense state) except * cpdef double complex expect_super_csr_dense(CSR op, Dense state) except * nogil cpdef double complex expect_dense(Dense op, Dense state) except * cpdef double complex expect_super_dense(Dense op, Dense state) except * nogil cpdef double complex expect_dia(Dia op, Dia state) except * cpdef double complex expect_super_dia(Dia op, Dia state) except * cpdef double complex expect_dia_dense(Dia op, Dense state) except * cpdef double complex expect_super_dia_dense(Dia op, Dense state) except * cdef double complex expect_data_dense(Data op, Dense state) except * cdef double complex expect_super_data_dense(Data op, Dense state) except * qutip-5.1.1/qutip/core/data/expect.pyx000066400000000000000000000410431474175217300177320ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False # The exported function `expect(op, state)` is equivalent to # `inner_op(state.adjoint(), op, state)` if `state` is a ket, or # `trace(op @ state)` if state is a density matrix, but it's optimised to not # make unnecessary extra allocations, or calculate extra factors. from libc.math cimport sqrt cdef extern from "" namespace "std" nogil: double complex conj(double complex x) from qutip.core.data.base cimport idxint, Data from qutip.core.data cimport csr, CSR, Dense, Dia from .inner import inner from .trace import trace, trace_oper_ket from .matmul import matmul __all__ = [ 'expect', 'expect_csr', 'expect_dense', 'expect_dia', 'expect_data', 'expect_csr_dense', 'expect_dia_dense', 'expect_super', 'expect_super_csr', 'expect_super_dia', 'expect_super_dense', 'expect_super_csr_dense', 'expect_super_dia_dense', 'expect_super_data', ] cdef int _check_shape_ket(Data op, Data state) except -1 nogil: if ( op.shape[1] != state.shape[0] # Matrix multiplication or state.shape[1] != 1 # State is ket or op.shape[0] != op.shape[1] # op must be square matrix ): raise ValueError("incorrect input shapes " + str(op.shape) + " and " + str(state.shape)) return 0 cdef int _check_shape_dm(Data op, Data state) except -1 nogil: if ( op.shape[1] != state.shape[0] # Matrix multiplication or state.shape[0] != state.shape[1] # State is square or op.shape[0] != op.shape[1] # Op is square ): raise ValueError("incorrect input shapes " + str(op.shape) + " and " + str(state.shape)) return 0 cdef int _check_shape_super(Data op, Data state) except -1 nogil: if state.shape[1] != 1: raise ValueError("expected a column-stacked matrix") if ( op.shape[1] != state.shape[0] # Matrix multiplication or op.shape[0] != op.shape[1] # Square matrix ): raise ValueError("incompatible shapes " + str(op.shape) + ", " + str(state.shape)) return 0 cdef double complex _expect_csr_ket(CSR op, CSR state) except * nogil: """ Perform the operation state.adjoint() @ op @ state for a ket `state` and a square operator `op`. """ _check_shape_ket(op, state) cdef double complex out=0, sum=0, mul cdef size_t row, col, ptr_op, ptr_ket for row in range(state.shape[0]): ptr_ket = state.row_index[row] if ptr_ket == state.row_index[row + 1]: continue sum = 0 mul = conj(state.data[ptr_ket]) for ptr_op in range(op.row_index[row], op.row_index[row + 1]): col = op.col_index[ptr_op] ptr_ket = state.row_index[col] if ptr_ket != state.row_index[col + 1]: sum += op.data[ptr_op] * state.data[ptr_ket] out += mul * sum return out cdef double complex _expect_csr_dm(CSR op, CSR state) except * nogil: """ Perform the operation tr(op @ state) for an operator `op` and a density matrix `state`. """ _check_shape_dm(op, state) cdef double complex out=0 cdef size_t row, col, ptr_op, ptr_state for row in range(op.shape[0]): for ptr_op in range(op.row_index[row], op.row_index[row + 1]): col = op.col_index[ptr_op] for ptr_state in range(state.row_index[col], state.row_index[col + 1]): if state.col_index[ptr_state] == row: out += op.data[ptr_op] * state.data[ptr_state] break return out cpdef double complex expect_super_csr(CSR op, CSR state) except *: """ Perform the operation `tr(op @ state)` where `op` is supplied as a superoperator, and `state` is a column-stacked operator. """ _check_shape_super(op, state) cdef double complex out = 0.0 cdef size_t row=0, ptr, col cdef size_t n = sqrt(state.shape[0]) for _ in range(n): for ptr in range(op.row_index[row], op.row_index[row + 1]): col = op.col_index[ptr] if state.row_index[col] != state.row_index[col + 1]: out += op.data[ptr] * state.data[state.row_index[col]] row += n + 1 return out cpdef double complex expect_csr(CSR op, CSR state) except *: """ Get the expectation value of the operator `op` over the state `state`. The state can be either a ket or a density matrix. The expectation of a state is defined as the operation: state.adjoint() @ op @ state and of a density matrix: tr(op @ state) """ if state.shape[1] == 1: return _expect_csr_ket(op, state) return _expect_csr_dm(op, state) cdef double complex _expect_csr_dense_ket(CSR op, Dense state) except * nogil: _check_shape_ket(op, state) cdef double complex out=0, sum cdef size_t row, ptr for row in range(op.shape[0]): if op.row_index[row] == op.row_index[row + 1]: continue sum = 0 for ptr in range(op.row_index[row], op.row_index[row + 1]): sum += op.data[ptr] * state.data[op.col_index[ptr]] out += sum * conj(state.data[row]) return out cdef double complex _expect_csr_dense_dm(CSR op, Dense state) except * nogil: _check_shape_dm(op, state) cdef double complex out=0 cdef size_t row, ptr_op, ptr_state=0, row_stride, col_stride row_stride = 1 if state.fortran else state.shape[1] col_stride = state.shape[0] if state.fortran else 1 for row in range(op.shape[0]): if op.row_index[row] == op.row_index[row + 1]: continue ptr_state = row * col_stride for ptr_op in range(op.row_index[row], op.row_index[row + 1]): out += op.data[ptr_op] * state.data[ptr_state + row_stride*op.col_index[ptr_op]] return out cdef double complex _expect_dense_ket(Dense op, Dense state) except * nogil: _check_shape_ket(op, state) cdef double complex out=0, sum cdef size_t row, col, op_row_stride, op_col_stride op_row_stride = 1 if op.fortran else op.shape[1] op_col_stride = op.shape[0] if op.fortran else 1 for row in range(op.shape[0]): sum = 0 for col in range(op.shape[0]): sum += (op.data[row * op_row_stride + col * op_col_stride] * state.data[col]) out += sum * conj(state.data[row]) return out cdef double complex _expect_dense_dense_dm(Dense op, Dense state) except * nogil: _check_shape_dm(op, state) cdef double complex out=0 cdef size_t row, col, op_row_stride, op_col_stride cdef size_t state_row_stride, state_col_stride state_row_stride = 1 if state.fortran else state.shape[1] state_col_stride = state.shape[0] if state.fortran else 1 op_row_stride = 1 if op.fortran else op.shape[1] op_col_stride = op.shape[0] if op.fortran else 1 for row in range(op.shape[0]): for col in range(op.shape[1]): out += op.data[row * op_row_stride + col * op_col_stride] * \ state.data[col * state_row_stride + row * state_col_stride] return out cpdef double complex expect_csr_dense(CSR op, Dense state) except *: """ Get the expectation value of the operator `op` over the state `state`. The state can be either a ket or a density matrix. The expectation of a state is defined as the operation: state.adjoint() @ op @ state and of a density matrix: tr(op @ state) """ if state.shape[1] == 1: return _expect_csr_dense_ket(op, state) return _expect_csr_dense_dm(op, state) cpdef double complex expect_dense(Dense op, Dense state) except *: """ Get the expectation value of the operator `op` over the state `state`. The state can be either a ket or a density matrix. The expectation of a state is defined as the operation: state.adjoint() @ op @ state and of a density matrix: tr(op @ state) """ if state.shape[1] == 1: return _expect_dense_ket(op, state) return _expect_dense_dense_dm(op, state) cpdef double complex expect_super_csr_dense(CSR op, Dense state) except * nogil: """ Perform the operation `tr(op @ state)` where `op` is supplied as a superoperator, and `state` is a column-stacked operator. """ _check_shape_super(op, state) cdef double complex out=0 cdef size_t row=0, ptr cdef size_t n = sqrt(state.shape[0]) for _ in range(n): for ptr in range(op.row_index[row], op.row_index[row + 1]): out += op.data[ptr] * state.data[op.col_index[ptr]] row += n + 1 return out cpdef double complex expect_super_dense(Dense op, Dense state) except * nogil: """ Perform the operation `tr(op @ state)` where `op` is supplied as a superoperator, and `state` is a column-stacked operator. """ _check_shape_super(op, state) cdef double complex out=0 cdef size_t row=0, col, N = state.shape[0] cdef size_t n = sqrt(state.shape[0]) cdef size_t op_row_stride, op_col_stride op_row_stride = 1 if op.fortran else op.shape[1] op_col_stride = op.shape[0] if op.fortran else 1 for _ in range(n): for col in range(N): out += op.data[row * op_row_stride + col * op_col_stride] * \ state.data[col] row += n + 1 return out cpdef double complex expect_dia(Dia op, Dia state) except *: cdef double complex expect = 0. cdef idxint diag_bra, diag_op, diag_ket, i, length cdef idxint start_op, start_state, end_op, end_state if state.shape[1] == 1: _check_shape_ket(op, state) # Since the ket is sparse and possibly unsorted. Taking the n'th # element of the state require a loop on the diags. Thus 3 loops are # needed. for diag_ket in range(state.num_diag): #if -state.offsets[diag_ket] >= op.shape[1]: # continue for diag_bra in range(state.num_diag): for diag_op in range(op.num_diag): if state.offsets[diag_ket] - state.offsets[diag_bra] + op.offsets[diag_op] == 0: expect += ( conj(state.data[diag_bra * state.shape[1]]) * state.data[diag_ket * state.shape[1]] * op.data[diag_op * op.shape[1] - state.offsets[diag_ket]] ) else: _check_shape_dm(op, state) for diag_op in range(op.num_diag): for diag_state in range(state.num_diag): if op.offsets[diag_op] == -state.offsets[diag_state]: start_op = max(0, op.offsets[diag_op]) start_state = max(0, state.offsets[diag_state]) end_op = min(op.shape[1], op.shape[0] + op.offsets[diag_op]) end_state = min(state.shape[1], state.shape[0] + state.offsets[diag_state]) length = min(end_op - start_op, end_state - start_state) for i in range(length): expect += ( op.data[diag_op * op.shape[1] + i + start_op] * state.data[diag_state * state.shape[1] + i + start_state] ) return expect cpdef double complex expect_dia_dense(Dia op, Dense state) except *: cdef double complex expect = 0. cdef idxint i, diag_op, start_op, end_op, strideR, stride, start_state if state.shape[1] == 1: _check_shape_ket(op, state) for diag_op in range(op.num_diag): start_op = max(0, op.offsets[diag_op]) end_op = min(op.shape[1], op.shape[0] + op.offsets[diag_op]) for i in range(start_op, end_op): expect += ( op.data[diag_op * op.shape[1] + i] * state.data[i] * conj(state.data[i - op.offsets[diag_op]]) ) else: _check_shape_dm(op, state) stride = state.shape[0] + 1 strideR = state.shape[0] if state.fortran else 1 for diag_op in range(op.num_diag): start_op = max(0, op.offsets[diag_op]) end_op = min(op.shape[1], op.shape[0] + op.offsets[diag_op]) start_state = -op.offsets[diag_op] * strideR for i in range(start_op, end_op): expect += ( op.data[diag_op * op.shape[1] + i] * state.data[start_state + i * stride] ) return expect cpdef double complex expect_super_dia(Dia op, Dia state) except *: cdef double complex expect = 0. _check_shape_super(op, state) cdef idxint diag_op, diag_state cdef idxint stride = sqrt(state.shape[0]) + 1 for diag_op in range(op.num_diag): for diag_state in range(state.num_diag): if ( -state.offsets[diag_state] < op.shape[1] and -op.offsets[diag_op] - state.offsets[diag_state] >= 0 and (-op.offsets[diag_op] - state.offsets[diag_state]) % stride == 0 ): expect += state.data[diag_state * state.shape[1]] * op.data[diag_op * op.shape[1] - state.offsets[diag_state]] return expect cpdef double complex expect_super_dia_dense(Dia op, Dense state) except *: cdef double complex expect = 0. _check_shape_super(op, state) cdef idxint col, diag_op, start, end cdef idxint stride = sqrt(state.shape[0]) + 1 for diag_op in range(op.num_diag): start = max(0, op.offsets[diag_op]) end = min(op.shape[1], op.shape[0] + op.offsets[diag_op]) col = (((start - op.offsets[diag_op] - 1) // stride) + 1) * stride + op.offsets[diag_op] while col < end: expect += op.data[diag_op * op.shape[1] + col] * state.data[col] col += stride return expect def expect_data(Data op, Data state): """ Get the expectation value of the operator `op` over the state `state`. The state can be either a ket or a density matrix. The expectation of a state is defined as the operation: state.adjoint() @ op @ state and of a density matrix: tr(op @ state) """ if state.shape[1] == 1: _check_shape_ket(op, state) return inner(state, matmul(op, state)) _check_shape_dm(op, state) return trace(matmul(op, state)) def expect_super_data(Data op, Data state): """ Perform the operation `tr(op @ state)` where `op` is supplied as a superoperator, and `state` is a column-stacked operator. """ _check_shape_super(op, state) return trace_oper_ket(matmul(op, state)) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect expect = _Dispatcher( _inspect.Signature([ _inspect.Parameter('op', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('state', _inspect.Parameter.POSITIONAL_ONLY), ]), name='expect', module=__name__, inputs=('op', 'state'), out=False, ) expect.__doc__ =\ """ Get the expectation value of the operator `op` over the state `state`. The state can be either a ket or a density matrix. Returns a complex number. The expectation of a state is defined as the operation: state.adjoint() @ op @ state and of a density matrix: tr(op @ state) """ expect.add_specialisations([ (CSR, CSR, expect_csr), (CSR, Dense, expect_csr_dense), (Dense, Dense, expect_dense), (Dia, Dense, expect_dia_dense), (Dia, Dia, expect_dia), (Data, Data, expect_data), ], _defer=True) expect_super = _Dispatcher( _inspect.Signature([ _inspect.Parameter('op', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('state', _inspect.Parameter.POSITIONAL_ONLY), ]), name='expect_super', module=__name__, inputs=('op', 'state'), out=False, ) expect_super.__doc__ =\ """ Perform the operation `tr(op @ state)` where `op` is supplied as a superoperator, and `state` is a column-stacked operator. Returns a complex number. """ expect_super.add_specialisations([ (CSR, CSR, expect_super_csr), (CSR, Dense, expect_super_csr_dense), (Dense, Dense, expect_super_dense), (Dia, Dense, expect_super_dia_dense), (Dia, Dia, expect_super_dia), (Data, Data, expect_super_data), ], _defer=True) del _inspect, _Dispatcher cdef double complex expect_data_dense(Data op, Dense state) except *: cdef double complex out if type(op) is CSR: out = expect_csr_dense(op, state) elif type(op) is Dense: out = expect_dense(op, state) else: out = expect(op, state) return out cdef double complex expect_super_data_dense(Data op, Dense state) except *: cdef double complex out if type(op) is CSR: out = expect_super_csr_dense(op, state) elif type(op) is Dense: out = expect_super_dense(op, state) else: out = expect_super(op, state) return out qutip-5.1.1/qutip/core/data/expm.py000066400000000000000000000111521474175217300172210ustar00rootroot00000000000000import numpy as np import scipy.sparse.linalg import scipy.linalg from .dense import Dense from .csr import CSR from .dia import Dia from . import dia from .properties import isdiag_csr, isdiag_dia from qutip.settings import settings from .base import idxint_dtype __all__ = [ 'expm', 'expm_csr', 'expm_csr_dense', 'expm_dense', 'expm_dia', 'logm', 'logm_dense', 'sqrtm', 'sqrtm_dense' ] def expm_csr(matrix: CSR) -> CSR: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only exponentiate square matrix") if isdiag_csr(matrix): matrix_sci = matrix.as_scipy() data = np.ones(matrix.shape[0], dtype=np.complex128) data[matrix_sci.indices] += np.expm1(matrix_sci.data) return CSR( ( data, np.arange(matrix.shape[0], dtype=idxint_dtype), np.arange(matrix.shape[0] + 1, dtype=idxint_dtype), ), shape=matrix.shape, copy=False, ) # The scipy solvers for the Pade approximant are more efficient with the # CSC format than the CSR one. csc = matrix.as_scipy().tocsc() return CSR(scipy.sparse.linalg.expm(csc).tocsr(), tidyup=settings.core['auto_tidyup']) def expm_dia(matrix: Dia) -> Dia: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only exponentiate square matrix") if matrix.num_diag == 0: out = dia.identity(matrix.shape[0]) elif matrix.num_diag > 1: csc = matrix.as_scipy().tocsc() out = Dia( scipy.sparse.linalg.expm(csc).todia(), tidyup=settings.core['auto_tidyup'], copy=False ) elif isdiag_dia(matrix): matrix_sci = matrix.as_scipy() data = np.exp(matrix_sci.data[0, :]) out = dia.diags(data, shape=matrix.shape) else: mat = matrix.as_scipy() size = matrix.shape[0] offset = mat.offsets[0] n_offset = offset a_offset = abs(offset) data = mat.data[0, max(0, offset): min(size, size + offset)] data_0 = data out_oufsets = np.arange(0, size, a_offset, dtype=idxint_dtype) out_oufsets *= np.sign(offset) out_data = np.zeros((len(out_oufsets), size), dtype=complex) out_data[0, :] += 1. for i in range(1, len(out_oufsets)): out_data[i, max(0, n_offset): min(size, size + n_offset)] = data data = data_0[:-abs(n_offset)] * data[a_offset:] / (i+1) n_offset += offset out = Dia((out_data, out_oufsets), shape=matrix.shape, copy=False) return out def expm_csr_dense(matrix: CSR) -> Dense: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only exponentiate square matrix") return Dense(scipy.sparse.linalg.expm(matrix.to_array())) def expm_dense(matrix: Dense) -> Dense: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only exponentiate square matrix") return Dense(scipy.linalg.expm(matrix.as_ndarray()), copy=False) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect expm = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='expm', module=__name__, inputs=('matrix',), out=True, ) expm.__doc__ = """Matrix exponential `e**A` for a matrix `A`.""" expm.add_specialisations([ (CSR, CSR, expm_csr), (CSR, Dense, expm_csr_dense), (Dense, Dense, expm_dense), (Dia, Dia, expm_dia), ], _defer=True) def logm_dense(matrix: Dense) -> Dense: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only compute logarithm square matrix") return Dense(scipy.linalg.logm(matrix.as_ndarray()), copy=False) logm = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='logm', module=__name__, inputs=('matrix',), out=True, ) logm.__doc__ = """Matrix logarithm `ln(A)` for a matrix `A`.""" logm.add_specialisations([ (Dense, Dense, logm_dense), ], _defer=True) def sqrtm_dense(matrix) -> Dense: if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only compute logarithm square matrix") return Dense(scipy.linalg.sqrtm(matrix.as_ndarray())) sqrtm = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='sqrtm', module=__name__, inputs=('matrix',), out=True, ) sqrtm.__doc__ = """Matrix square root `sqrt(A)` for a matrix `A`.""" sqrtm.add_specialisations([ (Dense, Dense, sqrtm_dense), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/extract.py000066400000000000000000000063121474175217300177240ustar00rootroot00000000000000from . import Dense, CSR, Dia from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect try: from scipy.sparse import csr_array except ImportError: csr_array = None from scipy.sparse import csr_matrix __all__ = ["extract"] def extract_dense(matrix, format=None, copy=True): """ Return an array representation of the Dense data object. Parameters ---------- matrix : Data The matrix to convert to the given format. format : str {"ndarray"}, default="ndarray" Type of the output. copy : bool, default: True Whether to return a copy of the data. If False, a view of the data is returned when possible. """ if format not in [None, "ndarray"]: raise ValueError( "Dense can only be extracted to 'ndarray'" ) if copy: return matrix.to_array() else: return matrix.as_ndarray() def extract_csr(matrix, format=None, copy=True): """ Return the scipy's object ``csr_matrix``. Parameters ---------- matrix : Data The matrix to convert to common type. format : str, {"csr_matrix"} Type of the output. copy : bool, default: True Whether to pass a copy of the object or not. """ if format not in [None, "scipy_csr", "csr_matrix"]: raise ValueError( "CSR can only be extracted to 'csr_matrix'" ) csr_mat = matrix.as_scipy() if copy: csr_mat = csr_mat.copy() return csr_mat def extract_dia(matrix, format=None, copy=True): """ Return the scipy's object ``dia_matrix``. Parameters ---------- matrix : Data The matrix to convert to common type. format : str, {"dia_matrix"} Type of the output. copy : bool, default: True Whether to pass a copy of the object or not. """ if format not in [None, "scipy_dia", "dia_matrix"]: raise ValueError( "Dia can only be extracted to 'dia_matrix'" ) dia_mat = matrix.as_scipy() if copy: dia_mat = dia_mat.copy() return dia_mat extract = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter( 'format', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=None ), _inspect.Parameter( 'copy', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=True ) ]), name='extract', module=__name__, inputs=('matrix',), out=False, ) extract.__doc__ =\ """ Return the common representation of the data layer object: scipy's ``csr_matrix`` for ``CSR``, numpy array for ``Dense``, Jax's ``Array`` for ``JaxArray``, etc. Parameters ---------- matrix : Data The matrix to convert to common type. format : str, default: None Type of the output, "ndarray" for ``Dense``, "csr_array" for ``CSR``. A ValueError will be raised if the format is not supported. copy : bool, default: True Whether to pass a copy of the object. """ extract.add_specialisations([ (CSR, extract_csr), (Dia, extract_dia), (Dense, extract_dense), ], _defer=True) del _Dispatcher, _inspect qutip-5.1.1/qutip/core/data/inner.pxd000066400000000000000000000003621474175217300175270ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR cpdef double complex inner_csr(CSR left, CSR right, bint scalar_is_ket=*) except * cpdef double complex inner_op_csr(CSR left, CSR op, CSR right, bint scalar_is_ket=*) except * qutip-5.1.1/qutip/core/data/inner.pyx000066400000000000000000000400771474175217300175630ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False cdef extern from "" namespace "std" nogil: double complex conj(double complex x) from qutip.core.data.base cimport idxint, Data from qutip.core.data cimport csr, dense from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia from qutip.core.data.matmul cimport matmul_dense from .matmul import matmul from .trace import trace from .adjoint import adjoint __all__ = [ 'inner', 'inner_csr', 'inner_dense', 'inner_dia', 'inner_data', 'inner_op', 'inner_op_csr', 'inner_op_dense', 'inner_op_dia', 'inner_op_data', ] cdef int _check_shape_inner(Data left, Data right) except -1 nogil: if ( (left.shape[0] != 1 and left.shape[1] != 1) or right.shape[1] != 1 ): raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) return 0 cdef int _check_shape_inner_op(Data left, Data op, Data right) except -1 nogil: cdef bint left_shape = left.shape[0] == 1 or left.shape[1] == 1 cdef bint left_op = ( (left.shape[0] == 1 and left.shape[1] == op.shape[0]) or (left.shape[1] == 1 and left.shape[0] == op.shape[0]) ) cdef bint op_right = op.shape[1] == right.shape[0] cdef bint right_shape = right.shape[1] == 1 if not (left_shape and left_op and op_right and right_shape): raise ValueError("".join([ "incompatible matrix shapes ", str(left.shape), ", ", str(op.shape), " and ", str(right.shape), ])) return 0 cdef double complex _inner_csr_bra_ket(CSR left, CSR right) nogil: cdef size_t col, ptr_bra, ptr_ket cdef double complex out = 0 # We actually don't care if left is sorted or not. for ptr_bra in range(csr.nnz(left)): col = left.col_index[ptr_bra] ptr_ket = right.row_index[col] if right.row_index[col + 1] != ptr_ket: out += left.data[ptr_bra] * right.data[ptr_ket] return out cdef double complex _inner_csr_ket_ket(CSR left, CSR right) nogil: cdef size_t row, ptr_l, ptr_r cdef double complex out = 0 for row in range(left.shape[0]): ptr_l = left.row_index[row] ptr_r = right.row_index[row] if left.row_index[row+1] != ptr_l and right.row_index[row+1] != ptr_r: out += conj(left.data[ptr_l]) * right.data[ptr_r] return out cpdef double complex inner_csr(CSR left, CSR right, bint scalar_is_ket=False) except *: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner(left, right) if left.shape[0] == left.shape[1] == right.shape[1] == 1: if csr.nnz(left) and csr.nnz(right): return ( conj(left.data[0]) * right.data[0] if scalar_is_ket else left.data[0] * right.data[0] ) return 0 if left.shape[0] == 1: return _inner_csr_bra_ket(left, right) return _inner_csr_ket_ket(left, right) cpdef double complex inner_dia(Dia left, Dia right, bint scalar_is_ket=False) except * nogil: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner(left, right) cdef double complex inner = 0. cdef idxint diag_left, diag_right cdef bint is_ket if right.shape[0] == 1: is_ket = scalar_is_ket else: is_ket = left.shape[0] == right.shape[0] if is_ket: for diag_right in range(right.num_diag): for diag_left in range(left.num_diag): if left.offsets[diag_left] - right.offsets[diag_right] == 0: inner += ( conj(left.data[diag_left * left.shape[1]]) * right.data[diag_right * right.shape[1]] ) else: for diag_right in range(right.num_diag): for diag_left in range(left.num_diag): if left.offsets[diag_left] + right.offsets[diag_right] == 0: inner += ( left.data[diag_left * left.shape[1] + left.offsets[diag_left]] * right.data[diag_right * right.shape[1]] ) return inner cpdef double complex inner_dense(Dense left, Dense right, bint scalar_is_ket=False) except * nogil: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner(left, right) if left.shape[0] == left.shape[1] == right.shape[1] == 1: return ( conj(left.data[0]) * right.data[0] if scalar_is_ket else left.data[0] * right.data[0] ) cdef double complex out = 0 cdef size_t i if left.shape[0] == 1: for i in range(right.shape[0]): out += left.data[i] * right.data[i] else: for i in range(right.shape[0]): out += conj(left.data[i]) * right.data[i] return out cdef double complex _inner_op_csr_bra_ket(CSR left, CSR op, CSR right) nogil: cdef size_t ptr_l, ptr_op, ptr_r, row, col cdef double complex sum, out=0 # left does not need to be sorted. for ptr_l in range(csr.nnz(left)): row = left.col_index[ptr_l] sum = 0 for ptr_op in range(op.row_index[row], op.row_index[row + 1]): col = op.col_index[ptr_op] ptr_r = right.row_index[col] if ptr_r != right.row_index[col + 1]: sum += op.data[ptr_op] * right.data[ptr_r] out += left.data[ptr_l] * sum return out cdef double complex _inner_op_csr_ket_ket(CSR left, CSR op, CSR right) nogil: cdef size_t ptr_l, ptr_op, ptr_r, row, col cdef double complex sum, out=0 for row in range(op.shape[0]): ptr_l = left.row_index[row] if left.row_index[row + 1] == ptr_l: continue sum = 0 for ptr_op in range(op.row_index[row], op.row_index[row + 1]): col = op.col_index[ptr_op] ptr_r = right.row_index[col] if ptr_r != right.row_index[col + 1]: sum += op.data[ptr_op] * right.data[ptr_r] out += conj(left.data[ptr_l]) * sum return out cpdef double complex inner_op_dia(Dia left, Dia op, Dia right, bint scalar_is_ket=False) except * nogil: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner_op(left, op, right) cdef double complex inner = 0., val cdef idxint diag_left, diag_op, diag_right cdef int is_ket if op.shape[0] == 1: is_ket = scalar_is_ket else: is_ket = left.shape[0] == op.shape[0] if is_ket: for diag_right in range(right.num_diag): for diag_left in range(left.num_diag): for diag_op in range(op.num_diag): if -left.offsets[diag_left] + right.offsets[diag_right] + op.offsets[diag_op] == 0: inner += ( conj(left.data[diag_left]) * right.data[diag_right] * op.data[diag_op * op.shape[1] - right.offsets[diag_right]] ) else: for diag_right in range(right.num_diag): for diag_left in range(left.num_diag): for diag_op in range(op.num_diag): if left.offsets[diag_left] + right.offsets[diag_right] + op.offsets[diag_op] == 0: inner += ( left.data[diag_left * left.shape[1] + left.offsets[diag_left]] * right.data[diag_right] * op.data[diag_op * op.shape[1] - right.offsets[diag_right]] ) return inner cpdef double complex inner_op_csr(CSR left, CSR op, CSR right, bint scalar_is_ket=False) except *: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner_op(left, op, right) cdef double complex l if 1 == left.shape[1] == left.shape[0] == op.shape[0] == op.shape[1] == right.shape[1]: if not (csr.nnz(left) and csr.nnz(op) and csr.nnz(right)): return 0 l = conj(left.data[0]) if scalar_is_ket else left.data[0] return l * op.data[0] * right.data[0] if left.shape[0] == 1: return _inner_op_csr_bra_ket(left, op, right) return _inner_op_csr_ket_ket(left, op, right) cpdef double complex inner_op_dense(Dense left, Dense op, Dense right, bint scalar_is_ket=False) except *: """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner_op(left, op, right) return inner_dense(left, matmul_dense(op, right), scalar_is_ket) cpdef inner_data(Data left, Data right, bint scalar_is_ket=False): """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner(left, right) if left.shape[0] == left.shape[1] == right.shape[1] == 1: return ( trace(left).conjugate() * trace(right) if scalar_is_ket else trace(left) * trace(right) ) if left.shape[0] != 1: left = adjoint(left) # We use trace so we don't force convertion to complex. return trace(matmul(left, right)) cpdef inner_op_data(Data left, Data op, Data right, bint scalar_is_ket=False): """ Compute the complex inner product . The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. """ _check_shape_inner_op(left, op, right) return inner_data(left, matmul(op, right), scalar_is_ket) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect inner = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('scalar_is_ket', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=False), ]), name='inner', module=__name__, inputs=('left', 'right'), out=False, ) inner.__doc__ =\ """ Compute the complex inner product . Return the complex value. The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. Parameters ---------- left : Data The left operand as either a bra or a ket matrix. right : Data The right operand as a ket matrix. scalar_is_ket : bool, optional (False) If `False`, then `left` is assumed to be a bra if it is one-dimensional. If `True`, then it is assumed to be a ket. This parameter is ignored if `left` and `right` are not one-dimensional. """ inner.add_specialisations([ (CSR, CSR, inner_csr), (Dia, Dia, inner_dia), (Dense, Dense, inner_dense), (Data, Data, inner_data), ], _defer=True) inner_op = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('op', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('scalar_is_ket', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=False), ]), name='inner_op', module=__name__, inputs=('left', 'op', 'right'), out=False, ) inner_op.__doc__ =\ """ Compute the complex inner product . Return the complex value. This operation is also known as taking a matrix element. The shape of `left` is used to determine if it has been supplied as a ket or a bra. The result of this function will be identical if passed `left` or `adjoint(left)`. The parameter `scalar_is_ket` is only intended for the case where `left` and `right` are both of shape (1, 1). In this case, `left` will be assumed to be a ket unless `scalar_is_ket` is False. This parameter is ignored at all other times. Parameters ---------- left : Data The left operand as either a bra or a ket matrix. op : Data The operator of which to take the matrix element. Must have dimensions which match `left` and `right`. right : Data The right operand as a ket matrix. scalar_is_ket : bool, optional (False) If `False`, then `left` is assumed to be a bra if it is one-dimensional. If `True`, then it is assumed to be a ket. This parameter is ignored if `left` and `right` are not one-dimensional. """ inner_op.add_specialisations([ (CSR, CSR, CSR, inner_op_csr), (Dia, Dia, Dia, inner_op_dia), (Dense, Dense, Dense, inner_op_dense), (Data, Data, Data, inner_op_data), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/kron.pxd000066400000000000000000000001511474175217300173610ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR cpdef CSR kron_csr(CSR left, CSR right) qutip-5.1.1/qutip/core/data/kron.pyx000066400000000000000000000176601474175217300174230ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False cimport cython from libc.string cimport memset from qutip.core.data.base cimport idxint, Data from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from .adjoint import transpose from qutip.core.data.dia cimport Dia from qutip.core.data cimport csr, dia from qutip.core.data.convert import to as _to import numpy __all__ = [ 'kron', 'kron_csr', 'kron_dense', 'kron_dia', 'kron_transpose', 'kron_transpose_dense', 'kron_transpose_data', ] @cython.overflowcheck(True) cdef idxint _mul_checked(idxint a, idxint b): return a * b cpdef Dense kron_dense(Dense left, Dense right): return Dense(numpy.kron(left.as_ndarray(), right.as_ndarray()), copy=False) cpdef CSR kron_csr(CSR left, CSR right): """Kronecker product of two CSR matrices.""" cdef idxint nrows_l=left.shape[0], nrows_r=right.shape[0] cdef idxint ncols_l=left.shape[1], ncols_r=right.shape[1] cdef idxint row_l, row_r, row_out cdef idxint ptr_start_l, ptr_end_l, ptr_start_r, ptr_end_r, dist_l, dist_r cdef idxint ptr_l, ptr_r, ptr_out, ptr_start_out, ptr_end_out cdef CSR out = csr.empty(_mul_checked(nrows_l, nrows_r), _mul_checked(ncols_l, ncols_r), _mul_checked(csr.nnz(left), csr.nnz(right))) with nogil: row_out = 0 out.row_index[row_out] = 0 for row_l in range(nrows_l): ptr_start_l = left.row_index[row_l] ptr_end_l = left.row_index[row_l + 1] dist_l = ptr_end_l - ptr_start_l for row_r in range(nrows_r): ptr_start_r = right.row_index[row_r] ptr_end_r = right.row_index[row_r + 1] dist_r = ptr_end_r - ptr_start_r ptr_start_out = out.row_index[row_out] ptr_end_out = ptr_start_out + dist_r out.row_index[row_out+1] = out.row_index[row_out] + dist_l*dist_r row_out += 1 for ptr_l in range(ptr_start_l, ptr_end_l): ptr_r = ptr_start_r for ptr_out in range(ptr_start_out, ptr_end_out): out.col_index[ptr_out] =\ left.col_index[ptr_l]*ncols_r + right.col_index[ptr_r] out.data[ptr_out] = left.data[ptr_l] * right.data[ptr_r] ptr_r += 1 ptr_start_out += dist_r ptr_end_out += dist_r return out cdef inline void _vec_kron( double complex * ptr_l, double complex * ptr_r, double complex * ptr_out, idxint size_l, idxint size_r, idxint step ): cdef idxint i, j for i in range(size_l): for j in range(size_r): ptr_out[i*step+j] = ptr_l[i] * ptr_r[j] cpdef Dia kron_dia(Dia left, Dia right): cdef idxint nrows_l=left.shape[0], nrows_r=right.shape[0] cdef idxint ncols_l=left.shape[1], ncols_r=right.shape[1] cdef idxint nrows=_mul_checked(nrows_l, nrows_r) cdef idxint ncols=_mul_checked(ncols_l, ncols_r) cdef idxint max_diag=_mul_checked(right.num_diag, left.num_diag) cdef idxint num_diag=0, diag_left, diag_right, delta, col_left, col_right cdef idxint start_left, end_left, start_right, end_right cdef Dia out if right.shape[0] == right.shape[1]: out = dia.empty(nrows, ncols, max_diag) memset( out.data, 0, max_diag * out.shape[1] * sizeof(double complex) ) for diag_left in range(left.num_diag): for diag_right in range(right.num_diag): out.offsets[num_diag] = ( left.offsets[diag_left] * right.shape[0] + right.offsets[diag_right] ) start_left = max(0, left.offsets[diag_left]) end_left = min(left.shape[1], left.offsets[diag_left] + left.shape[0]) _vec_kron( left.data + (diag_left * ncols_l) + max(0, left.offsets[diag_left]), right.data + (diag_right * ncols_r) + max(0, right.offsets[diag_right]), out.data + (num_diag * ncols) + max(0, left.offsets[diag_left]) * right.shape[0] + max(0, right.offsets[diag_right]), end_left - start_left, right.shape[1] - abs(right.offsets[diag_right]), right.shape[1] ) num_diag += 1 out.num_diag = num_diag else: max_diag = _mul_checked(max_diag, ncols_l) if max_diag < nrows: out = dia.empty(nrows, ncols, max_diag) delta = right.shape[0] - right.shape[1] for diag_left in range(left.num_diag): for diag_right in range(right.num_diag): start_left = max(0, left.offsets[diag_left]) end_left = min(left.shape[1], left.shape[0] + left.offsets[diag_left]) for col_left in range(start_left, end_left): memset( out.data + (num_diag * out.shape[1]), 0, out.shape[1] * sizeof(double complex) ) out.offsets[num_diag] = ( left.offsets[diag_left] * right.shape[0] + right.offsets[diag_right] - col_left * delta ) start_right = max(0, right.offsets[diag_right]) end_right = min(right.shape[1], right.shape[0] + right.offsets[diag_right]) for col_right in range(start_right, end_right): out.data[num_diag * out.shape[1] + col_left * right.shape[1] + col_right] = ( right.data[diag_right * right.shape[1] + col_right] * left.data[diag_left * left.shape[1] + col_left] ) num_diag += 1 out.num_diag = num_diag else: # The output is not sparse enough ant the empty data array would be # larger than the dense array. # Fallback on dense operation left_dense = _to(Dense, left) right_dense = _to(Dense, right) out_dense = kron_dense(left_dense, right_dense) out = _to(Dia, out_dense) out = dia.clean_dia(out, True) return out from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect kron = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), ]), name='kron', module=__name__, inputs=('left', 'right'), out=True, ) kron.__doc__ =\ """ Compute the Kronecker product of two matrices. This is used to represent quantum tensor products of vector spaces. """ kron.add_specialisations([ (CSR, CSR, CSR, kron_csr), (Dense, Dense, Dense, kron_dense), (Dia, Dia, Dia, kron_dia), ], _defer=True) cpdef Data kron_transpose_data(Data left, Data right): return kron(transpose(left), right) cpdef Dense kron_transpose_dense(Dense left, Dense right): return Dense(numpy.kron(left.as_ndarray().T, right.as_ndarray()), copy=False) kron_transpose = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), ]), name='kron_transpose', module=__name__, inputs=('left', 'right'), out=True, ) kron_transpose.__doc__ =\ """ Compute the Kronecker product of two matrices with transposing the first one. This is used to represent superoperator. """ kron_transpose.add_specialisations([ (Data, Data, Data, kron_transpose_data), (Dense, Dense, Dense, kron_transpose_dense), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/linalg.py000066400000000000000000000030241474175217300175150ustar00rootroot00000000000000import scipy.linalg import scipy.sparse from .dense import Dense from .csr import CSR __all__ = ['inv', 'inv_csr', 'inv_dense'] def inv_dense(data, /): """Compute the inverse of a matrix""" if not isinstance(data, Dense): raise TypeError("expected data in Dense format but got " + str(type(data))) if data.shape[0] != data.shape[1]: raise ValueError('Cannot compute the matrix inverse' ' of a nonsquare matrix') return Dense(scipy.linalg.inv(data.as_ndarray()), copy=False) def inv_csr(data, /): """Compute the inverse of a sparse matrix""" if not isinstance(data, CSR): raise TypeError("expected data in CSR format but got " + str(type(data))) if data.shape[0] != data.shape[1]: raise ValueError('Cannot compute the matrix inverse ' 'of a nonsquare matrix') inv = scipy.sparse.linalg.inv(data.as_scipy().tocsc()) # scipy.sparse.linalg.inv can return dense or sparse arrays. return CSR(scipy.sparse.csr_matrix(inv), copy=False) from .dispatch import Dispatcher as _Dispatcher inv = _Dispatcher(inv_dense, name='inv', inputs=('data',), out=True) inv.__doc__ =\ """ Return matrix inverse for a data-layer object. Parameters ---------- data : Data Input matrix Returns ------- inverse : Data Inverse of data """ inv.add_specialisations([ (CSR, CSR, inv_csr), (Dense, Dense, inv_dense), ], _defer=True) del _Dispatcher qutip-5.1.1/qutip/core/data/make.py000066400000000000000000000104111474175217300171620ustar00rootroot00000000000000from .dispatch import Dispatcher as _Dispatcher from . import csr, dense, dia, CSR, Dense, Dia import numpy as np __all__ = [ 'diag', 'one_element_csr', 'one_element_dense', 'one_element_dia', 'one_element' ] def _diag_signature(diagonals, offsets=0, shape=None): """ Construct a matrix from diagonals and their offsets. Using this function in single-argument form produces a square matrix with the given values on the main diagonal. With lists of diagonals and offsets, the matrix will be the smallest possible square matrix if shape is not given, but in all cases the diagonals must fit exactly with no extra or missing elements. Duplicated diagonals will be summed together in the output. Parameters ---------- diagonals : sequence of array_like of complex or array_like of complex The entries (including zeros) that should be placed on the diagonals in the output matrix. Each entry must have enough entries in it to fill the relevant diagonal and no more. offsets : sequence of integer or integer, optional The indices of the diagonals. `offsets[i]` is the location of the values `diagonals[i]`. An offset of 0 is the main diagonal, positive values are above the main diagonal and negative ones are below the main diagonal. shape : tuple, optional The shape of the output as (``rows``, ``columns``). The result does not need to be square, but the diagonals must be of the correct length to fit in exactly. """ pass diag = _Dispatcher(_diag_signature, name='diag', inputs=(), out=True) diag.add_specialisations([ (CSR, csr.diags), (Dia, dia.diags), (Dense, dense.diags), ], _defer=True) del _diag_signature def one_element_csr(shape, position, value=1.0): """ Create a matrix with only one nonzero element. Parameters ---------- shape : tuple The shape of the output as (``rows``, ``columns``). position : tuple The position of the non zero in the matrix as (``rows``, ``columns``). value : complex, optional The value of the non-null element. """ if not (0 <= position[0] < shape[0] and 0 <= position[1] < shape[1]): raise ValueError("Position of the elements out of bound: " + str(position) + " in " + str(shape)) data = csr.empty(*shape, 1) sci = data.as_scipy(full=True) sci.data[0] = value sci.indices[0] = position[1] sci.indptr[:position[0]+1] = 0 sci.indptr[position[0]+1:] = 1 return data def one_element_dense(shape, position, value=1.0): """ Create a matrix with only one nonzero element. Parameters ---------- shape : tuple The shape of the output as (``rows``, ``columns``). position : tuple The position of the non zero in the matrix as (``rows``, ``columns``). value : complex, optional The value of the non-null element. """ if not (0 <= position[0] < shape[0] and 0 <= position[1] < shape[1]): raise ValueError("Position of the elements out of bound: " + str(position) + " in " + str(shape)) data = dense.zeros(*shape, 1) nda = data.as_ndarray() nda[position] = value return data def one_element_dia(shape, position, value=1.0): """ Create a matrix with only one nonzero element. Parameters ---------- shape : tuple The shape of the output as (``rows``, ``columns``). position : tuple The position of the non zero in the matrix as (``rows``, ``columns``). value : complex, optional The value of the non-null element. """ if not (0 <= position[0] < shape[0] and 0 <= position[1] < shape[1]): raise ValueError("Position of the elements out of bound: " + str(position) + " in " + str(shape)) data = np.zeros((1, shape[1]), dtype=complex) data[0, position[1]] = value offsets = np.array([position[1]-position[0]]) return Dia((data, offsets), copy=None, shape=shape) one_element = _Dispatcher(one_element_dense, name='one_element', inputs=(), out=True) one_element.add_specialisations([ (CSR, one_element_csr), (Dense, one_element_dense), (Dia, one_element_dia), ], _defer=True) qutip-5.1.1/qutip/core/data/matmul.pxd000066400000000000000000000015621474175217300177160ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia from qutip.core.data.base cimport Data cpdef CSR matmul_csr(CSR left, CSR right, double complex scale=*, CSR out=*) cpdef Dense matmul_dense(Dense left, Dense right, double complex scale=*, Dense out=*) cpdef Dense matmul_csr_dense_dense(CSR left, Dense right, double complex scale=*, Dense out=*) cpdef Dia matmul_dia(Dia left, Dia right, double complex scale=*) cpdef Dense matmul_dia_dense_dense(Dia left, Dense right, double complex scale=*, Dense out=*) cdef Dense matmul_data_dense(Data left, Dense right) cdef void imatmul_data_dense(Data left, Dense right, double complex scale, Dense out) cpdef Dense multiply_dense(Dense left, Dense right) cpdef CSR multiply_csr(CSR left, CSR right) cpdef Dia multiply_dia(Dia left, Dia right) qutip-5.1.1/qutip/core/data/matmul.pyx000066400000000000000000000705331474175217300177470ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memset, memcpy from libc.math cimport fabs from libc.stdlib cimport abs from libcpp.algorithm cimport lower_bound import warnings from qutip.settings import settings cimport cython from cpython cimport mem import numpy as np cimport numpy as cnp from scipy.linalg cimport cython_blas as blas from qutip.core.data.base import idxint_dtype from qutip.core.data.base cimport idxint, Data from qutip.core.data.dense cimport Dense from qutip.core.data.csr cimport CSR from qutip.core.data.dia cimport Dia from qutip.core.data.tidyup cimport tidyup_dia from qutip.core.data cimport csr, dense, dia from qutip.core.data.add cimport iadd_dense, add_csr from qutip.core.data.mul cimport imul_dense from qutip.core.data.dense import OrderEfficiencyWarning cnp.import_array() cdef extern from *: void *PyMem_Calloc(size_t n, size_t elsize) # This function is templated over integral types on import to allow `idxint` to # be any signed integer (though likely things will only work for >=32-bit). To # change integral types, you only need to change the `idxint` definitions in # `core.data.base` at compile-time. cdef extern from "src/matmul_csr_vector.hpp" nogil: void _matmul_csr_vector[T]( double complex *data, T *col_index, T *row_index, double complex *vec, double complex scale, double complex *out, T nrows) cdef extern from "src/matmul_diag_vector.hpp" nogil: void _matmul_diag_vector[T]( double complex *data, double complex *vec, double complex *out, T length, double complex scale) void _matmul_diag_block[T]( double complex *data, double complex *vec, double complex *out, T length, T width) __all__ = [ 'matmul', 'matmul_csr', 'matmul_dense', 'matmul_dia', 'matmul_csr_dense_dense', 'matmul_dia_dense_dense', 'matmul_dense_dia_dense', 'multiply', 'multiply_csr', 'multiply_dense', 'multiply_dia', ] cdef int _check_shape(Data left, Data right, Data out=None) except -1 nogil: if left.shape[1] != right.shape[0]: raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) if ( out is not None and ( out.shape[0] != left.shape[0] or out.shape[1] != right.shape[1] ) ): raise ValueError( "incompatible output shape, got " + str(out.shape) + " but needed " + str((left.shape[0], right.shape[1])) ) return 0 cdef idxint _matmul_csr_estimate_nnz(CSR left, CSR right): """ Produce a sensible upper-bound for the number of non-zero elements that will be present in a matrix multiplication between the two matrices. """ cdef idxint j, k, nnz=0 cdef idxint ii, jj, kk cdef idxint nrows=left.shape[0], ncols=right.shape[1] # Setup mask array cdef idxint *mask = mem.PyMem_Malloc(ncols * sizeof(idxint)) with nogil: for ii in range(ncols): mask[ii] = -1 for ii in range(nrows): for jj in range(left.row_index[ii], left.row_index[ii+1]): j = left.col_index[jj] for kk in range(right.row_index[j], right.row_index[j+1]): k = right.col_index[kk] if mask[k] != ii: mask[k] = ii nnz += 1 mem.PyMem_Free(mask) return nnz cpdef CSR matmul_csr(CSR left, CSR right, double complex scale=1, CSR out=None): """ Multiply two CSR matrices together to produce another CSR. If `out` is specified, it must be pre-allocated with enough space to hold the output result. This is the operation ``out := left @ right`` where `out` will be allocated if not supplied. Parameters ---------- left : CSR CSR matrix on the left of the multiplication. right : CSR CSR matrix on the right of the multiplication. out : optional CSR Allocated space to store the result. This must have enough space in the `data`, `col_index` and `row_index` pointers already allocated. Returns ------- out : CSR The result of the matrix multiplication. This will be the same object as the input parameter `out` if that was supplied. """ _check_shape(left, right) cdef idxint nnz = _matmul_csr_estimate_nnz(left, right) if out is not None: raise TypeError("passing an `out` entry for CSR operations makes no sense") out = csr.empty(left.shape[0], right.shape[1], nnz if nnz != 0 else 1) if nnz == 0 or csr.nnz(left) == 0 or csr.nnz(right) == 0: # Ensure the out array row_index is zeroed. The others need not be, # because they don't represent valid entries since row_index is zeroed. with nogil: memset(&out.row_index[0], 0, (out.shape[0] + 1) * sizeof(idxint)) return out # Initialise actual matrix multiplication. nnz = 0 cdef idxint head, length, row_l, ptr_l, row_r, ptr_r, col_r, tmp cdef idxint nrows=left.shape[0], ncols=right.shape[1] cdef double complex val cdef double complex *sums cdef idxint *nxt cdef double tol = 0 if settings.core['auto_tidyup']: tol = settings.core['auto_tidyup_atol'] sums = PyMem_Calloc(ncols, sizeof(double complex)) nxt = mem.PyMem_Malloc(ncols * sizeof(idxint)) with nogil: for col_r in range(ncols): nxt[col_r] = -1 # Perform operation. out.row_index[0] = 0 for row_l in range(nrows): head = -2 length = 0 for ptr_l in range(left.row_index[row_l], left.row_index[row_l+1]): row_r = left.col_index[ptr_l] val = left.data[ptr_l] for ptr_r in range(right.row_index[row_r], right.row_index[row_r+1]): col_r = right.col_index[ptr_r] sums[col_r] += val * right.data[ptr_r] if nxt[col_r] == -1: nxt[col_r] = head head = col_r length += 1 for col_r in range(length): if fabs(sums[head].real) < tol: sums[head].real = 0 if fabs(sums[head].imag) < tol: sums[head].imag = 0 if sums[head] != 0: out.col_index[nnz] = head out.data[nnz] = scale * sums[head] nnz += 1 tmp = head head = nxt[head] nxt[tmp] = -1 sums[tmp] = 0 out.row_index[row_l + 1] = nnz mem.PyMem_Free(sums) mem.PyMem_Free(nxt) return out cpdef Dense matmul_csr_dense_dense(CSR left, Dense right, double complex scale=1, Dense out=None): """ Perform the operation ``out := scale * (left @ right) + out`` where `left`, `right` and `out` are matrices. `scale` is a complex scalar, defaulting to 1. If `out` is not given, it will be allocated as if it were a zero matrix. """ _check_shape(left, right, out) cdef Dense tmp = None if out is None: out = dense.zeros(left.shape[0], right.shape[1], right.fortran) if bool(right.fortran) != bool(out.fortran): msg = ( "out matrix is {}-ordered".format('Fortran' if out.fortran else 'C') + " but input is {}-ordered".format('Fortran' if right.fortran else 'C') ) warnings.warn(msg, OrderEfficiencyWarning) # Rather than making loads of copies of the same code, we just moan at # the user and then transpose one of the arrays. We prefer to have # `right` in Fortran-order for cache efficiency. if right.fortran: tmp = out out = out.reorder() else: right = right.reorder() cdef idxint row, ptr, idx_r, idx_out, nrows=left.shape[0], ncols=right.shape[1] cdef double complex val if right.fortran: idx_r = idx_out = 0 for _ in range(ncols): _matmul_csr_vector(left.data, left.col_index, left.row_index, right.data + idx_r, scale, out.data + idx_out, nrows) idx_out += nrows idx_r += right.shape[0] else: for row in range(nrows): for ptr in range(left.row_index[row], left.row_index[row + 1]): val = scale * left.data[ptr] idx_out = row * ncols idx_r = left.col_index[ptr] * ncols for _ in range(ncols): out.data[idx_out] += val * right.data[idx_r] idx_out += 1 idx_r += 1 if tmp is None: return out memcpy(tmp.data, out.data, ncols * nrows * sizeof(double complex)) return tmp cpdef Dense matmul_dense(Dense left, Dense right, double complex scale=1, Dense out=None): """ Perform the operation ``out := scale * (left @ right) + out`` where `left`, `right` and `out` are matrices. `scale` is a complex scalar, defaulting to 1. If `out` is not given, it will be allocated as if it were a zero matrix. """ _check_shape(left, right, out) cdef double complex out_scale # If not supplied, it's more efficient from a memory allocation perspective # to do the calculation as `a*A.B + 0*C` with arbitrary C. if out is None: out = dense.empty(left.shape[0], right.shape[1], right.fortran) out_scale = 0 else: out_scale = 1 cdef double complex *a cdef double complex *b cdef char transa, transb cdef int m, n, k=left.shape[1], lda, ldb if right.shape[1] == 1: # Matrix Vector product a, b = left.data, right.data if left.fortran: lda = left.shape[0] transa = b'n' m = left.shape[0] n = left.shape[1] else: lda = left.shape[1] transa = b't' m = left.shape[1] n = left.shape[0] ldb = 1 blas.zgemv(&transa, &m , &n, &scale, a, &lda, b, &ldb, &out_scale, out.data, &ldb) return out # We use the BLAS routine zgemm for every single call and pretend that # we're always supplying it with Fortran-ordered matrices, but to achieve # what we want, we use the property of matrix multiplication that # A.B = (B'.A')' # where ' is the matrix transpose, and that interpreting a Fortran-ordered # matrix as a C-ordered one is equivalent to taking the transpose. If # `right` is supplied in C-order, then from Fortran's perspective we # actually have `B'`, so to retrieve `B` should we want to use it, we set # `transb = b't'`. What we set `transa` and `transb` to depends on if we # need to switch the input order, _not_ whether we actually need B'. # # In order to make the output correct, we ensure that we put A.B in if the # output is Fortran ordered, or B'.A' (note no final transpose) if not. # This is actually more flexible than `np.dot` which requires that the # output is C-ordered. if out.fortran: # Need to make A.B a, b = left.data, right.data m, n = left.shape[0], right.shape[1] lda = left.shape[0] if left.fortran else left.shape[1] transa = b'n' if left.fortran else b't' ldb = right.shape[0] if right.fortran else right.shape[1] transb = b'n' if right.fortran else b't' else: # Need to make B'.A' a, b = right.data, left.data m, n = right.shape[1], left.shape[0] lda = right.shape[0] if right.fortran else right.shape[1] transa = b't' if right.fortran else b'n' ldb = left.shape[0] if left.fortran else left.shape[1] transb = b't' if left.fortran else b'n' blas.zgemm(&transa, &transb, &m, &n, &k, &scale, a, &lda, b, &ldb, &out_scale, out.data, &m) return out cpdef Dia matmul_dia(Dia left, Dia right, double complex scale=1): _check_shape(left, right, None) # We could probably do faster than this... npoffsets = np.unique(np.add.outer(left.as_scipy().offsets, right.as_scipy().offsets)) npoffsets = npoffsets[np.logical_and(npoffsets > -left.shape[0], npoffsets < right.shape[1])] cdef idxint[:] offsets = npoffsets if len(npoffsets) == 0: return dia.zeros(left.shape[0], right.shape[1]) cdef idxint *ptr = &offsets[0] cdef size_t num_diag = offsets.shape[0], diag_out, diag_left, diag_right cdef idxint start_left, end_left, start_out, end_out, start, end, col, off_out npdata = np.zeros((num_diag, right.shape[1]), dtype=complex) cdef double complex[:, ::1] data = npdata with nogil: for diag_left in range(left.num_diag): for diag_right in range(right.num_diag): off_out = left.offsets[diag_left] + right.offsets[diag_right] if off_out <= -left.shape[0] or off_out >= right.shape[1]: continue diag_out = (lower_bound(ptr, ptr + num_diag, off_out) - ptr) start_left = max(0, left.offsets[diag_left]) + right.offsets[diag_right] start_right = max(0, right.offsets[diag_right]) start_out = max(0, off_out) end_left = min(left.shape[1], left.shape[0] + left.offsets[diag_left]) + right.offsets[diag_right] end_right = min(right.shape[1], right.shape[0] + right.offsets[diag_right]) end_out = min(right.shape[1], left.shape[0] + off_out) start = max(start_left, start_right, start_out) end = min(end_left, end_right, end_out) for col in range(start, end): data[diag_out, col] += ( scale * left.data[diag_left * left.shape[1] + col - right.offsets[diag_right]] * right.data[diag_right * right.shape[1] + col] ) return Dia((npdata, npoffsets), shape=(left.shape[0], right.shape[1]), copy=False) cpdef Dense matmul_dia_dense_dense(Dia left, Dense right, double complex scale=1, Dense out=None): _check_shape(left, right, out) cdef Dense tmp if out is not None and scale == 1.: tmp = out out = None else: tmp = dense.zeros(left.shape[0], right.shape[1], right.fortran) cdef idxint start_left, end_left, start_out, end_out, length, i, start_right cdef idxint col, strideR_in, strideC_in, strideR_out, strideC_out cdef size_t diag with nogil: strideR_in = right.shape[1] if not right.fortran else 1 strideC_in = right.shape[0] if right.fortran else 1 strideR_out = tmp.shape[1] if not tmp.fortran else 1 strideC_out = tmp.shape[0] if tmp.fortran else 1 if ( (left.shape[0] == left.shape[1]) and (strideC_in == 1) and (strideC_out == 1) ): #Fast track for easy case for diag in range(left.num_diag): _matmul_diag_block( right.data + max(0, left.offsets[diag]) * strideR_in, left.data + diag * left.shape[1] + max(0, left.offsets[diag]), tmp.data + max(0, -left.offsets[diag]) * strideR_out, left.shape[1] - abs(left.offsets[diag]), right.shape[1] ) elif (strideR_in == 1) and (strideR_out == 1): for col in range(right.shape[1]): for diag in range(left.num_diag): start_left = max(0, left.offsets[diag]) end_left = min(left.shape[1], left.shape[0] + left.offsets[diag]) start_out = max(0, -left.offsets[diag]) end_out = min(left.shape[0], left.shape[1] - left.offsets[diag]) length = min(end_left - start_left, end_out - start_out) start_right = start_left + col * strideC_in start_left += diag * left.shape[1] start_out += col * strideC_out _matmul_diag_vector( left.data + start_left, right.data + start_right, tmp.data + start_out, length, 1. ) else: for col in range(right.shape[1]): for diag in range(left.num_diag): start_left = max(0, left.offsets[diag]) end_left = min(left.shape[1], left.shape[0] + left.offsets[diag]) start_out = max(0, -left.offsets[diag]) end_out = min(left.shape[0], left.shape[1] - left.offsets[diag]) length = min(end_left - start_left, end_out - start_out) for i in range(length): tmp.data[(start_out + i) * strideR_out + col * strideC_out] += ( left.data[diag * left.shape[1] + i + start_left] * right.data[(start_left + i) * strideR_in + col * strideC_in] ) if out is None and scale == 1.: out = tmp elif out is None: imul_dense(tmp, scale) out = tmp else: iadd_dense(out, tmp, scale) return out cpdef Dense matmul_dense_dia_dense(Dense left, Dia right, double complex scale=1, Dense out=None): _check_shape(left, right, out) cdef Dense tmp if out is not None and scale == 1.: tmp = out out = None else: tmp = dense.zeros(left.shape[0], right.shape[1], left.fortran) cdef idxint start_left, end_right, start_out, end_out, length, i, start_right cdef idxint row, strideR_in, strideC_in, strideR_out, strideC_out cdef size_t diag with nogil: strideR_in = left.shape[1] if not left.fortran else 1 strideC_in = left.shape[0] if left.fortran else 1 strideR_out = tmp.shape[1] if not tmp.fortran else 1 strideC_out = tmp.shape[0] if tmp.fortran else 1 if ( (right.shape[0] == right.shape[1]) and (strideR_in == 1) and (strideR_out == 1) ): #Fast track for easy case for diag in range(right.num_diag): _matmul_diag_block( left.data + max(0, -right.offsets[diag]) * strideC_in, right.data + diag * right.shape[1] + max(0, right.offsets[diag]), tmp.data + max(0, right.offsets[diag]) * strideC_out, right.shape[1] - abs(right.offsets[diag]), left.shape[0] ) elif (strideC_in == 1) and (strideC_out == 1): for row in range(left.shape[0]): for diag in range(right.num_diag): start_right = max(0, right.offsets[diag]) end_right = min(right.shape[1], right.shape[0] + right.offsets[diag]) start_out = max(0, right.offsets[diag]) length = end_right - start_right start_left = max(0, -right.offsets[diag]) + row * strideR_in start_right += diag * right.shape[1] start_out = max(0, right.offsets[diag]) + row * strideR_out _matmul_diag_vector( right.data + start_right, left.data + start_left, tmp.data + start_out, length, 1. ) else: for row in range(left.shape[0]): for diag in range(right.num_diag): start_right = max(0, right.offsets[diag]) end_right = min(right.shape[1], right.shape[0] + right.offsets[diag]) start_left = max(0, -right.offsets[diag]) length = end_right - start_right for i in range(length): tmp.data[(start_right + i) * strideC_out + row * strideR_out] += ( right.data[diag * right.shape[1] + i + start_right] * left.data[(start_left + i) * strideC_in + row * strideR_in] ) if out is None and scale == 1.: out = tmp elif out is None: imul_dense(tmp, scale) out = tmp else: iadd_dense(out, tmp, scale) return out cpdef CSR multiply_csr(CSR left, CSR right): """Element-wise multiplication of CSR matrices.""" if left.shape[0] != right.shape[0] or left.shape[1] != right.shape[1]: raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) left = left.sort_indices() right = right.sort_indices() cdef idxint col_left, left_nnz = csr.nnz(left) cdef idxint col_right, right_nnz = csr.nnz(right) cdef idxint ptr_left, ptr_right, ptr_left_max, ptr_right_max cdef idxint row, nnz=0, ncols=left.shape[1] cdef CSR out cdef list nans=[] # Fast paths for zero matrices. if right_nnz == 0 or left_nnz == 0: return csr.zeros(left.shape[0], left.shape[1]) # Main path. out = csr.empty(left.shape[0], left.shape[1], max(left_nnz, right_nnz)) out.row_index[0] = nnz ptr_left_max = ptr_right_max = 0 for row in range(left.shape[0]): ptr_left = ptr_left_max ptr_left_max = left.row_index[row + 1] ptr_right = ptr_right_max ptr_right_max = right.row_index[row + 1] while ptr_left < ptr_left_max or ptr_right < ptr_right_max: col_left = left.col_index[ptr_left] if ptr_left < ptr_left_max else ncols + 1 col_right = right.col_index[ptr_right] if ptr_right < ptr_right_max else ncols + 1 if col_left == col_right: out.col_index[nnz] = col_left out.data[nnz] = left.data[ptr_left] * right.data[ptr_right] ptr_left += 1 ptr_right += 1 nnz += 1 elif col_left <= col_right: if left.data[ptr_left] is np.nan: # Test for NaN since `NaN * 0 = NaN` nans.append((row, col_left)) ptr_left += 1 else: if right.data[ptr_right] != right.data[ptr_right]: nans.append((row, col_right)) ptr_right += 1 out.row_index[row + 1] = nnz if nans: # We expect Nan to be rare enough that we don't allocate memory for # them, but add them here after the loop. nans_pos = np.array(nans, order='F', dtype=idxint_dtype) nnz = nans_pos.shape[0] nans_csr = csr.from_coo_pointers( cnp.PyArray_GETPTR2(nans_pos, 0, 0), cnp.PyArray_GETPTR2(nans_pos, 0, 1), cnp.PyArray_GETPTR1( np.array([np.nan]*nnz, dtype=np.complex128), 0), left.shape[0], left.shape[1], nnz ) out = add_csr(out, nans_csr) return out cpdef Dia multiply_dia(Dia left, Dia right): if left.shape[0] != right.shape[0] or left.shape[1] != right.shape[1]: raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) cdef idxint diag_left=0, diag_right=0, out_diag=0, col cdef bint sorted=True cdef Dia out = dia.empty(left.shape[0], left.shape[1], min(left.num_diag, right.num_diag)) with nogil: for diag_left in range(1, left.num_diag): if left.offsets[diag_left-1] > left.offsets[diag_left]: sorted = False continue if sorted: for diag_right in range(1, right.num_diag): if right.offsets[diag_right-1] > right.offsets[diag_right]: sorted = False continue if sorted: diag_left = 0 diag_right = 0 while diag_left < left.num_diag and diag_right < right.num_diag: if left.offsets[diag_left] == right.offsets[diag_right]: out.offsets[out_diag] = left.offsets[diag_left] for col in range(out.shape[1]): if col >= left.shape[1] or col >= right.shape[1]: out.data[out_diag * out.shape[1] + col] = 0 else: out.data[out_diag * out.shape[1] + col] = ( left.data[diag_left * left.shape[1] + col] * right.data[diag_right * right.shape[1] + col] ) out_diag += 1 diag_left += 1 diag_right += 1 elif left.offsets[diag_left] < right.offsets[diag_right]: diag_left += 1 else: diag_right += 1 else: for diag_left in range(left.num_diag): for diag_right in range(right.num_diag): if left.offsets[diag_left] == right.offsets[diag_right]: out.offsets[out_diag] = left.offsets[diag_left] for col in range(right.shape[1]): out.data[out_diag * out.shape[1] + col] = ( left.data[diag_left * left.shape[1] + col] * right.data[diag_right * right.shape[1] + col] ) out_diag += 1 break out.num_diag = out_diag if settings.core['auto_tidyup']: tidyup_dia(out, settings.core['auto_tidyup_atol'], True) return out cpdef Dense multiply_dense(Dense left, Dense right): """Element-wise multiplication of Dense matrices.""" if left.shape[0] != right.shape[0] or left.shape[1] != right.shape[1]: raise ValueError( "incompatible matrix shapes " + str(left.shape) + " and " + str(right.shape) ) return Dense(left.as_ndarray() * right.as_ndarray(), copy=False) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect # At the time of putting in the dispatchers, the idea of an "out" parameter # isn't really supported in the model; since `out` would be potentially # modified in-place, it couldn't safely go through a conversion process. For # the dispatched operation, then, we omit the `scale` and `out` parameters, and # only dispatch on the operation `a @ b`. If the `out` and `scale` parameters # are needed, the library will have to manually do any relevant conversions, # and then call a direct specialisation (which are exported to the `data` # namespace). matmul = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('scale', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=1), ]), name='matmul', module=__name__, inputs=('left', 'right'), out=True, ) matmul.__doc__ =\ """ Compute the matrix multiplication of two matrices, with the operation scale * (left @ right) where `scale` is (optionally) a scalar, and `left` and `right` are matrices. Parameters ---------- left : Data The left operand as either a bra or a ket matrix. right : Data The right operand as a ket matrix. scale : complex, optional The scalar to multiply the output by. """ matmul.add_specialisations([ (CSR, CSR, CSR, matmul_csr), (CSR, Dense, Dense, matmul_csr_dense_dense), (Dense, Dense, Dense, matmul_dense), (Dia, Dia, Dia, matmul_dia), (Dia, Dense, Dense, matmul_dia_dense_dense), (Dense, Dia, Dense, matmul_dense_dia_dense), ], _defer=True) multiply = _Dispatcher( _inspect.Signature([ _inspect.Parameter('left', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('right', _inspect.Parameter.POSITIONAL_ONLY), ]), name='multiply', module=__name__, inputs=('left', 'right'), out=True, ) multiply.__doc__ =\ """Element-wise multiplication of matrices.""" multiply.add_specialisations([ (CSR, CSR, CSR, multiply_csr), (Dense, Dense, Dense, multiply_dense), (Dia, Dia, Dia, multiply_dia), ], _defer=True) del _inspect, _Dispatcher cdef Dense matmul_data_dense(Data left, Dense right): cdef Dense out if type(left) is CSR: out = matmul_csr_dense_dense(left, right) elif type(left) is Dense: out = matmul_dense(left, right) elif type(left) is Dia: out = matmul_dia_dense_dense(left, right) else: out = matmul(left, right) return out cdef void imatmul_data_dense(Data left, Dense right, double complex scale, Dense out): if type(left) is CSR: matmul_csr_dense_dense(left, right, scale, out) elif type(left) is Dia: matmul_dia_dense_dense(left, right, scale, out) elif type(left) is Dense: matmul_dense(left, right, scale, out) else: iadd_dense(out, matmul(left, right, dtype=Dense), scale) qutip-5.1.1/qutip/core/data/mul.pxd000066400000000000000000000010611474175217300172060ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data cimport CSR, Dense, Data, Dia cpdef CSR imul_csr(CSR matrix, double complex value) cpdef CSR mul_csr(CSR matrix, double complex value) cpdef CSR neg_csr(CSR matrix) cpdef Dense imul_dense(Dense matrix, double complex value) cpdef Dense mul_dense(Dense matrix, double complex value) cpdef Dense neg_dense(Dense matrix) cpdef Dia imul_dia(Dia matrix, double complex value) cpdef Dia mul_dia(Dia matrix, double complex value) cpdef Dia neg_dia(Dia matrix) cpdef Data imul_data(Data matrix, double complex value) qutip-5.1.1/qutip/core/data/mul.pyx000066400000000000000000000121761474175217300172440ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wrapround=False, initializedcheck=False from qutip.core.data cimport idxint, csr, CSR, dense, Dense, Data, Dia, dia from scipy.linalg.cython_blas cimport zscal __all__ = [ 'mul', 'mul_csr', 'mul_dense', 'mul_dia', 'imul', 'imul_csr', 'imul_dense', 'imul_dia', 'imul_data', 'neg', 'neg_csr', 'neg_dense', 'neg_dia', ] cpdef CSR imul_csr(CSR matrix, double complex value): """Multiply this CSR `matrix` by a complex scalar `value`.""" cdef idxint l = csr.nnz(matrix) cdef int ONE=1 zscal(&l, &value, matrix.data, &ONE) return matrix cpdef CSR mul_csr(CSR matrix, double complex value): """Multiply this CSR `matrix` by a complex scalar `value`.""" if value == 0: return csr.zeros(matrix.shape[0], matrix.shape[1]) cdef CSR out = csr.copy_structure(matrix) cdef idxint ptr with nogil: for ptr in range(csr.nnz(matrix)): out.data[ptr] = value * matrix.data[ptr] return out cpdef CSR neg_csr(CSR matrix): """Unary negation of this CSR `matrix`. Return a new object.""" cdef CSR out = csr.copy_structure(matrix) cdef idxint ptr with nogil: for ptr in range(csr.nnz(matrix)): out.data[ptr] = -matrix.data[ptr] return out cpdef Dia imul_dia(Dia matrix, double complex value): """Multiply this Dia `matrix` by a complex scalar `value`.""" cdef idxint l = matrix.num_diag * matrix.shape[1] cdef int ONE=1 zscal(&l, &value, matrix.data, &ONE) return matrix cpdef Dia mul_dia(Dia matrix, double complex value): """Multiply this Dia `matrix` by a complex scalar `value`.""" if value == 0: return dia.zeros(matrix.shape[0], matrix.shape[1]) cdef Dia out = dia.empty_like(matrix) cdef idxint ptr, diag, l = matrix.num_diag * matrix.shape[1] with nogil: for ptr in range(l): out.data[ptr] = value * matrix.data[ptr] for ptr in range(matrix.num_diag): out.offsets[ptr] = matrix.offsets[ptr] out.num_diag = matrix.num_diag return out cpdef Dia neg_dia(Dia matrix): """Unary negation of this Dia `matrix`. Return a new object.""" cdef Dia out = matrix.copy() cdef idxint ptr, l = matrix.num_diag * matrix.shape[1] with nogil: for ptr in range(l): out.data[ptr] = -matrix.data[ptr] return out cpdef Dense imul_dense(Dense matrix, double complex value): """Multiply this Dense `matrix` by a complex scalar `value`.""" cdef size_t ptr cdef int ONE=1 cdef idxint l = matrix.shape[0]*matrix.shape[1] zscal(&l, &value, matrix.data, &ONE) return matrix cpdef Dense mul_dense(Dense matrix, double complex value): """Multiply this Dense `matrix` by a complex scalar `value`.""" cdef Dense out = dense.empty_like(matrix) cdef size_t ptr with nogil: for ptr in range(matrix.shape[0]*matrix.shape[1]): out.data[ptr] = value * matrix.data[ptr] return out cpdef Dense neg_dense(Dense matrix): """Unary negation of this Dense `matrix`. Return a new object.""" cdef Dense out = dense.empty_like(matrix) cdef size_t ptr with nogil: for ptr in range(matrix.shape[0]*matrix.shape[1]): out.data[ptr] = -matrix.data[ptr] return out from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect mul = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('value', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='mul', module=__name__, inputs=('matrix',), out=True, ) mul.__doc__ =\ """Multiply a matrix element-wise by a scalar.""" mul.add_specialisations([ (CSR, CSR, mul_csr), (Dia, Dia, mul_dia), (Dense, Dense, mul_dense), ], _defer=True) imul = _Dispatcher( # Will not be inplce if specialisation does not exist but should still # give expected results if used as: # mat = imul(mat, x) _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('value', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='imul', module=__name__, inputs=('matrix',), out=True, ) imul.__doc__ =\ """Multiply inplace a matrix element-wise by a scalar.""" imul.add_specialisations([ (CSR, CSR, imul_csr), (Dia, Dia, imul_dia), (Dense, Dense, imul_dense), ], _defer=True) neg = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='neg', module=__name__, inputs=('matrix',), out=True, ) neg.__doc__ =\ """Unary element-wise negation of a matrix.""" neg.add_specialisations([ (CSR, CSR, neg_csr), (Dia, Dia, neg_dia), (Dense, Dense, neg_dense), ], _defer=True) del _inspect, _Dispatcher cpdef Data imul_data(Data matrix, double complex value): if type(matrix) is CSR: return imul_csr(matrix, value) elif type(matrix) is Dense: return imul_dense(matrix, value) elif type(matrix) is Dia: return imul_dia(matrix, value) else: return imul(matrix, value) qutip-5.1.1/qutip/core/data/norm.pxd000066400000000000000000000015021474175217300173640ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from qutip.core.data cimport CSR, Dense, Data, Dia cpdef double one_csr(CSR matrix) except -1 cpdef double trace_csr(CSR matrix) except -1 cpdef double max_csr(CSR matrix) nogil cpdef double frobenius_csr(CSR matrix) nogil cpdef double l2_csr(CSR matrix) except -1 nogil cpdef double frobenius_dense(Dense matrix) nogil cpdef double l2_dense(Dense matrix) except -1 nogil cpdef double one_dia(Dia matrix) except -1 cpdef double max_dia(Dia matrix) nogil cpdef double frobenius_dia(Dia matrix) nogil cpdef double l2_dia(Dia matrix) except -1 nogil cpdef double frobenius_data(Data state) except -1 cdef inline int int_max(int a, int b) nogil: # Name collision between the ``max`` builtin and norm.max return b if b > a else a qutip-5.1.1/qutip/core/data/norm.pyx000066400000000000000000000221261474175217300174160ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc cimport math from cpython cimport mem from scipy.linalg cimport cython_blas as blas import scipy import numpy as np from qutip.core.data cimport CSR, Dense, csr, Data, Dia from qutip.core.data.adjoint cimport adjoint_csr, adjoint_dense from qutip.core.data.matmul cimport matmul_csr from qutip.core.data import eigs_csr, eigs_dense cdef extern from *: # Not included in Cython for some reason? void *PyMem_Calloc(size_t n, size_t elsize) cdef extern from "" namespace "std" nogil: # abs is templated such that Cython treats std::abs as complex->complex double abs(double complex x) cdef double abssq(double complex x) nogil: return x.real*x.real + x.imag*x.imag # We always use BLAS routines where possible because architecture-specific # libraries will typically apply vectorised operations for us. # This module is meant to be accessed by dot-access (e.g. norm.one_csr). __all__ = [] cpdef double one_csr(CSR matrix) except -1: cdef int n=matrix.shape[1], inc=1 cdef size_t ptr cdef double *col = PyMem_Calloc(matrix.shape[1], sizeof(double)) try: for ptr in range(csr.nnz(matrix)): col[matrix.col_index[ptr]] += abs(matrix.data[ptr]) # BLAS is a Fortran library, so it's one-indexed of course... return col[blas.idamax(&n, col, &inc) - 1] finally: mem.PyMem_Free(col) cpdef double trace_dense(Dense matrix) except -1: """Compute the trace norm relaying scipy for dense operations.""" return scipy.linalg.norm(matrix.as_ndarray(), 'nuc') cpdef double trace_csr(CSR matrix, tol=0, maxiter=None) except -1: """Compute the trace norm using only sparse operations. These consist of determining the eigenvalues of `matrix @ matrix.adjoint()` and summing their square roots.""" # For column and row vectors we simply use the l2 norm as it is equivalent # to the trace norm. if matrix.shape[0]==1 or matrix.shape[1]==1: return l2_csr(matrix) cdef CSR op = matmul_csr(matrix, adjoint_csr(matrix)) cdef size_t i cdef double [::1] eigs eigs = eigs_csr(op, isherm=True, vecs=False, tol=tol, maxiter=maxiter) cdef double total = 0 for i in range(matrix.shape[0]): # The abs is technically not part of the definition, but since all # eigenvalues _should_ be > 0 (as X @ X.adjoint() is Hermitian), any # which are lower will just be ~1e-15 due to numerical approximations. total += math.sqrt(abs(eigs[i])) return total cpdef double max_csr(CSR matrix) nogil: cdef size_t ptr cdef double total=0, cur for ptr in range(csr.nnz(matrix)): # The positive square root is monotonic over positive reals, so we can # find the maximum value by considering the abs squared (which doesn't # require a sqrt) rather than the abs(which does), and then perform # only a single sqrt at the end. cur = abssq(matrix.data[ptr]) total = cur if cur > total else total return math.sqrt(total) cpdef double frobenius_csr(CSR matrix) nogil: # The Frobenius norm is effectively the same as the L2 norm when # considering the non-zero elements as a vector. cdef int n=csr.nnz(matrix), inc=1 return blas.dznrm2(&n, &matrix.data[0], &inc) cpdef double l2_csr(CSR matrix) except -1 nogil: if matrix.shape[0] != 1 and matrix.shape[1] != 1: raise ValueError("L2 norm is only defined on vectors") return frobenius_csr(matrix) cpdef double one_dense(Dense matrix) nogil: cdef size_t ptr, col, row, col_stride, row_stride cdef double out=0, cur col_stride = matrix.shape[0] if matrix.fortran else 1 row_stride = 1 if matrix.fortran else matrix.shape[1] for col in range(matrix.shape[1]): ptr = col * col_stride cur = 0 for row in range(matrix.shape[0]): cur += abs(matrix.data[ptr]) ptr += row_stride out = cur if cur > out else out return out cpdef double max_dense(Dense matrix) nogil: cdef size_t ptr cdef double total=0, cur for ptr in range(matrix.shape[0] * matrix.shape[1]): # The positive square root is monotonic over positive reals, so we can # find the maximum value by considering the abs squared (which doesn't # require a sqrt) rather than the abs(which does), and then perform # only a single sqrt at the end. cur = abssq(matrix.data[ptr]) total = cur if cur > total else total return math.sqrt(total) cpdef double frobenius_dense(Dense matrix) nogil: cdef int n = matrix.shape[0] * matrix.shape[1] cdef int inc = 1 return blas.dznrm2(&n, matrix.data, &inc) cpdef double l2_dense(Dense matrix) except -1 nogil: if matrix.shape[0] != 1 and matrix.shape[1] != 1: raise ValueError("L2 norm is only defined on vectors") return frobenius_dense(matrix) cpdef double frobenius_dia(Dia matrix) nogil: cdef int offset, diag, start, end, col=1 cdef double total=0, cur for diag in range(matrix.num_diag): offset = matrix.offsets[diag] start = int_max(0, offset) end = min(matrix.shape[1], matrix.shape[0] + offset) for col in range(start, end): total += abssq(matrix.data[diag * matrix.shape[1] + col]) return math.sqrt(total) cpdef double l2_dia(Dia matrix) except -1 nogil: if matrix.shape[0] != 1 and matrix.shape[1] != 1: raise ValueError("L2 norm is only defined on vectors") return frobenius_dia(matrix) cpdef double max_dia(Dia matrix) nogil: cdef int offset, diag, start, end, col=1 cdef double total=0, cur for diag in range(matrix.num_diag): offset = matrix.offsets[diag] start = int_max(0, offset) end = min(matrix.shape[1], matrix.shape[0] + offset) for col in range(start, end): cur = abssq(matrix.data[diag * matrix.shape[1] + col]) total = cur if cur > total else total return math.sqrt(total) cpdef double one_dia(Dia matrix) except -1: cdef int offset, diag, start, end, col=1 cols_one = np.zeros(matrix.shape[1], dtype=float) for diag in range(matrix.num_diag): offset = matrix.offsets[diag] start = int_max(0, offset) end = min(matrix.shape[1], matrix.shape[0] + offset) for col in range(start, end): cols_one[col] += abs(matrix.data[diag * matrix.shape[1] + col]) return np.max(cols_one) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect l2 = _Dispatcher( _inspect.Signature([ _inspect.Parameter('vector', _inspect.Parameter.POSITIONAL_ONLY), ]), name='l2', module=__name__, inputs=('vector',), ) l2.__doc__ =\ """ Compute the L2 (Euclidean) norm of a bra or ket vector. This is equal to sqrt(|v[0]|**2 + |v[1]|**2 + ...) This is only defined for vectors, but see `norm.frobenius` for the similar norm defined on all matrices. """ l2.add_specialisations([ (Dense, l2_dense), (Dia, l2_dia), (CSR, l2_csr), ], _defer=True) _norm_signature = _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]) frobenius = _Dispatcher(_norm_signature, name='frobenius', module=__name__, inputs=('matrix',)) frobenius.__doc__ =\ """ Compute the Frobenius (Hilbert-Schmidt) norm of a matrix. This is defined as the sqrt(sum_i sum_j |matrix[i, j]|**2) and is similar to an extension of the vector L2 norm to all matrices. """ frobenius.add_specialisations([ (Dense, frobenius_dense), (Dia, frobenius_dia), (CSR, frobenius_csr), ], _defer=True) max = _Dispatcher(_norm_signature, name='max', module=__name__, inputs=('matrix',)) max.__doc__ =\ """ Compute the max norm of a matrix. This is the largest absolute value of an entry in the matrix, or mathematically max_{i,j} |matrix[i, j]| """ max.add_specialisations([ (Dense, max_dense), (Dia, max_dia), (CSR, max_csr), ], _defer=True) one = _Dispatcher(_norm_signature, name='one', module=__name__, inputs=('matrix',)) one.__doc__ =\ """ Compute the one-norm (L1--L1) norm of a matrix. This is the value of the largest L1 norm of a column in the matrix, where the L1 norm of a vector is the sum of the absolute values. """ one.add_specialisations([ (Dense, one_dense), (Dia, one_dia), (CSR, one_csr), ], _defer=True) trace = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), inputs=('matrix',), name='trace', module=__name__, out=False, ) trace.__doc__ =\ """ Compute the trace-norm of a matrix. This is the sum of the singular values of the matrix, or equivalently Tr(sqrt(A @ A.adjoint())) """ trace.add_specialisations([ (CSR, trace_csr), (Dense, trace_dense), ], _defer=True) cpdef double frobenius_data(Data state) except -1: if type(state) is Dense: return frobenius_dense(state) elif type(state) is CSR: return frobenius_csr(state) else: return frobenius(state) qutip-5.1.1/qutip/core/data/permute.pxd000066400000000000000000000004241474175217300200740ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from qutip.core.data.csr cimport CSR cpdef CSR indices_csr(CSR matrix, object row_perm=*, object col_perm=*) cpdef CSR dimensions_csr(CSR matrix, object dimensions, object order) qutip-5.1.1/qutip/core/data/permute.pyx000066400000000000000000000377521474175217300201370ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memset, memcpy from libcpp cimport bool from libcpp.algorithm cimport sort cimport cython from cpython cimport mem import numpy as np cimport numpy as cnp from qutip.core.data.base cimport idxint, idxint_DTYPE from qutip.core.data cimport csr, dense, CSR, Dense from qutip.core.data.base import idxint_dtype cnp.import_array() cdef extern from *: void *PyMem_Calloc(size_t n, size_t elsize) # This module is meant to be used with dot-access (e.g. `permute.dimensions`). __all__ = [] cdef class _Indexer: cdef size_t ndims, size cdef readonly cnp.ndarray new_dimensions cdef idxint[:] dimensions cdef idxint *cumprod def __init__(self, idxint[:] dimensions, idxint[:] order): cdef size_t i cdef idxint dim, ord cdef idxint prev self.ndims = dimensions.shape[0] self.dimensions = dimensions self.new_dimensions = cnp.PyArray_EMPTY(1, [self.ndims], idxint_DTYPE, False) cdef idxint[:] new_dimensions = self.new_dimensions if order.shape[0] != self.ndims: raise ValueError("invalid order: wrong number of elements") cdef bint *tmp = PyMem_Calloc(self.ndims, sizeof(bint)) try: for i in range(self.ndims): ord = order[i] if ord < 0 or ord >= self.ndims: raise ValueError("invalid order element: " + str(ord)) if tmp[ord]: raise ValueError("duplicate order element: " + str(ord)) tmp[ord] = True dim = self.dimensions[ord] if dim < 0: raise ValueError("found negative dimension: " + str(dim)) elif dim == 0: raise ValueError("found zero dimension") new_dimensions[i] = dim finally: mem.PyMem_Free(tmp) self.cumprod = mem.PyMem_Malloc(self.ndims * sizeof(idxint)) prev = self.cumprod[order[self.ndims - 1]] = 1 for i in range(self.ndims - 2, -1, -1): prev = self.cumprod[order[i]] = prev * new_dimensions[i + 1] self.size = self.cumprod[order[0]] * new_dimensions[0] @cython.cdivision(True) cdef cnp.ndarray all(self): cdef object out = cnp.PyArray_EMPTY(1, [self.size], idxint_DTYPE, False) cdef idxint *_out = cnp.PyArray_GETPTR1(out, 0) cdef idxint i for i in range(self.size): _out[i] = self.single(i) return out @cython.cdivision(True) cdef idxint single(self, idxint idx) nogil: cdef size_t i cdef idxint out=0, dim for i in range(self.ndims - 1, -1, -1): dim = self.dimensions[i] # Dimensions cannot be zero due to the check in __init__. out += self.cumprod[i] * (idx % dim) idx //= dim if idx == 0: break return out def __dealloc__(self): if self.cumprod != NULL: mem.PyMem_Free(self.cumprod) cdef bint _check_indices(size_t size, idxint[:] order) except True: """ Test whether the permutation `order` is a valid permutation of `size` number of elements. This is functionally equivalent to ``` if np.sort(order) != np.arange(size): raise ValueError return False ``` In other words, we test that each integer on [0, size) is present exactly once in `order`, and raise ValueError if that is not the case (returns True if an error is detected, and False if not to help pure Cython avoiding exceptions). """ if order.shape[0] != size: raise ValueError("invalid permutation: wrong number of elements") cdef size_t ptr cdef idxint value cdef bint *test = PyMem_Calloc(size, sizeof(bint)) if test == NULL: raise MemoryError try: for ptr in range(size): value = order[ptr] if not 0 <= value < size: raise ValueError("invalid entry in permutation: " + str(value)) if test[value]: raise ValueError("duplicate entry in permutation: " + str(value)) test[value] = True return False finally: mem.PyMem_Free(test) cdef CSR _indices_csr_rowonly(CSR matrix, idxint[:] rows): cdef size_t n_rows=matrix.shape[0] _check_indices(n_rows, rows) cdef CSR out = csr.empty_like(matrix) cdef size_t row, ptr_in, ptr_out, len out.row_index[0] = 0 for row in range(matrix.shape[0]): out.row_index[rows[row] + 1] =\ matrix.row_index[row + 1] - matrix.row_index[row] for row in range(matrix.shape[0]): out.row_index[row + 1] += out.row_index[row] for row in range(matrix.shape[0]): ptr_in = matrix.row_index[row] ptr_out = out.row_index[rows[row]] len = matrix.row_index[row + 1] - ptr_in memcpy(&out.col_index[ptr_out], &matrix.col_index[ptr_in], len * sizeof(idxint)) memcpy(&out.data[ptr_out], &matrix.data[ptr_in], len * sizeof(double complex)) return out cdef CSR _indices_csr_full(CSR matrix, idxint[:] rows, idxint[:] cols): _check_indices(matrix.shape[0], rows) _check_indices(matrix.shape[1], cols) cdef CSR out = csr.empty_like(matrix) cdef size_t row, ptr_in, ptr_out, len, n # First build up the row index structure by cumulative sum, so we know # where to place the data and column indices. We also use this opportunity # to find the maximum number of non-zero elements in a row. with nogil: len = 0 out.row_index[0] = 0 for row in range(matrix.shape[0]): n = matrix.row_index[row + 1] - matrix.row_index[row] out.row_index[rows[row] + 1] = n len = n if n > len else len for row in range(matrix.shape[0]): out.row_index[row + 1] += out.row_index[row] # Now we know that `len` is the most number of non-zero elements in a row, # so we can allocate space to sort only once. cdef idxint *new_cols = mem.PyMem_Malloc(len * sizeof(idxint)) cdef csr.Sorter sort = csr.Sorter(len) for row in range(matrix.shape[0]): ptr_in = matrix.row_index[row] ptr_out = out.row_index[rows[row]] len = matrix.row_index[row + 1] - ptr_in for n in range(len): new_cols[n] = cols[matrix.col_index[ptr_in + n]] sort.copy(&out.data[ptr_out], &out.col_index[ptr_out], &matrix.data[ptr_in], new_cols, len) mem.PyMem_Free(new_cols) return out cpdef CSR indices_csr(CSR matrix, object row_perm=None, object col_perm=None): if row_perm is None and col_perm is None: return matrix.copy() if col_perm is None: return _indices_csr_rowonly(matrix, np.asarray(row_perm, dtype=idxint_dtype)) cdef idxint *rows = NULL cdef idxint n if row_perm is None: rows = mem.PyMem_Malloc(matrix.shape[0] * sizeof(idxint)) for n in range(matrix.shape[0]): rows[n] = n try: return _indices_csr_full(matrix, rows, np.asarray(col_perm, dtype=idxint_dtype)) finally: mem.PyMem_Free(rows) return _indices_csr_full(matrix, np.asarray(row_perm, dtype=idxint_dtype), np.asarray(col_perm, dtype=idxint_dtype)) cpdef Dense indices_dense(Dense matrix, object row_perm=None, object col_perm=None): if row_perm is None and col_perm is None: return matrix.copy() array = matrix.as_ndarray() if row_perm is not None: array = array[np.argsort(row_perm), :] if col_perm is not None: array = array[:, np.argsort(col_perm)] return Dense(array) cdef CSR _dimensions_csr_columns(CSR matrix, _Indexer index): if matrix.shape[0] != 1: raise ValueError("expected bra-like matrix") cdef size_t nnz = csr.nnz(matrix) cdef CSR out = csr.empty_like(matrix) out.row_index[0] = 0 out.row_index[1] = nnz cdef size_t n cdef csr.Sorter sort = csr.Sorter(nnz) cdef idxint *new_cols = mem.PyMem_Malloc(nnz * sizeof(idxint)) try: for n in range(nnz): new_cols[n] = index.single(matrix.col_index[n]) sort.copy(&out.data[0], &out.col_index[0], &matrix.data[0], new_cols, nnz) return out finally: mem.PyMem_Free(new_cols) cdef CSR _dimensions_csr_sparse(CSR matrix, _Indexer index): cdef CSR out = csr.empty_like(matrix) cdef csr.Sorter sort cdef size_t row, n, len=0 cdef idxint ptr_in, ptr_out, col cdef idxint *idx_lookup = mem.PyMem_Malloc(matrix.shape[0] * sizeof(idxint)) try: memset(&out.row_index[0], 0, (matrix.shape[0] + 1) * sizeof(idxint)) with nogil: for row in range(matrix.shape[0]): n = matrix.row_index[row + 1] - matrix.row_index[row] if n: idx_lookup[row] = index.single(row) out.row_index[idx_lookup[row] + 1] = n len = n if n > len else len else: # Use a sentinel value so we can avoid looking up columns # that we already know about later. Not all values in # idx_lookup will even be filled---this is the speed up # this function achieves over `_indices_csr_all`. idx_lookup[row] = -1 for row in range(matrix.shape[0]): out.row_index[row + 1] += out.row_index[row] # Since this is very sparse, we expect almost all rows to have at most two # elements in them. It will be faster to copy them across, and perform the # sort in place rather than allocating temporary space and making an # additional copy. This will still work even if there are more in a row, # it just won't be quite as efficient in that case (which should be rare). sort = csr.Sorter(len) for row in range(matrix.shape[0]): ptr_in = matrix.row_index[row] len = matrix.row_index[row + 1] - ptr_in if len == 0: continue ptr_out = out.row_index[idx_lookup[row]] for n in range(len): col = matrix.col_index[ptr_in + n] if idx_lookup[col] == -1: idx_lookup[col] = index.single(col) out.col_index[ptr_out + n] = idx_lookup[col] memcpy(&out.data[ptr_out], &matrix.data[ptr_in], len*sizeof(double complex)) sort.inplace(out, ptr_out, len) return out finally: mem.PyMem_Free(idx_lookup) @cython.cdivision(True) cpdef CSR dimensions_csr(CSR matrix, object dimensions, object order): cdef _Indexer index = _Indexer(np.asarray(dimensions, dtype=idxint_dtype), np.asarray(order, dtype=idxint_dtype)) cdef idxint[:] permutation if matrix.shape[0] == 1 and matrix.shape[1] == 1 or csr.nnz(matrix) == 0: return matrix.copy() if matrix.shape[0] == 1: return _dimensions_csr_columns(matrix, index) if matrix.shape[1] == 1: return _indices_csr_rowonly(matrix, index.all()) if matrix.shape[0] != matrix.shape[1]: raise ValueError("dimensional permute requires square operators") cdef double row_density = ( csr.nnz(matrix)) / ( matrix.shape[0]) # The speed-up for _dimensions_csr_sparse is only achieved by having fewer # calls to `index.single()` than the matrix dimension. To be sure of this, # we actually require the density per row to be less than 1/2, because we # have to look up both the row _and_ column on output. This only # corresponds to exceptionally sparse matrices. We try to avoid these # calls because index.single has ~logarithmic complexity in the dimension # (so for qubit systems it's linear in the number of qubits), and # consequently `index.all()` is a hidden quadratic complexity. if row_density >= 0.5: permutation = index.all() return _indices_csr_full(matrix, permutation, permutation) return _dimensions_csr_sparse(matrix, index) @cython.cdivision(True) cpdef Dense dimensions_dense(Dense matrix, object dimensions, object order): cdef _Indexer index = _Indexer(np.asarray(dimensions, dtype=idxint_dtype), np.asarray(order, dtype=idxint_dtype)) cdef idxint[:] permutation = index.all() row_perm, col_perm = None, None if matrix.shape[0] != 1: row_perm = permutation if matrix.shape[1] != 1: col_perm = permutation return indices_dense(matrix, row_perm, col_perm) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect dimensions = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('dimensions', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('order', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='dimensions', module=__name__, inputs=('matrix',), out=True, ) dimensions.__doc__ =\ """ Reorder the tensor-product structure of a matrix, assuming that the underlying structure is defined by `dimensions`. For a separable system, this function produces a matrix which is equivalent to having performed `kron` in a different order on the separable parts. For example if `a`, `b` and `c` are matrices with sizes 2, 3 and 4 respectively, then kron(kron(c, a), b) == permute.dimensions(kron(kron(a, b), c), [2, 3, 4], [1, 2, 0]) In other words, the inputs to `kron` are reordered so that input `n` moves to position `order[n]`. Parameters ---------- matrix : Data Input matrix to reorder. This can either be a square matrix representing an operator, or a bra- or ket-like vector. dimensions : 1D array_like of integers The tensor-product structure of the space the matrix lives on. This will typically be one of the two elements of `Qobj.dims` (e.g. for a ket, it will be `Qobj.dims[0]`). order : 1D array_like of integers The new order of the tensor-product elements. This should be a 1D list with the integers from `0` to `N - 1` inclusive, if there are `N` elements in the tensor product. """ dimensions.add_specialisations([ (CSR, CSR, dimensions_csr), (Dense, Dense, dimensions_dense), ], _defer=True) indices = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('row_perm', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=None), _inspect.Parameter('col_perm', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=None), ]), name='indices', module=__name__, inputs=('matrix',), out=True, ) indices.__doc__ =\ """ Permute the rows and columns of a matrix according to a row and column permutation. This is a "dumb" operation with regards to the representation of quantum states; if you want to "reorder" the tensor-product structure of a system, you want `permute.dimensions` instead. Parameters ---------- matrix : Data The input matrix. row_perm, col_perm : 1D array_like of integer, optional The new order that the rows or columns should be shuffled into. If the input matrix is `N x M`, then `row_perm` would be an array containing all the integers from `0` to `N - 1` inclusive in some new order. Row `n` in the input will be at row `row_perm[n]` in the output, and similar for the column permutation. """ indices.add_specialisations([ (CSR, CSR, indices_csr), (Dense, Dense, indices_dense), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/pow.pxd000066400000000000000000000001651474175217300172220ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR cpdef CSR pow_csr(CSR matrix, unsigned long long n) qutip-5.1.1/qutip/core/data/pow.pyx000066400000000000000000000067451474175217300172610ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False cimport cython from qutip.core.data cimport csr, dense, dia from qutip.core.data.csr cimport CSR from qutip.core.data.dense cimport Dense from qutip.core.data.dia cimport Dia from qutip.core.data.matmul cimport matmul_csr, matmul_dia import numpy as np __all__ = [ 'pow', 'pow_csr', 'pow_dense', 'pow_dia', ] @cython.nonecheck(False) @cython.cdivision(True) cpdef CSR pow_csr(CSR matrix, unsigned long long n): if matrix.shape[0] != matrix.shape[1]: raise ValueError("matrix power only works with square matrices") if n == 0: return csr.identity(matrix.shape[0]) if n == 1: return matrix.copy() # We do the matrix power in terms of powers of two, so we can do it # ceil(lg(n)) + bits(n) - 1 matrix mulitplications, where `bits` is the # number of set bits in the input. # # We don't have to do matrix.copy() or pow.copy() here, because we've # guaranteed that we won't be returning without at least one matrix # multiplcation, which will allocate a new matrix. cdef CSR pow = matrix cdef CSR out = pow if n & 1 else None n >>= 1 while n: pow = matmul_csr(pow, pow) if n & 1: out = pow if out is None else matmul_csr(out, pow) n >>= 1 return out @cython.nonecheck(False) @cython.cdivision(True) cpdef Dia pow_dia(Dia matrix, unsigned long long n): if matrix.shape[0] != matrix.shape[1]: raise ValueError("matrix power only works with square matrices") if n == 0: return dia.identity(matrix.shape[0]) if n == 1: return matrix.copy() # We do the matrix power in terms of powers of two, so we can do it # ceil(lg(n)) + bits(n) - 1 matrix mulitplications, where `bits` is the # number of set bits in the input. # # We don't have to do matrix.copy() or pow.copy() here, because we've # guaranteed that we won't be returning without at least one matrix # multiplcation, which will allocate a new matrix. cdef Dia pow = matrix cdef Dia out = pow if n & 1 else None n >>= 1 while n: pow = matmul_dia(pow, pow) if n & 1: out = pow if out is None else matmul_dia(out, pow) n >>= 1 return out cpdef Dense pow_dense(Dense matrix, unsigned long long n): if matrix.shape[0] != matrix.shape[1]: raise ValueError("matrix power only works with square matrices") if n == 0: return dense.identity(matrix.shape[0]) if n == 1: return matrix.copy() return Dense(np.linalg.matrix_power(matrix.as_ndarray(), n)) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect pow = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('n', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='pow', module=__name__, inputs=('matrix',), out=True, ) pow.__doc__ =\ """ Compute the integer matrix power of the square input matrix. The power must be an integer >= 0. `A ** 0` is defined to be the identity matrix of the same shape. Parameters ---------- matrix : Data Input matrix to take the power of. n : non-negative integer The power to which to raise the matrix. """ pow.add_specialisations([ (CSR, CSR, pow_csr), (Dense, Dense, pow_dense), (Dia, Dia, pow_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/project.pxd000066400000000000000000000001421474175217300200560ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.csr cimport CSR cpdef CSR project_csr(CSR state) qutip-5.1.1/qutip/core/data/project.pyx000066400000000000000000000157501474175217300201160ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.string cimport memcpy, memset from qutip.core.data.base cimport idxint from qutip.core.data cimport csr, dense, Dense, dia, Dia from qutip.core.data.csr cimport CSR cdef extern from "" namespace "std" nogil: double complex conj(double complex x) __all__ = [ 'project', 'project_csr', 'project_dense', 'project_dia', ] cdef int _project_ket_csr(CSR ket, CSR out) except -1 nogil: """ Calculate the projection of the given ket, and place the output in out. """ cdef size_t row, ptr, offset=0 cdef idxint nnz_in = csr.nnz(ket) for row in range(ket.shape[0]): out.row_index[row] = ket.row_index[row] * nnz_in if ket.row_index[row + 1] != ket.row_index[row]: for ptr in range(nnz_in): out.col_index[offset + ptr*nnz_in] = row offset += 1 out.row_index[ket.shape[0]] = nnz_in * nnz_in offset = 0 for row in range(nnz_in): for ptr in range(nnz_in): out.data[offset + ptr] = ket.data[row] * conj(ket.data[ptr]) offset += nnz_in return 0 cdef int _project_bra_csr(CSR bra, CSR out) except -1 nogil: """ Calculate the projection of the given bra, and place the output in out. """ cdef size_t row_out=0, ptr_bra, ptr, ptr_out=0, cur=0 cdef double complex mul cdef idxint nnz_in = csr.nnz(bra) # The algorithm is much more simple conceptually if the indices are sorted, # and doesn't affect runtime much since sorting is worst-case # O(nnz log(nnz)) and the projection is O(nnz^2). Also, much better to # sort now than later while there are fewer entries. No need to sort when # projecting a ket because all the col_index values are 0. with gil: bra.sort_indices() out.row_index[0] = cur for ptr_bra in range(nnz_in): # Handle all zero rows between the last non-zero entry and this one. for row_out in range(row_out, bra.col_index[ptr_bra]): out.row_index[row_out + 1] = cur row_out = bra.col_index[ptr_bra] cur += nnz_in out.row_index[row_out + 1] = cur memcpy(&out.col_index[ptr_out], &bra.col_index[0], nnz_in * sizeof(idxint)) mul = conj(bra.data[ptr_bra]) for ptr in range(nnz_in): out.data[ptr_out] = mul * bra.data[ptr] ptr_out += 1 row_out += 1 # Handle all zero rows after the last non-zero entry. for row_out in range(row_out, out.shape[0]): out.row_index[row_out + 1] = cur return 0 cpdef CSR project_csr(CSR state): """ Calculate the projection |state>` or `= 0 else settings.core["atol"] cdef size_t row, col, ptr, ptr_t, nrows=matrix.shape[0] if matrix.shape[0] != matrix.shape[1]: return False cdef idxint *out_row_index = PyMem_Calloc(nrows + 1, sizeof(idxint)) if out_row_index == NULL: raise MemoryError matrix.sort_indices() try: for row in range(nrows): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] + 1 out_row_index[col] += 1 for row in range(nrows): out_row_index[row+1] += out_row_index[row] if out_row_index[row + 1] != matrix.row_index[row + 1]: # Structures are not the same, but it could still be Hermitian # if any value is less than the tolerance. That is the # worst-case scenario, so we sacrifice its speed in favour of # returning faster for the more common failure cases. for ptr in range(matrix.row_index[nrows]): if _conj_feq(matrix.data[ptr], 0, tol): return _isherm_csr_full(matrix, tol) return False for row in range(nrows): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): col = matrix.col_index[ptr] # Pointer into the "transposed" matrix. ptr_t = out_row_index[col] out_row_index[col] += 1 if row != matrix.col_index[ptr_t]: return _isherm_csr_full(matrix, tol) if not _conj_feq(matrix.data[ptr], matrix.data[ptr_t], tol): return False return True finally: mem.PyMem_Free(out_row_index) cpdef bint isherm_dia(Dia matrix, double tol=-1) nogil: cdef double complex val, valT cdef size_t diag, other_diag, col, start, end, other_start if tol < 0: with gil: tol = settings.core["atol"] if matrix.shape[0] != matrix.shape[1]: return False for diag in range(matrix.num_diag): if matrix.offsets[diag] == 0: for col in range(matrix.shape[1]): val = valT = matrix.data[diag * matrix.shape[1] + col] if not _conj_feq(val, valT, tol): return False continue other_diag = 0 while other_diag < matrix.num_diag: if matrix.offsets[diag] == -matrix.offsets[other_diag]: break other_diag += 1 if other_diag < diag: continue start = max(0, matrix.offsets[diag]) end = min(matrix.shape[1], matrix.shape[0] + matrix.offsets[diag]) if other_diag == matrix.num_diag: # No matching diag, should be 0 for col in range(start, end): val = matrix.data[diag * matrix.shape[1] + col] if not _feq_zero(val, tol): return False continue other_start = max(0, matrix.offsets[other_diag]) for col in range(end - start): val = matrix.data[diag * matrix.shape[1] + col + start] valT = matrix.data[other_diag * matrix.shape[1] + col + other_start] if not _conj_feq(val, valT, tol): return False return True cpdef bint isherm_dense(Dense matrix, double tol=-1): """ Determine whether an input Dense matrix is Hermitian up to a given floating-point tolerance. Parameters ---------- matrix : Dense Input matrix to test tol : double, optional Absolute tolerance value to use. Defaults to :obj:`settings.core['atol']`. Returns ------- bint Boolean True if it is Hermitian, False if not. """ if matrix.shape[0] != matrix.shape[1]: return False tol = tol if tol >= 0 else settings.core["atol"] cdef size_t row, col, size=matrix.shape[0] for row in range(size): for col in range(row + 1): if not _conj_feq( matrix.data[col*size+row], matrix.data[row*size+col], tol ): return False return True cpdef bint isdiag_dia(Dia matrix, double tol=-1) nogil: cdef size_t diag, start, end, col if tol < 0: with gil: tol = settings.core["atol"] cdef double tolsq = tol*tol for diag in range(matrix.num_diag): if matrix.offsets[diag] == 0: continue start = max(0, matrix.offsets[diag]) end = min(matrix.shape[1], matrix.shape[0] + matrix.offsets[diag]) for col in range(start, end): if _abssq(matrix.data[diag * matrix.shape[1] + col]) > tolsq: return False return True cpdef bint isdiag_csr(CSR matrix) nogil: cdef size_t row, ptr_start, ptr_end=matrix.row_index[0] for row in range(matrix.shape[0]): ptr_start, ptr_end = ptr_end, matrix.row_index[row + 1] if ptr_end - ptr_start > 1: return False if ptr_end - ptr_start == 1: if matrix.col_index[ptr_start] != row: return False return True cpdef bint isdiag_dense(Dense matrix) nogil: cdef size_t row, row_stride = 1 if matrix.fortran else matrix.shape[1] cdef size_t col, col_stride = matrix.shape[0] if matrix.fortran else 1 for row in range(matrix.shape[0]): for col in range(matrix.shape[1]): if (col != row) and matrix.data[col * col_stride + row * row_stride] != 0.: return False return True cpdef bint iszero_dia(Dia matrix, double tol=-1) nogil: cdef size_t diag, start, end, col if tol < 0: with gil: tol = settings.core["atol"] cdef double tolsq = tol*tol for diag in range(matrix.num_diag): start = max(0, matrix.offsets[diag]) end = min(matrix.shape[1], matrix.shape[0] + matrix.offsets[diag]) for col in range(start, end): if _abssq(matrix.data[diag * matrix.shape[1] + col]) > tolsq: return False return True cpdef bint iszero_csr(CSR matrix, double tol=-1) nogil: cdef size_t ptr if tol < 0: with gil: tol = settings.core["atol"] tolsq = tol*tol for ptr in range(csr.nnz(matrix)): if _abssq(matrix.data[ptr]) > tolsq: return False return True cpdef bint iszero_dense(Dense matrix, double tol=-1) nogil: cdef size_t ptr if tol < 0: with gil: tol = settings.core["atol"] tolsq = tol*tol for ptr in range(matrix.shape[0]*matrix.shape[1]): if _abssq(matrix.data[ptr]) > tolsq: return False return True cpdef bint isequal_dia(Dia A, Dia B, double atol=-1, double rtol=-1): if A.shape[0] != B.shape[0] or A.shape[1] != B.shape[1]: return False if atol < 0: atol = settings.core["atol"] if rtol < 0: rtol = settings.core["rtol"] cdef idxint diag_a=0, diag_b=0 cdef double complex *ptr_a cdef double complex *ptr_b cdef idxint size=A.shape[1] # TODO: # Works only for a sorted offsets list. # We don't have a check for whether it's already sorted, but it should be # in most cases. Could be improved by tracking whether it is or not. A = dia.clean_dia(A) B = dia.clean_dia(B) ptr_a = A.data ptr_b = B.data with nogil: while diag_a < A.num_diag and diag_b < B.num_diag: if A.offsets[diag_a] == B.offsets[diag_b]: for i in range(size): if not _feq(ptr_a[i], ptr_b[i], atol, rtol): return False ptr_a += size diag_a += 1 ptr_b += size diag_b += 1 elif A.offsets[diag_a] <= B.offsets[diag_b]: for i in range(size): if not _feq(ptr_a[i], 0., atol, rtol): return False ptr_a += size diag_a += 1 else: for i in range(size): if not _feq(0., ptr_b[i], atol, rtol): return False ptr_b += size diag_b += 1 return True cpdef bint isequal_dense(Dense A, Dense B, double atol=-1, double rtol=-1): if A.shape[0] != B.shape[0] or A.shape[1] != B.shape[1]: return False if atol < 0: atol = settings.core["atol"] if rtol < 0: rtol = settings.core["rtol"] return np.allclose(A.as_ndarray(), B.as_ndarray(), rtol, atol) cpdef bint isequal_csr(CSR A, CSR B, double atol=-1, double rtol=-1): if A.shape[0] != B.shape[0] or A.shape[1] != B.shape[1]: return False if atol < 0: atol = settings.core["atol"] if rtol < 0: rtol = settings.core["rtol"] cdef idxint row, ptr_a, ptr_b, ptr_a_max, ptr_b_max, col_a, col_b cdef idxint ncols = A.shape[1], prev_col_a, prev_col_b # TODO: # Works only for sorted indices. # We don't have a check for whether it's already sorted, but it should be # in most cases. A = A.sort_indices() B = B.sort_indices() with nogil: ptr_a_max = ptr_b_max = 0 for row in range(A.shape[0]): ptr_a = ptr_a_max ptr_a_max = A.row_index[row + 1] ptr_b = ptr_b_max ptr_b_max = B.row_index[row + 1] col_a = A.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 col_b = B.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 prev_col_a = -1 prev_col_b = -1 while ptr_a < ptr_a_max or ptr_b < ptr_b_max: if col_a == col_b: if not _feq(A.data[ptr_a], B.data[ptr_b], atol, rtol): return False ptr_a += 1 ptr_b += 1 col_a = A.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 col_b = B.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 elif col_a < col_b: if not _feq(A.data[ptr_a], 0., atol, rtol): return False ptr_a += 1 col_a = A.col_index[ptr_a] if ptr_a < ptr_a_max else ncols + 1 else: if not _feq(0., B.data[ptr_b], atol, rtol): return False ptr_b += 1 col_b = B.col_index[ptr_b] if ptr_b < ptr_b_max else ncols + 1 return True from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect isherm = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('tol', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=-1), ]), name='isherm', module=__name__, inputs=('matrix',), out=False, ) isherm.__doc__ =\ """ Check if the matrix is Hermitian up to a optional element-wise absolute tolerance. If the tolerance given is less than zero, the global settings value `qutip.settings.atol` will be used instead. Only square matrices can possibly be Hermitian. Parameters ---------- matrix : Data The matrix to test for Hermicity. tol : real, optional If given, the absolute tolerance used to compare two values for equality. If not given, or given and negative, the value of `qutip.settings.atol` is used instead. """ isherm.add_specialisations([ (Dense, isherm_dense), (Dia, isherm_dia), (CSR, isherm_csr), ], _defer=True) isdiag = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='isdiag', module=__name__, inputs=('matrix',), out=False, ) isdiag.__doc__ =\ """ Check if the matrix is diagonal. The matrix need not be square to test. Parameters ---------- matrix : Data The matrix to test for diagonality. """ isdiag.add_specialisations([ (Dense, isdiag_dense), (Dia, isdiag_dia), (CSR, isdiag_csr), ], _defer=True) iszero = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('tol', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=-1), ]), name='iszero', module=__name__, inputs=('matrix',), out=False, ) iszero.__doc__ =\ """ Test if this matrix is the zero matrix, up to a certain absolute tolerance. Parameters ---------- matrix : Data The matrix to test. tol : real, optional The absolute tolerance to use when comparing to zero. If not given, or less than 0, use the core setting `atol`. Returns ------- bool Whether the matrix is equivalent to 0 under the given absolute tolerance. """ iszero.add_specialisations([ (CSR, iszero_csr), (Dia, iszero_dia), (Dense, iszero_dense), ], _defer=True) isequal = _Dispatcher( _inspect.Signature([ _inspect.Parameter('A', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('B', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('atol', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=-1), _inspect.Parameter('rtol', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=-1), ]), name='isequal', module=__name__, inputs=('A', 'B',), out=False, ) isequal.__doc__ =\ """ Test if two matrices are equal up to absolute and relative tolerance: |A - B| <= atol + rtol * |b| Similar to ``numpy.allclose``. Parameters ---------- A, B : Data Matrices to compare. atol : real, optional The absolute tolerance to use. If not given, or less than 0, use the core setting `atol`. rtol : real, optional The relative tolerance to use. If not given, or less than 0, use the core setting `atol`. Returns ------- bool Whether the matrix are equal. """ isequal.add_specialisations([ (CSR, CSR, isequal_csr), (Dia, Dia, isequal_dia), (Dense, Dense, isequal_dense), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/ptrace.pxd000066400000000000000000000004001474175217300176630ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data cimport CSR, Dense cpdef CSR ptrace_csr(CSR matrix, object dims, object sel) cpdef Dense ptrace_dense(Dense matrix, object dims, object sel) cpdef Dense ptrace_csr_dense(CSR matrix, object dims, object sel) qutip-5.1.1/qutip/core/data/ptrace.pyx000066400000000000000000000217411474175217300177230ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False, cdivision=True import numbers import numpy as np cimport numpy as cnp cimport cython from qutip.core.data cimport csr, dense, idxint, CSR, Dense, Data, Dia, dia from qutip.core.data.base import idxint_dtype from qutip.settings import settings cnp.import_array() __all__ = [ 'ptrace', 'ptrace_csr', 'ptrace_dense', 'ptrace_csr_dense', 'ptrace_dia', ] cdef tuple _parse_inputs(object dims, object sel, tuple shape): cdef Py_ssize_t i dims = np.atleast_1d(dims).astype(idxint_dtype).ravel() sel = np.atleast_1d(sel).astype(idxint_dtype) sel.sort() if shape[0] != shape[1]: raise ValueError("ptrace is only defined for square density matrices") if shape[0] != np.prod(dims, dtype=int): raise ValueError(f"the input matrix shape, {shape} and the" f" dimension argument, {dims}, are not compatible.") if sel.ndim != 1: raise ValueError("Selection must be one-dimensional") if any(d < 1 for d in dims): raise ValueError("dimensions must be greated than zero but where" f" dims={dims}.") for i in range(sel.shape[0]): if sel[i] < 0 or sel[i] >= dims.size: raise IndexError("Invalid selection index in ptrace.") if i > 0 and sel[i] == sel[i - 1]: raise ValueError("Duplicate selection index in ptrace.") return dims, sel cdef idxint _populate_tensor_table(dims, sel, idxint[:, ::1] tensor_table) except -1: """ Populate the helper structure `tensor_table`. Returns the size (number of rows and number of columns) of the matrix which will be output. """ cdef size_t ii cdef idxint[::1] _dims = np.asarray(dims, dtype=idxint_dtype).ravel() cdef size_t num_dims = _dims.shape[0] cdef idxint factor_tensor=1, factor_keep=1, factor_trace=1 cdef idxint[::1] _sel = np.asarray(sel, dtype=idxint_dtype) for ii in range(_sel.shape[0]): if _sel[ii] < 0 or _sel[ii] >= num_dims: raise TypeError("Invalid selection index in ptrace.") for ii in range(num_dims - 1,-1,-1): tensor_table[ii, 0] = factor_tensor factor_tensor *= _dims[ii] if _in(ii, _sel): tensor_table[ii, 1] = factor_keep factor_keep *= _dims[ii] else: tensor_table[ii, 2] = factor_trace factor_trace *= _dims[ii] return factor_keep cdef bint _in(idxint val, idxint[::1] vec): cdef int ii for ii in range(vec.shape[0]): if val == vec[ii]: return True return False cdef inline void _i2_k_t(idxint N, idxint[:, ::1] tensor_table, idxint out[2]): # indices determining function for ptrace cdef size_t ii cdef idxint t1, t2 out[0] = out[1] = 0 for ii in range(tensor_table.shape[0]): t1 = tensor_table[ii, 0] t2 = N / t1 N = N % t1 out[0] += tensor_table[ii, 1] * t2 out[1] += tensor_table[ii, 2] * t2 cpdef CSR ptrace_csr(CSR matrix, object dims, object sel): dims, sel = _parse_inputs(dims, sel, matrix.shape) if len(sel) == len(dims): return matrix.copy() cdef idxint[:, ::1] tensor_table = np.zeros((dims.shape[0], 3), dtype=idxint_dtype) cdef idxint size size = _populate_tensor_table(dims, sel, tensor_table) cdef size_t p=0, nnz=csr.nnz(matrix), row, ptr cdef idxint pos_c[2] cdef idxint pos_r[2] cdef cnp.ndarray[double complex, ndim=1, mode='c'] new_data = np.zeros(nnz, dtype=complex) cdef cnp.ndarray[idxint, ndim=1, mode='c'] new_col = np.zeros(nnz, dtype=idxint_dtype) cdef cnp.ndarray[idxint, ndim=1, mode='c'] new_row = np.zeros(nnz, dtype=idxint_dtype) cdef double tol = 0 if settings.core['auto_tidyup']: tol = settings.core['auto_tidyup_atol'] for row in range(matrix.shape[0]): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): _i2_k_t(matrix.col_index[ptr], tensor_table, pos_c) _i2_k_t(row, tensor_table, pos_r) if pos_c[1] == pos_r[1]: new_data[p] = matrix.data[ptr] new_row[p] = pos_r[0] new_col[p] = pos_c[0] p += 1 return csr.from_coo_pointers(&new_row[0], &new_col[0], &new_data[0], size, size, p, tol) def ptrace_dia(matrix, dims, sel): if len(sel) == len(dims): return matrix.copy() dims, sel = _parse_inputs(dims, sel, matrix.shape) mat = matrix.as_scipy() cdef idxint[:, ::1] tensor_table = np.zeros((dims.shape[0], 3), dtype=idxint_dtype) cdef idxint pos_row[2] cdef idxint pos_col[2] size = _populate_tensor_table(dims, sel, tensor_table) data = {} for i, offset in enumerate(mat.offsets): start = max(0, offset) end = min(matrix.shape[0] + offset, matrix.shape[1]) for col in range(start, end): _i2_k_t(col - offset, tensor_table, pos_row) _i2_k_t(col, tensor_table, pos_col) if pos_row[1] == pos_col[1]: new_offset = pos_col[0] - pos_row[0] if new_offset not in data: data[new_offset] = np.zeros(size, dtype=complex) data[new_offset][pos_col[0]] += mat.data[i, col] if len(data) == 0: return dia.zeros(size, size) offsets = np.array(list(data.keys()), dtype=idxint_dtype) data = np.array(list(data.values()), dtype=complex) out = Dia((data, offsets), shape=(size, size), copy=False) out = dia.clean_dia(out, True) return out cpdef Dense ptrace_csr_dense(CSR matrix, object dims, object sel): dims, sel = _parse_inputs(dims, sel, matrix.shape) if len(sel) == len(dims): return dense.from_csr(matrix) cdef idxint[:, ::1] tensor_table = np.zeros((dims.shape[0], 3), dtype=idxint_dtype) cdef idxint size size = _populate_tensor_table(dims, sel, tensor_table) cdef size_t ii, jj cdef idxint pos_c[2] cdef idxint pos_r[2] cdef Dense out = dense.zeros(size, size, fortran=False) for ii in range(matrix.shape[0]): for jj in range(matrix.row_index[ii], matrix.row_index[ii+1]): _i2_k_t(matrix.col_index[jj], tensor_table, pos_c) _i2_k_t(ii, tensor_table, pos_r) if pos_c[1] == pos_r[1]: out.data[pos_r[0]*size + pos_c[0]] += matrix.data[jj] return out cpdef Dense ptrace_dense(Dense matrix, object dims, object sel): dims, sel = _parse_inputs(dims, sel, matrix.shape) if len(sel) == len(dims): return matrix.copy() nd = dims.shape[0] dkeep = [dims[x] for x in sel] qtrace = list(set(np.arange(nd)) - set(sel)) dtrace = [dims[x] for x in qtrace] dims = list(dims) sel = list(sel) rhomat = np.trace(matrix.as_ndarray() .reshape(dims + dims) .transpose(qtrace + [nd + q for q in qtrace] + sel + [nd + q for q in sel]) .reshape([np.prod(dtrace, dtype=int), np.prod(dtrace, dtype=int), np.prod(dkeep, dtype=int), np.prod(dkeep, dtype=int)])) return dense.fast_from_numpy(rhomat) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect ptrace = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('dims', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('sel', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='ptrace', module=__name__, inputs=('matrix',), out=True, ) ptrace.__doc__ =\ """ Compute the partial trace of this matrix, leaving the subspaces whose indices are in `sel`. This is only defined for square density matrices, and always returns a density matrix. The order of the indices in `sel` do not matter; the output matrix will always have the selected subspaces in the same order that they are in the input matrix. For example, if the input is the matrix backing a `Qobj` with `dims = [[2, 3, 4], [2, 3, 4]]`, then the output of ptrace(data, [2, 3, 4], [0, 2]) will be a matrix with effective dimensions `[[2, 4], [2, 4]]`. Parameters ---------- matrix : Data The density matrix to be partially traced. dims : array_like of integer The dimensions of the subspaces. This is most likely a 1D list, and since this is only defined on square matrices, there is no need to pass before the left and right sides. Typically the input matrix will be taken from a `Qobj`, and then this parameter will be `Qobj.dims[0]`. sel : integer or array_like of integer The indices of the subspaces which should be _kept_. """ ptrace.add_specialisations([ (CSR, CSR, ptrace_csr), (CSR, Dense, ptrace_csr_dense), (Dense, Dense, ptrace_dense), (Dia, Dia, ptrace_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/reshape.pxd000066400000000000000000000012251474175217300200420ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data.base cimport idxint from qutip.core.data cimport CSR, Dense, Dia cpdef CSR reshape_csr(CSR matrix, idxint n_rows_out, idxint n_cols_out) cpdef CSR column_stack_csr(CSR matrix) cpdef CSR column_unstack_csr(CSR matrix, idxint rows) cpdef Dia reshape_dia(Dia matrix, idxint n_rows_out, idxint n_cols_out) cpdef Dia column_stack_dia(Dia matrix) cpdef Dia column_unstack_dia(Dia matrix, idxint rows) cpdef Dense reshape_dense(Dense matrix, idxint n_rows_out, idxint n_cols_out) cpdef Dense column_stack_dense(Dense matrix, bint inplace=*) cpdef Dense column_unstack_dense(Dense matrix, idxint rows, bint inplace=*) qutip-5.1.1/qutip/core/data/reshape.pyx000066400000000000000000000244051474175217300200740ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False, cdivision=True from libc.string cimport memcpy, memset from scipy.linalg cimport cython_blas as blas cimport cython import warnings from qutip.core.data.base cimport idxint from qutip.core.data cimport csr, dense, CSR, Dense, Data, Dia __all__ = [ 'reshape', 'reshape_csr', 'reshape_dense', 'reshape_dia', 'column_stack', 'column_stack_csr', 'column_stack_dense', 'column_stack_dia', 'column_unstack', 'column_unstack_csr', 'column_unstack_dense', 'column_unstack_dia', 'split_columns', 'split_columns_dense', 'split_columns_csr', 'split_columns_dia', ] cdef void _reshape_check_input(Data matrix, idxint n_rows_out, idxint n_cols_out) except *: if n_rows_out * n_cols_out != matrix.shape[0] * matrix.shape[1]: message = "".join([ "cannot reshape ", str(matrix.shape), " to ", "(", str(n_rows_out), ", ", str(n_cols_out), ")", ]) raise ValueError(message) if n_rows_out <= 0 or n_cols_out <= 0: raise ValueError("must have > 0 rows and columns") cpdef CSR reshape_csr(CSR matrix, idxint n_rows_out, idxint n_cols_out): cdef size_t ptr, row_in, row_out=0, loc, cur=0 cdef size_t n_rows_in=matrix.shape[0], n_cols_in=matrix.shape[1] cdef idxint nnz = csr.nnz(matrix) cdef CSR out _reshape_check_input(matrix, n_rows_out, n_cols_out) out = csr.empty(n_rows_out, n_cols_out, nnz) matrix.sort_indices() with nogil: # Since the indices are now sorted, the data arrays will be identical. memcpy(out.data, matrix.data, nnz*sizeof(double complex)) memset(out.row_index, 0, (n_rows_out + 1) * sizeof(idxint)) for row_in in range(n_rows_in): for ptr in range(matrix.row_index[row_in], matrix.row_index[row_in+1]): loc = cur + matrix.col_index[ptr] out.row_index[loc // n_cols_out + 1] += 1 out.col_index[ptr] = loc % n_cols_out cur += n_cols_in for row_out in range(n_rows_out): out.row_index[row_out + 1] += out.row_index[row_out] return out cdef inline size_t _reshape_dense_reindex(size_t idx, size_t size): return (idx // size) + (idx % size) cpdef Dense reshape_dense(Dense matrix, idxint n_rows_out, idxint n_cols_out): _reshape_check_input(matrix, n_rows_out, n_cols_out) cdef Dense out if not matrix.fortran: out = matrix.copy() out.shape = (n_rows_out, n_cols_out) return out out = dense.zeros(n_rows_out, n_cols_out) cdef size_t idx_in=0, idx_out=0 cdef size_t size = n_rows_out * n_cols_out cdef size_t tmp = ( matrix.shape[1]) * ( n_rows_out) # TODO: improve the algorithm here. cdef size_t stride = _reshape_dense_reindex(tmp, size) for idx_in in range(size): out.data[idx_out] = matrix.data[idx_in] idx_out = _reshape_dense_reindex(idx_out + stride, size) return out cpdef Dia reshape_dia(Dia matrix, idxint n_rows_out, idxint n_cols_out): _reshape_check_input(matrix, n_rows_out, n_cols_out) # Once reshaped, diagonals are no longer ligned up. return Dia( matrix.as_scipy().reshape((n_rows_out, n_cols_out)).todia(), copy=False ) cpdef CSR column_stack_csr(CSR matrix): if matrix.shape[1] == 1: return matrix.copy() return reshape_csr(matrix.transpose(), matrix.shape[0]*matrix.shape[1], 1) cpdef Dense column_stack_dense(Dense matrix, bint inplace=False): cdef Dense out if inplace and matrix.fortran: matrix.shape = (matrix.shape[0] * matrix.shape[1], 1) return matrix if matrix.fortran: out = matrix.copy() out.shape = (matrix.shape[0]*matrix.shape[1], 1) return out if inplace: warnings.warn("cannot stack columns inplace for C-ordered matrix") out = dense.zeros(matrix.shape[0] * matrix.shape[1], 1) cdef idxint col cdef int ONE=1 for col in range(matrix.shape[1]): blas.zcopy( &matrix.shape[0], &matrix.data[col], &matrix.shape[1], &out.data[col * matrix.shape[0]], &ONE ) return out cpdef Dia column_stack_dia(Dia matrix): if matrix.shape[1] == 1: return matrix.copy() return reshape_dia(matrix.transpose(), matrix.shape[0]*matrix.shape[1], 1) cdef void _column_unstack_check_shape(Data matrix, idxint rows) except *: if matrix.shape[1] != 1: raise ValueError("input is not a single column") if rows < 1: raise ValueError("rows must be a positive integer") if matrix.shape[0] % rows: raise ValueError("number of rows does not divide into the shape") cpdef CSR column_unstack_csr(CSR matrix, idxint rows): _column_unstack_check_shape(matrix, rows) cdef idxint cols = matrix.shape[0] // rows return reshape_csr(matrix, cols, rows).transpose() cpdef Dense column_unstack_dense(Dense matrix, idxint rows, bint inplace=False): _column_unstack_check_shape(matrix, rows) cdef idxint cols = matrix.shape[0] // rows if inplace and matrix.fortran: matrix.shape = (rows, cols) return matrix elif inplace: warnings.warn("cannot unstack columns inplace for C-ordered matrix") out = dense.empty(rows, cols, fortran=True) memcpy(out.data, matrix.data, rows*cols * sizeof(double complex)) return out cpdef Dia column_unstack_dia(Dia matrix, idxint rows): _column_unstack_check_shape(matrix, rows) cdef idxint cols = matrix.shape[0] // rows return reshape_dia(matrix, cols, rows).transpose() cpdef list split_columns_dense(Dense matrix, copy=True): return [Dense(matrix.as_ndarray()[:, k], copy=copy) for k in range(matrix.shape[1])] cpdef list split_columns_csr(CSR matrix, copy=True): return [CSR(matrix.as_scipy()[:, k], copy=copy) for k in range(matrix.shape[1])] cpdef list split_columns_dia(Dia matrix, copy=None): as_array = matrix.to_array() return [Dense(as_array[:, k], copy=False) for k in range(matrix.shape[1])] from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect reshape = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('n_rows_out', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('n_cols_out', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='reshape', module=__name__, inputs=('matrix',), out=True, ) reshape.__doc__ =\ """ Reshape the input matrix. The values of `n_rows_out` and `n_cols_out` must match the current total number of elements of the matrix. Parameters ---------- matrix : Data The input matrix to reshape. n_rows_out, n_cols_out : integer The number of rows and columns in the output matrix. """ reshape.add_specialisations([ (CSR, CSR, reshape_csr), (Dense, Dense, reshape_dense), (Dia, Dia, reshape_dia), ], _defer=True) # Similar to the `out` parameter of `matmul`, we don't include `inplace` in the # signature of `column_stack` because the dispatcher logic currently doesn't # support the idea of an input parameter also being the output. column_stack = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='column_stack', module=__name__, inputs=('matrix',), out=True, ) column_stack.__doc__ =\ """ Stack the columns of a matrix so it becomes a ket-like vector. For example, the matrix [[0, 1, 2], [3, 4, 5], [6, 7, 8]] would be transformed to [[0], [3], [6], [1], ... [5], [8]] This is used for transforming between operator and operator-ket representations in the super-operator formalism. The inverse of this operation is `column_unstack`. Parameters ---------- matrix : Data The matrix to stack the columns of. """ column_stack.add_specialisations([ (CSR, CSR, column_stack_csr), (Dense, Dense, column_stack_dense), (Dia, Dia, column_stack_dia), ], _defer=True) column_unstack = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('rows', _inspect.Parameter.POSITIONAL_OR_KEYWORD), ]), name='column_unstack', module=__name__, inputs=('matrix',), out=True, ) column_unstack.__doc__ =\ """ Unstack the columns of a ket-like vector so it becomes a matrix with `rows` number of rows. For example, the matrix [[0], [1], [2], [3]] would be unstacked with `rows = 2` to [[0, 2], [1, 3]] This is used for transforming between the operator-ket and operator representations in the super-operator formalism. The inverse of this operation is `column_stack`. Parameters ---------- matrix : Data The matrix to unstack the columns of. rows : integer The number of rows there should be in the output matrix. This must divide into the total number of elements in the input. """ column_unstack.add_specialisations([ (CSR, CSR, column_unstack_csr), (Dense, Dense, column_unstack_dense), (Dia, Dia, column_unstack_dia), ], _defer=True) split_columns = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('copy', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=1), ]), name='split_columns', module=__name__, inputs=('matrix',), out=False, ) split_columns.__doc__ =\ """ Make a ket-shaped data out of each columns of the matrix. This is used for to split the eigenvectors from :obj:`eigs`. Parameters ---------- matrix : Data The matrix to unstack the columns of. copy : bool, optional [True] Whether to return copy of the data or a view. View may not be a possible in all cases. Returns ------- kets : list list of Data of each columns of the matrix. """ split_columns.add_specialisations([ (CSR, split_columns_csr), (Dense, split_columns_dense), (Dia, split_columns_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/solve.py000066400000000000000000000151571474175217300174110ustar00rootroot00000000000000from qutip.core.data import CSR, Data, csr, Dense, Dia import qutip.core.data as _data import scipy.sparse.linalg as splinalg import numpy as np from qutip.settings import settings import warnings from typing import Union if settings.has_mkl: from qutip._mkl.spsolve import mkl_spsolve else: mkl_spsolve = None __all__ = ["solve_csr_dense", "solve_dia_dense", "solve_dense", "solve"] def _splu(A, B, **kwargs): lu = splinalg.splu(A, **kwargs) return lu.solve(B) def solve_csr_dense(matrix: Union[CSR, Dia], target: Dense, method=None, options: dict={}) -> Dense: """ Solve ``Ax=b`` for ``x``. Parameters: ----------- matrix : CSR, Dia The matrix ``A``. target : Data The matrix or vector ``b``. method : str {"spsolve", "splu", "mkl_spsolve", etc.}, default="spsolve" The function to use to solve the system. Any function from scipy.sparse.linalg which solve the equation Ax=b can be used. `splu` from the same and `mkl_spsolve` are also valid choice. options : dict Keywork options to pass to the solver. Refer to the documenentation in scipy.sparse.linalg of the used method for a list of supported keyword. The keyword "csc" can be set to ``True`` to convert the sparse matrix before passing it to the solver. .. note:: Options for ``mkl_spsolve`` are presently only found in the source code. Returns: -------- x : Dense Solution to the system Ax = b. """ if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only solve using square matrix") if matrix.shape[1] != target.shape[0]: raise ValueError("target does not match the system") b = target.as_ndarray() method = method or "spsolve" if method == "splu": solver = _splu elif method == "lstsq": solver = splinalg.lsqr elif method == "solve": solver = splinalg.spsolve elif hasattr(splinalg, method): solver = getattr(splinalg, method) elif method == "mkl_spsolve" and mkl_spsolve is None: raise ValueError("mkl is not available") elif method == "mkl_spsolve": solver = mkl_spsolve # mkl does not support dia. if isinstance(matrix, Dia): matrix = _data.to("CSR", matrix) else: raise ValueError(f"Unknown sparse solver {method}.") options = options.copy() M = matrix.as_scipy() if options.pop("csc", False) or isinstance(matrix, Dia): M = M.tocsc() with warnings.catch_warnings(): warnings.simplefilter("error") try: out = solver(M, b, **options) except splinalg.MatrixRankWarning: raise ValueError("Matrix is singular") if isinstance(out, tuple) and len(out) == 2: # iterative method return a success flag out, check = out if check == 0: # Successful pass elif check > 0: raise RuntimeError( f"scipy.sparse.linalg.{method} error: Tolerance was not" f" reached. Error code: {check}" ) elif check < 0: raise RuntimeError( f"scipy.sparse.linalg.{method} error: Bad input. " f"Error code: {check}" ) elif isinstance(out, tuple) and len(out) > 2: # least sqare method return residual, flag, etc. out, *_ = out return Dense(out, copy=False) solve_dia_dense = solve_csr_dense def solve_dense(matrix: Dense, target: Data, method=None, options: dict={}) -> Dense: """ Solve ``Ax=b`` for ``x``. Parameters: ----------- matrix : Dense The matrix ``A``. target : Data The matrix or vector ``b``. method : str {"solve", "lstsq"}, default="solve" The function from numpy.linalg to use to solve the system. options : dict Options to pass to the solver. "lstsq" use "rcond" while, "solve" do not use any. Returns: -------- x : Dense Solution to the system Ax = b. """ if matrix.shape[0] != matrix.shape[1]: raise ValueError("can only solve using square matrix") if matrix.shape[1] != target.shape[0]: raise ValueError("target does not match the system") if isinstance(target, Dense): b = target.as_ndarray() else: b = target.to_array() if method in ["solve", None]: try: out = np.linalg.solve(matrix.as_ndarray(), b) except np.linalg.LinAlgError: raise ValueError("Matrix is singular") elif method == "lstsq": out, *_ = np.linalg.lstsq( matrix.as_ndarray(), b, rcond=options.get("rcond", None) ) else: raise ValueError(f"Unknown solver {method}," " 'solve' and 'lstsq' are supported.") return Dense(out, copy=False) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect solve = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('target', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('method', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=None), _inspect.Parameter('options', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default={}), ]), name='solve', module=__name__, inputs=('matrix', 'target'), out=True, ) solve.__doc__ = """ Solve ``Ax=b`` for ``x``. Parameters: ----------- matrix : Data The matrix ``A``. target : Data The matrix or vector ``b``. method : str The function to use to solve the system. Function which solve the equation Ax=b from scipy.sparse.linalg (CSR ``matrix``) or numpy.linalg (Dense ``matrix``) can be used. Sparse cases also accept `splu` and `mkl_spsolve`. `solve` and `lstsq` will work for any data-type. options : dict Keywork options to pass to the solver. Refer to the documenentation for the chosen method in scipy.sparse.linalg or numpy.linalg. The keyword "csc" can be set to ``True`` to convert the sparse matrix in sparse cases. .. note:: Options for ``mkl_spsolve`` are presently only found in the source code. Returns: -------- x : Data Solution to the system Ax = b. """ solve.add_specialisations([ (CSR, Dense, Dense, solve_csr_dense), (Dia, Dense, Dense, solve_dia_dense), (Dense, Dense, Dense, solve_dense), ], _defer=True) del _Dispatcher del _inspect qutip-5.1.1/qutip/core/data/src/000077500000000000000000000000001474175217300164655ustar00rootroot00000000000000qutip-5.1.1/qutip/core/data/src/intdtype.h000066400000000000000000000000551474175217300204760ustar00rootroot00000000000000typedef int32_t idxint; int _idxint_size=32; qutip-5.1.1/qutip/core/data/src/matmul_csr_vector.cpp000066400000000000000000000104741474175217300227270ustar00rootroot00000000000000#include #if \ (defined(__GNUC__) && defined(__SSE3__))\ || (defined(_MSC_VER) && defined(__AVX__)) /* If we're going to manually do the vectorisation, we need to make sure we've * included the preprocessor directives. */ # include #endif #include "matmul_csr_vector.hpp" template #if \ (defined(__GNUC__) && defined(__SSE3__))\ || (defined(_MSC_VER) && defined(__AVX__)) /* Manually apply the vectorisation. */ void _matmul_csr_vector( const std::complex * _RESTRICT data, const IntT * _RESTRICT col_index, const IntT * _RESTRICT row_index, const std::complex * _RESTRICT vec, const std::complex scale, std::complex * _RESTRICT out, const IntT nrows) { IntT row_start, row_end; __m128d num1, num2, num3, num4; for (IntT row=0; row < nrows; row++) { num4 = _mm_setzero_pd(); row_start = row_index[row]; row_end = row_index[row+1]; for (IntT ptr=row_start; ptr < row_end; ptr++) { num1 = _mm_loaddup_pd(&reinterpret_cast(data[ptr])[0]); num2 = _mm_set_pd(std::imag(vec[col_index[ptr]]), std::real(vec[col_index[ptr]])); num3 = _mm_mul_pd(num2, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(data[ptr])[1]); num2 = _mm_shuffle_pd(num2, num2, 1); num2 = _mm_mul_pd(num2, num1); num3 = _mm_addsub_pd(num3, num2); num4 = _mm_add_pd(num3, num4); } num1 = _mm_loaddup_pd(&reinterpret_cast(scale)[0]); num3 = _mm_mul_pd(num4, num1); num1 = _mm_loaddup_pd(&reinterpret_cast(scale)[1]); num4 = _mm_shuffle_pd(num4, num4, 1); num4 = _mm_mul_pd(num4, num1); num3 = _mm_addsub_pd(num3, num4); num2 = _mm_loadu_pd((double *)&out[row]); num3 = _mm_add_pd(num2, num3); _mm_storeu_pd((double *)&out[row], num3); } } #else /* No manual vectorisation. */ void _matmul_csr_vector( const std::complex * _RESTRICT data, const IntT * _RESTRICT col_index, const IntT * _RESTRICT row_index, const std::complex * _RESTRICT vec, const std::complex scale, std::complex * _RESTRICT out, const IntT nrows) { IntT row_start, row_end; std::complex dot; for (size_t row=0; row < nrows; row++) { dot = 0; row_start = row_index[row]; row_end = row_index[row+1]; for (size_t ptr=row_start; ptr < row_end; ptr++) { dot += data[ptr]*vec[col_index[ptr]]; } out[row] += scale * dot; } } #endif /* It seems wrong to me to specify the integer specialisations as `int`, `long` and * `long long` rather than just `int32_t` and `int64_t`, but for some reason the * latter causes compatibility issues with defining the sized types with the * numpy `cnp.npy_int32` and `cnp.npy_int64` typedefs. We need to specify all * three of `int`, `long` and `long long` when doing things this way (despite * the almost certain duplication) because on Unix-likes (where `int`[`long`] is * typically 32[64]-bit) numpy typedef's int32 to int and int64 to long, whereas * on Windows (where `int` and `long` are both 32-bit), it typedef's to `long` * and `long long`. * - Jake Lishman 2020-08-10. */ template void _matmul_csr_vector<>( const std::complex * _RESTRICT, const int * _RESTRICT, const int * _RESTRICT, const std::complex * _RESTRICT, const std::complex, std::complex * _RESTRICT, const int); template void _matmul_csr_vector<>( const std::complex * _RESTRICT, const long * _RESTRICT, const long * _RESTRICT, const std::complex * _RESTRICT, const std::complex, std::complex * _RESTRICT, const long); template void _matmul_csr_vector<>( const std::complex * _RESTRICT, const long long * _RESTRICT, const long long * _RESTRICT, const std::complex * _RESTRICT, const std::complex, std::complex * _RESTRICT, const long long); qutip-5.1.1/qutip/core/data/src/matmul_csr_vector.hpp000077500000000000000000000007401474175217300227320ustar00rootroot00000000000000#include #if defined(__GNUC__) || defined(_MSC_VER) # define _RESTRICT __restrict #else # define _RESTRICT #endif template void _matmul_csr_vector( const std::complex * _RESTRICT data, const IntT * _RESTRICT col_index, const IntT * _RESTRICT row_index, const std::complex * _RESTRICT vec, const std::complex scale, std::complex * _RESTRICT out, const IntT nrows); qutip-5.1.1/qutip/core/data/src/matmul_diag_vector.cpp000066400000000000000000000057201474175217300230420ustar00rootroot00000000000000#include #include "matmul_diag_vector.hpp" template void _matmul_diag_vector( const std::complex * _RESTRICT data, const std::complex * _RESTRICT vec, std::complex * _RESTRICT out, const IntT length, const std::complex scale ){ const double * data_dbl = reinterpret_cast(data); const double * vec_dbl = reinterpret_cast(vec); double * out_dbl = reinterpret_cast(out); // Gcc does not vectorize complex automatically? for (IntT i=0; i( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const int, const std::complex); template void _matmul_diag_vector<>( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const long, const std::complex); template void _matmul_diag_vector<>( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const long long, const std::complex); template void _matmul_diag_block( const std::complex * _RESTRICT data, const std::complex * _RESTRICT vec, std::complex * _RESTRICT out, const IntT length, const IntT width ){ const double * data_dbl = reinterpret_cast(data); const double * vec_dbl = reinterpret_cast(vec); double * out_dbl = reinterpret_cast(out); IntT ptr = 0; // Gcc does not vectorize complex automatically? for (IntT i=0; i( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const int, const int); template void _matmul_diag_block<>( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const long, const long); template void _matmul_diag_block<>( const std::complex * _RESTRICT, const std::complex * _RESTRICT, std::complex * _RESTRICT, const long long, const long long); qutip-5.1.1/qutip/core/data/src/matmul_diag_vector.hpp000066400000000000000000000012211474175217300230370ustar00rootroot00000000000000#include #if defined(__GNUC__) || defined(_MSC_VER) # define _RESTRICT __restrict #else # define _RESTRICT #endif template void _matmul_diag_vector( const std::complex * _RESTRICT data, const std::complex * _RESTRICT vec, std::complex * _RESTRICT out, const IntT length, const std::complex scale ); template void _matmul_diag_block( const std::complex * _RESTRICT data, const std::complex * _RESTRICT vec, std::complex * _RESTRICT out, const IntT length, const IntT width ); qutip-5.1.1/qutip/core/data/tidyup.pxd000066400000000000000000000005131474175217300177300ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from qutip.core.data cimport CSR, Dense, Dia cpdef CSR tidyup_csr(CSR matrix, double tol, bint inplace=*) cpdef Dense tidyup_dense(Dense matrix, double tol, bint inplace=*) cpdef Dia tidyup_dia(Dia matrix, double tol, bint inplace=*) qutip-5.1.1/qutip/core/data/tidyup.pyx000066400000000000000000000113231474175217300177560ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False from libc.math cimport fabs cimport numpy as cnp from scipy.linalg cimport cython_blas as blas from qutip.core.data cimport csr, dense, CSR, Dense, dia, Dia, base cdef extern from "" namespace "std" nogil: # abs is templated such that Cython treats std::abs as complex->complex double abs(double complex x) __all__ = [ 'tidyup', 'tidyup_csr', 'tidyup_dense', 'tidyup_dia', ] cpdef CSR tidyup_csr(CSR matrix, double tol, bint inplace=True): cdef bint re, im cdef size_t row, ptr, ptr_start, ptr_end=0, nnz cdef double complex value cdef CSR out = matrix if inplace else matrix.copy() nnz = 0 out.row_index[0] = 0 for row in range(matrix.shape[0]): ptr_start, ptr_end = ptr_end, matrix.row_index[row + 1] for ptr in range(ptr_start, ptr_end): re = im = False value = matrix.data[ptr] if fabs(value.real) < tol: re = True value.real = 0 if fabs(value.imag) < tol: im = True value.imag = 0 if not (re & im): out.data[nnz] = value out.col_index[nnz] = matrix.col_index[ptr] nnz += 1 out.row_index[row + 1] = nnz return out cpdef Dense tidyup_dense(Dense matrix, double tol, bint inplace=True): cdef Dense out = matrix if inplace else matrix.copy() cdef double complex value cdef size_t ptr for ptr in range(matrix.shape[0] * matrix.shape[1]): value = matrix.data[ptr] if fabs(value.real) < tol: matrix.data[ptr].real = 0 if fabs(value.imag) < tol: matrix.data[ptr].imag = 0 return out cpdef Dia tidyup_dia(Dia matrix, double tol, bint inplace=True): cdef Dia out = matrix if inplace else matrix.copy() cdef base.idxint diag=0, new_diag=0, ONE=1, start, end, col cdef bint re, im, has_data cdef double complex value cdef int length while diag < out.num_diag: start = max(0, out.offsets[diag]) end = min(out.shape[1], out.shape[0] + out.offsets[diag]) has_data = False for col in range(start, end): re = False im = False if fabs(out.data[diag * out.shape[1] + col].real) < tol: re = True out.data[diag * out.shape[1] + col].real = 0 if fabs(out.data[diag * out.shape[1] + col].imag) < tol: im = True out.data[diag * out.shape[1] + col].imag = 0 has_data |= not (re & im) if has_data and new_diag < diag: length = out.shape[1] blas.zcopy( &length, &out.data[diag * out.shape[1]], &ONE, &out.data[new_diag * out.shape[1]], &ONE ) out.offsets[new_diag] = out.offsets[diag] if has_data: new_diag += 1 diag += 1 out.num_diag = new_diag if out._scipy is not None: out._scipy.data = out._scipy.data[:new_diag] out._scipy.offsets = out._scipy.offsets[:new_diag] return out from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect # In this case, to support the `inplace` argument, we do not support # dispatching on the output. tidyup = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), _inspect.Parameter('tol', _inspect.Parameter.POSITIONAL_OR_KEYWORD), _inspect.Parameter('inplace', _inspect.Parameter.POSITIONAL_OR_KEYWORD, default=True), ]), name='tidyup', module=__name__, inputs=('matrix',), out=False, ) tidyup.__doc__ =\ """ Tidy up the input matrix by truncating small values to zero. The real and imaginary parts are treated individually, so (for example) the number 1e-18 + 2j would be truncated with a tolerance of `1e-15` to just 2j By default, this operation is in-place. The output type will always match the input type; no dispatching takes place on the output. Parameters ---------- matrix : Data The matrix to tidy up. tol : real The absolute tolerance to use to determine whether a real or imaginary part should be truncated to zero. inplace : bool, optional (True) Whether to do the operation in-place. The output matrix will always be returned, even if this argument is `True`; it will just be the same Python object as was input. """ tidyup.add_specialisations([ (CSR, tidyup_csr), (Dense, tidyup_dense), (Dia, tidyup_dia), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/data/trace.pxd000066400000000000000000000007111474175217300175100ustar00rootroot00000000000000#cython: language_level=3 from qutip.core.data cimport CSR, Dense, Dia cpdef double complex trace_csr(CSR matrix) except * nogil cpdef double complex trace_dense(Dense matrix) except * nogil cpdef double complex trace_dia(Dia matrix) except * nogil cpdef double complex trace_oper_ket_csr(CSR matrix) except * nogil cpdef double complex trace_oper_ket_dense(Dense matrix) except * nogil cpdef double complex trace_oper_ket_dia(Dia matrix) except * nogil qutip-5.1.1/qutip/core/data/trace.pyx000066400000000000000000000104261474175217300175410ustar00rootroot00000000000000#cython: language_level=3 #cython: boundscheck=False, wraparound=False, initializedcheck=False cimport cython from libc.math cimport sqrt from qutip.core.data cimport Data, CSR, Dense, Dia from qutip.core.data cimport base from .reshape import column_unstack __all__ = [ 'trace', 'trace_csr', 'trace_dense', 'trace_dia', 'trace_oper_ket', 'trace_oper_ket_csr', 'trace_oper_ket_dense', 'trace_oper_ket_dia', 'trace_oper_ket_data', ] cdef int _check_shape(Data matrix) except -1 nogil: if matrix.shape[0] != matrix.shape[1]: raise ValueError("".join([ "matrix shape ", str(matrix.shape), " is not square.", ])) return 0 cdef int _check_shape_oper_ket(int N, Data matrix) except -1 nogil: if matrix.shape[0] != N * N or matrix.shape[1] != 1: raise ValueError("".join([ "matrix ", str(matrix.shape), " is not a stacked square matrix." ])) return 0 cpdef double complex trace_csr(CSR matrix) except * nogil: _check_shape(matrix) cdef size_t row, ptr cdef double complex trace = 0 for row in range(matrix.shape[0]): for ptr in range(matrix.row_index[row], matrix.row_index[row + 1]): if matrix.col_index[ptr] == row: trace += matrix.data[ptr] break return trace cpdef double complex trace_dense(Dense matrix) except * nogil: _check_shape(matrix) cdef double complex trace = 0 cdef size_t ptr = 0 cdef size_t stride = matrix.shape[0] + 1 for _ in range(matrix.shape[0]): trace += matrix.data[ptr] ptr += stride return trace cpdef double complex trace_dia(Dia matrix) except * nogil: _check_shape(matrix) cdef double complex trace = 0 cdef size_t diag, j for diag in range(matrix.num_diag): if matrix.offsets[diag] == 0: for j in range(matrix.shape[1]): trace += matrix.data[diag * matrix.shape[1] + j] break return trace cpdef double complex trace_oper_ket_csr(CSR matrix) except * nogil: cdef size_t N = sqrt(matrix.shape[0]) _check_shape_oper_ket(N, matrix) cdef size_t row cdef double complex trace = 0 cdef size_t stride = N + 1 for row in range(N): if matrix.row_index[row * stride] != matrix.row_index[row * stride + 1]: trace += matrix.data[matrix.row_index[row * stride]] return trace cpdef double complex trace_oper_ket_dense(Dense matrix) except * nogil: cdef size_t N = sqrt(matrix.shape[0]) _check_shape_oper_ket(N, matrix) cdef double complex trace = 0 cdef size_t ptr = 0 cdef size_t stride = N + 1 for ptr in range(N): trace += matrix.data[ptr * stride] return trace cpdef double complex trace_oper_ket_dia(Dia matrix) except * nogil: cdef size_t N = sqrt(matrix.shape[0]) _check_shape_oper_ket(N, matrix) cdef double complex trace = 0 cdef size_t diag = 0 cdef size_t stride = N + 1 for diag in range(matrix.num_diag): if -matrix.offsets[diag] % stride == 0: trace += matrix.data[diag * matrix.shape[1]] return trace cpdef trace_oper_ket_data(Data matrix): cdef size_t N = sqrt(matrix.shape[0]) _check_shape_oper_ket(N, matrix) return trace(column_unstack(matrix, N)) from .dispatch import Dispatcher as _Dispatcher import inspect as _inspect trace = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='trace', module=__name__, inputs=('matrix',), out=False, ) trace.__doc__ =\ """Compute the trace (sum of digaonal elements) of a square matrix.""" trace.add_specialisations([ (CSR, trace_csr), (Dia, trace_dia), (Dense, trace_dense), ], _defer=True) trace_oper_ket = _Dispatcher( _inspect.Signature([ _inspect.Parameter('matrix', _inspect.Parameter.POSITIONAL_ONLY), ]), name='trace_oper_ket', module=__name__, inputs=('matrix',), out=False, ) trace_oper_ket.__doc__ =\ """Compute the trace (sum of digaonal elements) of a stacked square matrix .""" trace_oper_ket.add_specialisations([ (CSR, trace_oper_ket_csr), (Dia, trace_oper_ket_dia), (Dense, trace_oper_ket_dense), (Data, trace_oper_ket_data), ], _defer=True) del _inspect, _Dispatcher qutip-5.1.1/qutip/core/dimensions.py000066400000000000000000000730251474175217300175160ustar00rootroot00000000000000""" Internal use module for manipulating dims specifications. """ # Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations import numpy as np import numbers from operator import getitem from functools import partial from typing import Literal from qutip.settings import settings from qutip.typing import SpaceLike, DimensionLike __all__ = ["to_tensor_rep", "from_tensor_rep", "Space", "Dimensions"] def flatten(l): """Flattens a list of lists to the first level. Given a list containing a mix of scalars and lists or a dimension object, flattens it down to a list of the scalars within the original list. Parameters ---------- l : scalar, list, Space, Dimension Object to flatten. Examples -------- >>> flatten([[[0], 1], 2]) # doctest: +SKIP [0, 1, 2] Notes ----- Any scalar will be returned wrapped in a list: ``flaten(1) == [1]``. A non-list iterable will not be treated as a list by flatten. For example, flatten would treat a tuple as a scalar. """ if isinstance(l, (Space, Dimensions)): l = l.as_list() if not isinstance(l, list): return [l] else: return sum(map(flatten, l), []) def deep_remove(l, *what): """Removes scalars from all levels of a nested list. Given a list containing a mix of scalars and lists, returns a list of the same structure, but where one or more scalars have been removed. Examples -------- >>> deep_remove([[[[0, 1, 2]], [3, 4], [5], [6, 7]]], 0, 5) # doctest: +SKIP [[[[1, 2]], [3, 4], [], [6, 7]]] """ if isinstance(l, list): # Make a shallow copy at this level. l = l[:] for to_remove in what: if to_remove in l: l.remove(to_remove) else: l = [deep_remove(elem, to_remove) for elem in l] return l def unflatten(l, idxs): """Unflattens a list by a given structure. Given a list of scalars and a deep list of indices as produced by `flatten`, returns an "unflattened" form of the list. This perfectly inverts `flatten`. Examples -------- >>> l = [[[10, 20, 30], [40, 50, 60]], [[70, 80, 90], [100, 110, 120]]] # doctest: +SKIP >>> idxs = enumerate_flat(l) # doctest: +SKIP >>> unflatten(flatten(l), idxs) == l # doctest: +SKIP True """ acc = [] for idx in idxs: if isinstance(idx, list): acc.append(unflatten(l, idx)) else: acc.append(l[idx]) return acc def _enumerate_flat(l, idx=0): if not isinstance(l, list): # Found a scalar, so return and increment. return idx, idx + 1 else: # Found a list, so append all the scalars # from it and recurse to keep the increment # correct. acc = [] for elem in l: labels, idx = _enumerate_flat(elem, idx) acc.append(labels) return acc, idx def _collapse_composite_index(dims): """ Given the dimensions specification for a composite index (e.g.: [2, 3] for the right index of a ket with dims [[1], [2, 3]]), returns a dimensions specification for an index of the same shape, but collapsed to a single "leg." In the previous example, [2, 3] would collapse to [6]. """ return [np.prod(dims)] def _collapse_dims_to_level(dims, level=1): """ Recursively collapses all indices in a dimensions specification appearing at a given level, such that the returned dimensions specification does not represent any composite systems. """ if level == 0: return _collapse_composite_index(dims) return [_collapse_dims_to_level(index, level=level - 1) for index in dims] def collapse_dims_oper(dims): """ Given the dimensions specifications for a ket-, bra- or oper-type Qobj, returns a dimensions specification describing the same shape by collapsing all composite systems. For instance, the bra-type dimensions specification ``[[2, 3], [1]]`` collapses to ``[[6], [1]]``. Parameters ---------- dims : list of lists of ints Dimensions specifications to be collapsed. Returns ------- collapsed_dims : list of lists of ints Collapsed dimensions specification describing the same shape such that ``len(collapsed_dims[0]) == len(collapsed_dims[1]) == 1``. """ return _collapse_dims_to_level(dims, 1) def collapse_dims_super(dims): """ Given the dimensions specifications for an operator-ket-, operator-bra- or super-type Qobj, returns a dimensions specification describing the same shape by collapsing all composite systems. For instance, the super-type dimensions specification ``[[[2, 3], [2, 3]], [[2, 3], [2, 3]]]`` collapses to ``[[[6], [6]], [[6], [6]]]``. Parameters ---------- dims : list of lists of ints Dimensions specifications to be collapsed. Returns ------- collapsed_dims : list of lists of ints Collapsed dimensions specification describing the same shape such that ``len(collapsed_dims[i][j]) == 1`` for ``i`` and ``j`` in ``range(2)``. """ return _collapse_dims_to_level(dims, 2) def enumerate_flat(l): """Labels the indices at which scalars occur in a flattened list. Given a list containing a mix of scalars and lists, returns a list of the same structure, where each scalar has been replaced by an index into the flattened list. Examples -------- >>> print(enumerate_flat([[[10], [20, 30]], 40])) # doctest: +SKIP [[[0], [1, 2]], 3] """ return _enumerate_flat(l)[0] def deep_map(fn, collection, over=(tuple, list)): if isinstance(collection, over): return type(collection)(deep_map(fn, el, over) for el in collection) else: return fn(collection) def dims_to_tensor_perm(dims): """ Given the dims of a Qobj instance, returns a list representing a permutation from the flattening of that dims specification to the corresponding tensor indices. Parameters ---------- dims : list, Dimensions Dimensions specification for a Qobj. Returns ------- perm : list A list such that ``data[flatten(dims)[idx]]`` gives the index of the tensor ``data`` corresponding to the ``idx``th dimension of ``dims``. """ if isinstance(dims, list): dims = Dimensions(dims) return dims._get_tensor_perm() def dims_to_tensor_shape(dims): """ Given the dims of a Qobj instance, returns the shape of the corresponding tensor. This helps, for instance, resolve the column-stacking convention for superoperators. Parameters ---------- dims : list, Dimensions Dimensions specification for a Qobj. Returns ------- tensor_shape : tuple NumPy shape of the corresponding tensor. """ perm = np.argsort(dims_to_tensor_perm(dims)) dims = flatten(dims) return tuple(map(partial(getitem, dims), perm)) def dims_idxs_to_tensor_idxs(dims, indices): """ Given the dims of a Qobj instance, and some indices into dims, returns the corresponding tensor indices. This helps resolve, for instance, that column-stacking for superoperators, oper-ket and oper-bra implies that the input and output tensor indices are reversed from their order in dims. Parameters ---------- dims : list, Dimensions Dimensions specification for a Qobj. indices : int, list or tuple Indices to convert to tensor indices. Can be specified as a single index, or as a collection of indices. In the latter case, this can be nested arbitrarily deep. For instance, [0, [0, (2, 3)]]. Returns ------- tens_indices : int, list or tuple Container of the same structure as indices containing the tensor indices for each element of indices. """ perm = dims_to_tensor_perm(dims) return deep_map(partial(getitem, perm), indices) def to_tensor_rep(q_oper): """ Transform a ``Qobj`` to a numpy array whose shape is the flattened dimensions. Parameters ---------- q_oper: Qobj Object to reshape Returns ------- ndarray: Numpy array with one dimension for each index in dims. Examples -------- >>> ket.dims [[2, 3], [1]] >>> to_tensor_rep(ket).shape (2, 3, 1) >>> oper.dims [[2, 3], [2, 3]] >>> to_tensor_rep(oper).shape (2, 3, 2, 3) >>> super_oper.dims [[[2, 3], [2, 3]], [[2, 3], [2, 3]]] >>> to_tensor_rep(super_oper).shape (2, 3, 2, 3, 2, 3, 2, 3) """ dims = q_oper._dims data = q_oper.full().reshape(dims._get_tensor_shape()) return data.transpose(dims._get_tensor_perm()) def from_tensor_rep(tensorrep, dims): """ Reverse operator of :func:`to_tensor_rep`. Create a Qobj From a N-dimensions numpy array and dimensions with N indices. Parameters ---------- tensorrep: ndarray Numpy array with one dimension for each index in dims. dims: list of list, Dimensions Dimensions of the Qobj. Returns ------- Qobj Re constructed Qobj """ from . import Qobj dims = Dimensions(dims) data = tensorrep.transpose(np.argsort(dims._get_tensor_perm())) return Qobj(data.reshape(dims.shape), dims=dims) def _frozen(*args, **kwargs): raise RuntimeError("Dimension cannot be modified.") def einsum(subscripts, *operands): """ Implementation of numpy.einsum for Qobj. Evaluates the Einstein summation convention on the operands. Parameters ---------- subscripts: str Specifies the subscripts for summation as comma separated list of subscript labels. operands: list of array_like These are the arrays for the operation. Returns ------- Qobj (numpy.complex128) Result of einsum as Qobj (numpy.complex128 if result is scalar) """ operands_array = [to_tensor_rep(op) for op in operands] result = np.einsum(subscripts, *operands_array) if result.shape == (): return result dims = [ [d for d in result.shape[:result.ndim // 2]], [d for d in result.shape[result.ndim // 2:]] ] return from_tensor_rep(result, dims) class MetaSpace(type): def __call__(cls, *args: SpaceLike, rep: str = None) -> "Space": """ Select which subclass is instantiated. """ if cls is Space and len(args) == 1 and isinstance(args[0], list): # From a list of int. return cls.from_list(args[0], rep=rep) elif len(args) == 1 and isinstance(args[0], Space): # Already a Space return args[0] if cls is Space: if len(args) == 0: # Empty space: a Field. cls = Field elif len(args) == 1 and args[0] == 1: # Space(1): a Field. cls = Field elif len(args) == 1 and isinstance(args[0], Dimensions): # Making a Space out of a Dimensions object: Super Operator. cls = SuperSpace elif len(args) > 1 and all(isinstance(arg, Space) for arg in args): # list of space: tensor product space. cls = Compound if settings.core['auto_tidyup_dims']: if cls is Compound and all(isinstance(arg, Field) for arg in args): cls = Field if cls is SuperSpace and args[0].type == "scalar": cls = Field args = tuple([ tuple(arg) if isinstance(arg, list) else arg for arg in args ]) if cls is Field: return cls.field_instance if cls is SuperSpace: args = (*args, rep or 'super') if args not in cls._stored_dims: instance = cls.__new__(cls) instance.__init__(*args) cls._stored_dims[args] = instance return cls._stored_dims[args] def from_list( cls, list_dims: list[int] | list[list[int]], rep: str = None ) -> "Space": if len(list_dims) == 0: raise ValueError("Empty list can't be used as dims.") elif ( sum(isinstance(entry, list) for entry in list_dims) not in [0, len(list_dims)] ): raise ValueError(f"Format dims not understood {list_dims}.") elif not isinstance(list_dims[0], list): # Tensor spaces = [Space(size) for size in list_dims] elif len(list_dims) == 1: # [[2, 3]]: tensor with an extra layer of list. spaces = [Space(size) for size in list_dims[0]] elif len(list_dims) % 2 == 0: # Superoperators or tensor of Superoperators spaces = [ Space(Dimensions( Space(list_dims[i+1]), Space(list_dims[i]) ), rep=rep) for i in range(0, len(list_dims), 2) ] else: raise ValueError(f'Format not understood {list_dims}') if len(spaces) == 1: return spaces[0] elif len(spaces) >= 2: return Space(*spaces) else: raise ValueError(f'Format not understood {list_dims}') class Space(metaclass=MetaSpace): _stored_dims = {} def __init__(self, dims): idims = int(dims) if idims <= 0 or idims != dims: raise ValueError("Dimensions must be integers > 0") # Size of the hilbert space self.size = dims self.issuper = False # Super representation, should be an empty string except for SuperSpace self.superrep = None # Does the size and dims match directly: size == prod(dims) self._pure_dims = True self.__setitem__ = _frozen def __eq__(self, other) -> bool: return self is other or ( type(other) is type(self) and other.size == self.size ) def __hash__(self): return hash(self.size) def __repr__(self) -> str: return f"Space({self.size})" def as_list(self) -> list[int]: return [self.size] def __str__(self) -> str: return str(self.as_list()) def dims2idx(self, dims: list[int]) -> int: """ Transform dimensions indices to full array indices. """ if not isinstance(dims, list) or len(dims) != 1: raise ValueError("Dimensions must be a list of one element") if not (0 <= dims[0] < self.size): raise IndexError("Dimensions out of range") if not isinstance(dims[0], numbers.Integral): raise TypeError("Dimensions must be integers") return dims[0] def idx2dims(self, idx: int) -> list[int]: """ Transform full array indices to dimensions indices. """ if not (0 <= idx < self.size): raise IndexError("Index out of range") return [idx] def step(self) -> list[int]: """ Get the step in the array between for each dimensions index. If element ``[i, j, k]`` is ``ket.full()[m, 0]`` then element ``[i, j+1, k]`` is ``ket.full()[m + ket._dims.step()[1], 0]``. """ return [1] def flat(self) -> list[int]: """ Dimensions as a flat list. """ return [self.size] def remove(self, idx: int): """ Remove a Space from a Dimensons or complex Space. ``Space([2, 3, 4]).remove(1) == Space([2, 4])`` """ raise RuntimeError("Cannot delete a flat space.") def replace(self, idx: int, new: int) -> "Space": """ Reshape a Space from a Dimensons or complex Space. ``Space([2, 3, 4]).replace(1, 5) == Space([2, 5, 4])`` """ if idx != 0: raise ValueError( "Cannot replace a non-zero index in a flat space." ) return Space(new) def replace_superrep(self, super_rep: str) -> "Space": return self def scalar_like(self) -> "Space": return Field() class Field(Space): field_instance = None def __init__(self): self.size = 1 self.issuper = False self.superrep = None self._pure_dims = True self.__setitem__ = _frozen def __eq__(self, other) -> bool: return type(other) is Field def __hash__(self): return hash(0) def __repr__(self) -> str: return "Field()" def as_list(self) -> list[int]: return [1] def step(self) -> list[int]: return [1] def flat(self) -> list[int]: return [1] def remove(self, idx: int) -> Space: return self def replace(self, idx: int, new: int) -> Space: return Space(new) Field.field_instance = Field.__new__(Field) Field.field_instance.__init__() class Compound(Space): _stored_dims = {} def __init__(self, *spaces: Space): spaces_ = [] if len(spaces) <= 1: raise ValueError("Compound need multiple space to join.") for space in spaces: if isinstance(space, Compound): spaces_ += space.spaces else: spaces_ += [space] self.spaces = tuple(spaces_) self.size = np.prod([space.size for space in self.spaces]) self.issuper = all(space.issuper for space in self.spaces) if not self.issuper and any(space.issuper for space in self.spaces): raise TypeError( "Cannot create compound space of super and non super." ) self._pure_dims = all(space._pure_dims for space in self.spaces) superrep = [space.superrep for space in self.spaces] if all(superrep[0] == rep for rep in superrep): self.superrep = superrep[0] else: raise TypeError( "Cannot create compound space of of super operators " "with different representation." ) self.__setitem__ = _frozen def __eq__(self, other) -> bool: return self is other or ( type(other) is type(self) and self.spaces == other.spaces ) def __hash__(self): return hash(self.spaces) def __repr__(self) -> str: parts_rep = ", ".join(repr(space) for space in self.spaces) return f"Compound({parts_rep})" def as_list(self) -> list[int]: return sum([space.as_list() for space in self.spaces], []) def dims2idx(self, dims: list[int]) -> int: if len(dims) != len(self.spaces): raise ValueError("Length of supplied dims does not match the number of subspaces.") pos = 0 step = 1 for space, dim in zip(self.spaces[::-1], dims[::-1]): pos += space.dims2idx([dim]) * step step *= space.size return pos def idx2dims(self, idx: int) -> list[int]: dims = [] for space in self.spaces[::-1]: idx, dim = divmod(idx, space.size) dims = space.idx2dims(dim) + dims return dims def step(self) -> list[int]: steps = [] step = 1 for space in self.spaces[::-1]: steps = [step * N for N in space.step()] + steps step *= space.size return steps def flat(self) -> list[int]: return sum([space.flat() for space in self.spaces], []) def remove(self, idx: int) -> Space: new_spaces = [] for space in self.spaces: n_indices = len(space.flat()) idx_space = [i for i in idx if i < n_indices] idx = [i-n_indices for i in idx if i >= n_indices] new_space = space.remove(idx_space) if new_spaces: return Compound(*new_spaces) return Field() def replace(self, idx: int, new: int) -> Space: new_spaces = [] for space in self.spaces: n_indices = len(space.flat()) if 0 <= idx < n_indices: new_spaces.append(space.replace(idx, new)) else: new_spaces.append(space) idx -= n_indices return Compound(*new_spaces) def replace_superrep(self, super_rep: str) -> Space: return Compound( *[space.replace_superrep(super_rep) for space in self.spaces] ) def scalar_like(self) -> Space: return Space([space.scalar_like() for space in self.spaces]) class SuperSpace(Space): _stored_dims = {} def __init__(self, oper: "Dimensions", rep: str = 'super'): self.oper = oper self.superrep = rep self.size = oper.shape[0] * oper.shape[1] self.issuper = True self._pure_dims = oper._pure_dims self.__setitem__ = _frozen def __eq__(self, other) -> bool: return ( self is other or self.oper == other or ( type(other) is type(self) and self.oper == other.oper and self.superrep == other.superrep ) ) def __hash__(self): return hash((self.oper, self.superrep)) def __repr__(self) -> str: return f"Super({repr(self.oper)}, rep={self.superrep})" def as_list(self) -> list[list[int]]: return self.oper.as_list() def dims2idx(self, dims: list[int]) -> int: posl, posr = self.oper.dims2idx(dims) return posl + posr * self.oper.shape[0] def idx2dims(self, idx: int) -> list[int]: posl = idx % self.oper.shape[0] posr = idx // self.oper.shape[0] return self.oper.idx2dims(posl, posr) def step(self) -> list[int]: stepl, stepr = self.oper.step() step = self.oper.shape[0] return stepl + [step * N for N in stepr] def flat(self) -> list[int]: return sum(self.oper.flat(), []) def remove(self, idx: int) -> Space: new_dims = self.oper.remove(idx) if new_dims.type == 'scalar': return Field() return SuperSpace(new_dims, rep=self.superrep) def replace(self, idx: int, new: int) -> Space: return SuperSpace(self.oper.replace(idx, new), rep=self.superrep) def replace_superrep(self, super_rep: str) -> Space: return SuperSpace(self.oper, rep=super_rep) def scalar_like(self) -> Space: return SuperSpace(self.oper.scalar_like(), rep=self.superrep) class MetaDims(type): def __call__(cls, *args: DimensionLike, rep: str = None) -> "Dimensions": if len(args) == 1 and isinstance(args[0], Dimensions): return args[0] elif len(args) == 1 and len(args[0]) == 2: args = ( Space(args[0][1], rep=rep), Space(args[0][0], rep=rep) ) elif len(args) != 2: raise NotImplementedError('No Dual, Ket, Bra...', args) elif ( settings.core["auto_tidyup_dims"] and args[0] == args[1] == Field() ): return Field() if args not in cls._stored_dims: instance = cls.__new__(cls) instance.__init__(*args) cls._stored_dims[args] = instance return cls._stored_dims[args] class Dimensions(metaclass=MetaDims): _stored_dims = {} _type: str = None def __init__(self, from_: Space, to_: Space): self.from_ = from_ self.to_ = to_ self.shape = to_.size, from_.size self.issuper = from_.issuper self._pure_dims = from_._pure_dims and to_._pure_dims self.issquare = False if self.from_.size == 1 and self.to_.size == 1: self.type = 'scalar' self.issquare = True self.superrep = None elif self.from_.size == 1: self.issuper = self.to_.issuper self.type = 'operator-ket' if self.issuper else 'ket' self.superrep = self.to_.superrep elif self.to_.size == 1: self.issuper = self.from_.issuper self.type = 'operator-bra' if self.issuper else 'bra' self.superrep = self.from_.superrep elif self.from_ == self.to_: self.issuper = self.from_.issuper self.type = 'super' if self.issuper else 'oper' self.superrep = self.from_.superrep self.issquare = True else: if from_.issuper != to_.issuper: raise NotImplementedError( "Operator with both space and superspace dimensions are " "not supported. Please open an issue if you have an use " f"case for these: {from_}, {to_}]" ) self.type = 'super' if self.from_.issuper else 'oper' if self.from_.superrep == self.to_.superrep: self.superrep = self.from_.superrep else: self.superrep = 'mixed' self.__setitem__ = _frozen def __eq__(self, other: "Dimensions") -> bool: if isinstance(other, Dimensions): return ( self is other or ( self.to_ == other.to_ and self.from_ == other.from_ ) ) return NotImplemented def __ne__(self, other: "Dimensions") -> bool: if isinstance(other, Dimensions): return not ( self is other or ( self.to_ == other.to_ and self.from_ == other.from_ ) ) return NotImplemented def __matmul__(self, other: "Dimensions") -> "Dimensions": if self.from_ != other.to_: raise TypeError(f"incompatible dimensions {self} and {other}") args = other.from_, self.to_ if args in Dimensions._stored_dims: return Dimensions._stored_dims[args] return Dimensions(*args) def __hash__(self): return hash((self.to_, self.from_)) def __repr__(self) -> str: return f"Dimensions({repr(self.from_)}, {repr(self.to_)})" def __str__(self) -> str: return str(self.as_list()) def as_list(self) -> list: """ Return the list representation of the Dimensions object. """ return [self.to_.as_list(), self.from_.as_list()] def __getitem__(self, key: Literal[0, 1]) -> Space: if key == 0: return self.to_ elif key == 1: return self.from_ raise IndexError("Dimensions index out of range") def dims2idx(self, dims): """ Transform dimensions indices to full array indices. """ return self.to_.dims2idx(dims[0]), self.from_.dims2idx(dims[1]) def idx2dims(self, idxl, idxr): """ Transform full array indices to dimensions indices. """ return [self.to_.idx2dims(idxl), self.from_.idx2dims(idxr)] def step(self) -> list[list[int]]: """ Get the step in the array between for each dimensions index. If element ``[i, j, k]`` is ``ket.full()[m, 0]`` then element ``[i, j+1, k]`` is ``ket.full()[m + ket._dims.step()[1], 0]``. """ return [self.to_.step(), self.from_.step()] def flat(self) -> list[list[int]]: """ Dimensions as a flat list. """ return [self.to_.flat(), self.from_.flat()] def _get_tensor_shape(self): """ Get the shape to of the Nd tensor with one dimensions for each Dimension index. The order of the space values are not in the order of the Dimension index. """ # dims_to_tensor_shape stepl = self.to_.step() flatl = self.to_.flat() stepr = self.from_.step() flatr = self.from_.flat() return tuple(np.concatenate([ np.array(flatl)[np.argsort(stepl)[::-1]], np.array(flatr)[np.argsort(stepr)[::-1]], ])) def _get_tensor_perm(self): """ Get the permutation of a tensor created using ``_get_tensor_shape`` to reorder the tensor dimensions with those of the Dimensions object. """ # dims_to_tensor_perm stepl = self.to_.step() stepr = self.from_.step() return list(np.argsort(np.concatenate([ np.argsort(stepl)[::-1], np.argsort(stepr)[::-1] + len(stepl) ]))) def remove(self, idx: int | list[int]) -> "Dimensions": """ Remove a Space from a Dimensons or complex Space. ``Space([2, 3, 4]).remove(1) == Space([2, 4])`` """ if not isinstance(idx, list): idx = [idx] if not idx: return self idx = sorted(idx) n_indices = len(self.to_.flat()) idx_to = [i for i in idx if i < n_indices] idx_from = [i-n_indices for i in idx if i >= n_indices] return Dimensions( self.from_.remove(idx_from), self.to_.remove(idx_to), ) def replace(self, idx: int, new: int) -> "Dimensions": """ Reshape a Space from a Dimensons or complex Space. ``Space([2, 3, 4]).replace(1, 5) == Space([2, 5, 4])`` """ n_indices = len(self.to_.flat()) if idx < n_indices: new_to = self.to_.replace(idx, new) new_from = self.from_ else: new_to = self.to_ new_from = self.from_.replace(idx-n_indices, new) return Dimensions(new_from, new_to) def replace_superrep(self, super_rep: str) -> "Dimensions": if not self.issuper and super_rep is not None: raise TypeError("Can't set a superrep of a non super object.") return Dimensions( self.from_.replace_superrep(super_rep), self.to_.replace_superrep(super_rep) ) def scalar_like(self) -> "Dimensions": return Dimensions([self.to_.scalar_like(), self.from_.scalar_like()]) qutip-5.1.1/qutip/core/energy_restricted.py000066400000000000000000000223451474175217300210660ustar00rootroot00000000000000from .dimensions import Space from .states import state_number_enumerate from . import data as _data from . import Qobj, qdiags import numpy as np import scipy.sparse from .. import settings __all__ = ['enr_state_dictionaries', 'enr_fock', 'enr_thermal_dm', 'enr_destroy', 'enr_identity'] def enr_state_dictionaries(dims, excitations): """ Return the number of states, and lookup-dictionaries for translating a state tuple to a state index, and vice versa, for a system with a given number of components and maximum number of excitations. Parameters ---------- dims: list A list with the number of states in each sub-system. excitations : integer The maximum numbers of dimension Returns ------- nstates, state2idx, idx2state: integer, dict, dict The number of states `nstates`, a dictionary for looking up state indices from a state tuple, and a dictionary for looking up state state tuples from state indices. state2idx and idx2state are reverses of each other, i.e., ``state2idx[idx2state[idx]] = idx`` and ``idx2state[state2idx[state]] = state``. """ nstates = 0 state2idx = {} idx2state = {} for state in state_number_enumerate(dims, excitations): state2idx[state] = nstates idx2state[nstates] = state nstates += 1 return nstates, state2idx, idx2state class EnrSpace(Space): _stored_dims = {} def __init__(self, dims, excitations): self.dims = tuple(dims) self.n_excitations = excitations enr_dicts = enr_state_dictionaries(dims, excitations) self.size, self.state2idx, self.idx2state = enr_dicts self.issuper = False self.superrep = None self._pure_dims = False def __eq__(self, other): return ( self is other or ( type(other) is type(self) and self.dims == other.dims and self.n_excitations == other.n_excitations ) ) def __hash__(self): return hash((self.dims, self.n_excitations)) def __repr__(self): return f"EnrSpace({self.dims}, {self.n_excitations})" def as_list(self): return list(self.dims) def dims2idx(self, dims): return self.state2idx[tuple(dims)] def idx2dims(self, idx): return self.idx2state[idx] def enr_fock(dims, excitations, state, *, dtype=None): """ Generate the Fock state representation in a excitation-number restricted state space. The `dims` argument is a list of integers that define the number of quantums states of each component of a composite quantum system, and the `excitations` specifies the maximum number of excitations for the basis states that are to be included in the state space. The `state` argument is a tuple of integers that specifies the state (in the number basis representation) for which to generate the Fock state representation. Parameters ---------- dims : list A list of the dimensions of each subsystem of a composite quantum system. excitations : integer The maximum number of excitations that are to be included in the state space. state : list of integers The state in the number basis representation. dtype : type or str, optional Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- ket : Qobj A Qobj instance that represent a Fock state in the exication-number- restricted state space defined by `dims` and `exciations`. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense nstates, state2idx, _ = enr_state_dictionaries(dims, excitations) try: data = _data.one_element[dtype]( (nstates, 1), (state2idx[tuple(state)], 0), 1 ) except KeyError: msg = ( "state tuple " + str(tuple(state)) + " is not in the restricted state space." ) raise ValueError(msg) from None return Qobj(data, dims=[EnrSpace(dims, excitations), [1]*len(dims)], copy=False) def enr_thermal_dm(dims, excitations, n, *, dtype=None): """ Generate the density operator for a thermal state in the excitation-number- restricted state space defined by the `dims` and `exciations` arguments. See the documentation for enr_fock for a more detailed description of these arguments. The temperature of each mode in dims is specified by the average number of excitatons `n`. Parameters ---------- dims : list A list of the dimensions of each subsystem of a composite quantum system. excitations : integer The maximum number of excitations that are to be included in the state space. n : integer The average number of exciations in the thermal state. `n` can be a float (which then applies to each mode), or a list/array of the same length as dims, in which each element corresponds specifies the temperature of the corresponding mode. dtype : type or str, optional Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- dm : Qobj Thermal state density matrix. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR nstates, _, idx2state = enr_state_dictionaries(dims, excitations) enr_dims = [EnrSpace(dims, excitations)] * 2 if not isinstance(n, (list, np.ndarray)): n = np.ones(len(dims)) * n else: n = np.asarray(n) diags = [np.prod((n / (n + 1)) ** np.array(state)) for idx, state in idx2state.items()] diags /= np.sum(diags) out = qdiags(diags, 0, dims=enr_dims, shape=(nstates, nstates), dtype=dtype) out._isherm = True return out def enr_destroy(dims, excitations, *, dtype=None): """ Generate annilation operators for modes in a excitation-number-restricted state space. For example, consider a system consisting of 4 modes, each with 5 states. The total hilbert space size is 5**4 = 625. If we are only interested in states that contain up to 2 excitations, we only need to include states such as (0, 0, 0, 0) (0, 0, 0, 1) (0, 0, 0, 2) (0, 0, 1, 0) (0, 0, 1, 1) (0, 0, 2, 0) ... This function creates annihilation operators for the 4 modes that act within this state space: a1, a2, a3, a4 = enr_destroy([5, 5, 5, 5], excitations=2) From this point onwards, the annihiltion operators a1, ..., a4 can be used to setup a Hamiltonian, collapse operators and expectation-value operators, etc., following the usual pattern. Parameters ---------- dims : list A list of the dimensions of each subsystem of a composite quantum system. excitations : integer The maximum number of excitations that are to be included in the state space. dtype : type or str, optional Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- a_ops : list of qobj A list of annihilation operators for each mode in the composite quantum system described by dims. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR nstates, state2idx, idx2state = enr_state_dictionaries(dims, excitations) enr_dims = [EnrSpace(dims, excitations)] * 2 a_ops = [scipy.sparse.lil_matrix((nstates, nstates), dtype=np.complex128) for _ in dims] for n1, state1 in idx2state.items(): for idx, s in enumerate(state1): # if s > 0, the annihilation operator of mode idx has a non-zero # entry with one less excitation in mode idx in the final state if s > 0: state2 = state1[:idx] + (s-1,) + state1[idx+1:] n2 = state2idx[state2] a_ops[idx][n2, n1] = np.sqrt(s) return [ Qobj(a, dims=enr_dims, isunitary=False, isherm=False).to(dtype) for a in a_ops ] def enr_identity(dims, excitations, *, dtype=None): """ Generate the identity operator for the excitation-number restricted state space defined by the `dims` and `exciations` arguments. See the docstring for enr_fock for a more detailed description of these arguments. Parameters ---------- dims : list A list of the dimensions of each subsystem of a composite quantum system. excitations : integer The maximum number of excitations that are to be included in the state space. dtype : type or str, optional Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- op : Qobj A Qobj instance that represent the identity operator in the exication-number-restricted state space defined by `dims` and `exciations`. """ dtype = dtype or settings.core["default_dtype"] or _data.Dia dims = EnrSpace(dims, excitations) return Qobj(_data.identity[dtype](dims.size), dims=[dims, dims], isherm=True, isunitary=True, copy=False) qutip-5.1.1/qutip/core/environment.py000066400000000000000000002733161474175217300177170ustar00rootroot00000000000000""" Classes that describe environments of open quantum systems """ # Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations __all__ = ['BosonicEnvironment', 'DrudeLorentzEnvironment', 'UnderDampedEnvironment', 'OhmicEnvironment', 'ExponentialBosonicEnvironment', 'FermionicEnvironment', 'LorentzianEnvironment', 'ExponentialFermionicEnvironment', 'CFExponent', 'system_terminator'] import abc import enum from time import time from typing import Any, Callable, Literal, Sequence, overload import warnings import numpy as np from numpy.typing import ArrayLike from scipy.linalg import eigvalsh from scipy.interpolate import CubicSpline try: from mpmath import mp _mpmath_available = True except ModuleNotFoundError: _mpmath_available = False from ..utilities import (n_thermal, iterated_fit) from .superoperator import spre, spost from .qobj import Qobj class BosonicEnvironment(abc.ABC): """ The bosonic environment of an open quantum system. It is characterized by its spectral density and temperature or, equivalently, its power spectrum or its two-time auto-correlation function. Use one of the classmethods :meth:`from_spectral_density`, :meth:`from_power_spectrum` or :meth:`from_correlation_function` to construct an environment manually from one of these characteristic functions, or use a predefined sub-class such as the :class:`DrudeLorentzEnvironment`, the :class:`UnderDampedEnvironment` or the :class:`OhmicEnvironment`. Bosonic environments offer various ways to approximate the environment with a multi-exponential correlation function, which can be used for example in the HEOM solver. The approximated environment is represented as a :class:`ExponentialBosonicEnvironment`. All bosonic environments can be approximated by directly fitting their correlation function with a multi-exponential ansatz (:meth:`approx_by_cf_fit`) or by fitting their spectral density with a sum of Lorentzians (:meth:`approx_by_sd_fit`), which correspond to underdamped environments with known multi-exponential decompositions. Subclasses may offer additional approximation methods such as :meth:`DrudeLorentzEnvironment.approx_by_matsubara` or :meth:`DrudeLorentzEnvironment.approx_by_pade` in the case of a Drude-Lorentz environment. Parameters ---------- T : optional, float The temperature of this environment. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__(self, T: float = None, tag: Any = None): self.T = T self.tag = tag @abc.abstractmethod def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ The spectral density of this environment. For negative frequencies, a value of zero will be returned. See the Users Guide on :ref:`bosonic environments ` for specifics on the definitions used by QuTiP. If no analytical expression for the spectral density is known, it will be derived from the power spectrum. In this case, the temperature of this environment must be specified. If no analytical expression for the power spectrum is known either, it will be derived from the correlation function via a fast fourier transform. Parameters ---------- w : array_like or float The frequencies at which to evaluate the spectral density. """ ... @abc.abstractmethod def correlation_function( self, t: float | ArrayLike, *, eps: float = 1e-10 ) -> (float | ArrayLike): """ The two-time auto-correlation function of this environment. See the Users Guide on :ref:`bosonic environments ` for specifics on the definitions used by QuTiP. If no analytical expression for the correlation function is known, it will be derived from the power spectrum via a fast fourier transform. If no analytical expression for the power spectrum is known either, it will be derived from the spectral density. In this case, the temperature of this environment must be specified. Parameters ---------- t : array_like or float The times at which to evaluate the correlation function. eps : optional, float Used in case the power spectrum is derived from the spectral density; see the documentation of :meth:`BosonicEnvironment.power_spectrum`. """ ... @abc.abstractmethod def power_spectrum( self, w: float | ArrayLike, *, eps: float = 1e-10 ) -> (float | ArrayLike): """ The power spectrum of this environment. See the Users Guide on :ref:`bosonic environments ` for specifics on the definitions used by QuTiP. If no analytical expression for the power spectrum is known, it will be derived from the spectral density. In this case, the temperature of this environment must be specified. If no analytical expression for the spectral density is known either, the power spectrum will instead be derived from the correlation function via a fast fourier transform. Parameters ---------- w : array_like or float The frequencies at which to evaluate the power spectrum. eps : optional, float To derive the zero-frequency power spectrum from the spectral density, the spectral density must be differentiated numerically. In that case, this parameter is used as the finite difference in the numerical differentiation. """ ... # --- user-defined environment creation @classmethod def from_correlation_function( cls, C: Callable[[float], complex] | ArrayLike, tlist: ArrayLike = None, tMax: float = None, *, T: float = None, tag: Any = None, args: dict[str, Any] = None, ) -> BosonicEnvironment: r""" Constructs a bosonic environment from the provided correlation function. The provided function will only be used for times :math:`t \geq 0`. At times :math:`t < 0`, the symmetry relation :math:`C(-t) = C(t)^\ast` is enforced. Parameters ---------- C : callable or array_like The correlation function. Can be provided as a Python function or as an array. When using a function, the signature should be ``C(t: array_like, **args) -> array_like`` where ``t`` is time and ``args`` is a dict containing the other parameters of the function. tlist : optional, array_like The times where the correlation function is sampled (if it is provided as an array). tMax : optional, float Specifies that the correlation function is essentially zero outside the interval [-tMax, tMax]. Used for numerical integration purposes. T : optional, float Environment temperature. (The spectral density of this environment can only be calculated from the correlation function if a temperature is provided.) tag : optional, str, tuple or any other object An identifier (name) for this environment. args : optional, dict Extra arguments for the correlation function ``C``. """ return _BosonicEnvironment_fromCF(C, tlist, tMax, T, tag, args) @classmethod def from_power_spectrum( cls, S: Callable[[float], float] | ArrayLike, wlist: ArrayLike = None, wMax: float = None, *, T: float = None, tag: Any = None, args: dict[str, Any] = None, ) -> BosonicEnvironment: r""" Constructs a bosonic environment with the provided power spectrum. Parameters ---------- S : callable or array_like The power spectrum. Can be provided as a Python function or as an array. When using a function, the signature should be ``S(w: array_like, **args) -> array_like`` where ``w`` is the frequency and ``args`` is a dict containing the other parameters of the function. wlist : optional, array_like The frequencies where the power spectrum is sampled (if it is provided as an array). wMax : optional, float Specifies that the power spectrum is essentially zero outside the interval [-wMax, wMax]. Used for numerical integration purposes. T : optional, float Environment temperature. (The spectral density of this environment can only be calculated from the powr spectrum if a temperature is provided.) tag : optional, str, tuple or any other object An identifier (name) for this environment. args : optional, dict Extra arguments for the power spectrum ``S``. """ return _BosonicEnvironment_fromPS(S, wlist, wMax, T, tag, args) @classmethod def from_spectral_density( cls, J: Callable[[float], float] | ArrayLike, wlist: ArrayLike = None, wMax: float = None, *, T: float = None, tag: Any = None, args: dict[str, Any] = None, ) -> BosonicEnvironment: r""" Constructs a bosonic environment with the provided spectral density. The provided function will only be used for frequencies :math:`\omega > 0`. At frequencies :math:`\omega \leq 0`, the spectral density is zero according to the definition used by QuTiP. See the Users Guide on :ref:`bosonic environments ` for a note on spectral densities with support at negative frequencies. Parameters ---------- J : callable or array_like The spectral density. Can be provided as a Python function or as an array. When using a function, the signature should be ``J(w: array_like, **args) -> array_like`` where ``w`` is the frequency and ``args`` is a tuple containing the other parameters of the function. wlist : optional, array_like The frequencies where the spectral density is sampled (if it is provided as an array). wMax : optional, float Specifies that the spectral density is essentially zero outside the interval [-wMax, wMax]. Used for numerical integration purposes. T : optional, float Environment temperature. (The correlation function and the power spectrum of this environment can only be calculated from the spectral density if a temperature is provided.) tag : optional, str, tuple or any other object An identifier (name) for this environment. args : optional, dict Extra arguments for the spectral density ``S``. """ return _BosonicEnvironment_fromSD(J, wlist, wMax, T, tag, args) # --- spectral density, power spectrum, correlation function conversions def _ps_from_sd(self, w, eps, derivative=None): # derivative: value of J'(0) if self.T is None: raise ValueError( "The temperature must be specified for this operation.") w = np.asarray(w, dtype=float) if self.T == 0: return 2 * np.heaviside(w, 0) * self.spectral_density(w) # at zero frequency, we do numerical differentiation # S(0) = 2 J'(0) / beta zero_mask = (w == 0) nonzero_mask = np.invert(zero_mask) S = np.zeros_like(w) if derivative is None: S[zero_mask] = 2 * self.T * self.spectral_density(eps) / eps else: S[zero_mask] = 2 * self.T * derivative S[nonzero_mask] = ( 2 * np.sign(w[nonzero_mask]) * self.spectral_density(np.abs(w[nonzero_mask])) * (n_thermal(w[nonzero_mask], self.T) + 1) ) return S.item() if w.ndim == 0 else S def _sd_from_ps(self, w): w = np.asarray(w, dtype=float) J = np.zeros_like(w) positive_mask = (w > 0) power_spectrum = self.power_spectrum(w[positive_mask]) if self.T is None: raise ValueError( "The temperature must be specified for this operation.") J[positive_mask] = ( power_spectrum / 2 / (n_thermal(w[positive_mask], self.T) + 1) ) return J.item() if w.ndim == 0 else J def _ps_from_cf(self, w, tMax): w = np.asarray(w, dtype=float) if w.ndim == 0: wMax = np.abs(w) elif len(w) == 0: return np.array([]) else: wMax = max(np.abs(w[0]), np.abs(w[-1])) mirrored_result = _fft(self.correlation_function, wMax, tMax=tMax) result = np.real(mirrored_result(-w)) return result.item() if w.ndim == 0 else result def _cf_from_ps(self, t, wMax, **ps_kwargs): t = np.asarray(t, dtype=float) if t.ndim == 0: tMax = np.abs(t) elif len(t) == 0: return np.array([]) else: tMax = max(np.abs(t[0]), np.abs(t[-1])) result_fct = _fft(lambda w: self.power_spectrum(w, **ps_kwargs), tMax, tMax=wMax) result = result_fct(t) / (2 * np.pi) return result.item() if t.ndim == 0 else result # --- fitting def approx_by_cf_fit( self, tlist: ArrayLike, target_rsme: float = 2e-5, Nr_max: int = 10, Ni_max: int = 10, guess: list[float] = None, lower: list[float] = None, upper: list[float] = None, sigma: float | ArrayLike = None, maxfev: int = None, full_ansatz: bool = False, combine: bool = True, tag: Any = None, ) -> tuple[ExponentialBosonicEnvironment, dict[str, Any]]: r""" Generates an approximation to this environment by fitting its correlation function with a multi-exponential ansatz. The number of exponents is determined iteratively based on reducing the normalized root mean squared error below a given threshold. Specifically, the real and imaginary parts are fit by the following model functions: .. math:: \operatorname{Re}[C(t)] = \sum_{k=1}^{N_r} \operatorname{Re}\Bigl[ (a_k + \mathrm i d_k) \mathrm e^{(b_k + \mathrm i c_k) t}\Bigl] , \\ \operatorname{Im}[C(t)] = \sum_{k=1}^{N_i} \operatorname{Im}\Bigl[ (a'_k + \mathrm i d'_k) \mathrm e^{(b'_k + \mathrm i c'_k) t} \Bigr]. If the parameter `full_ansatz` is `False`, :math:`d_k` and :math:`d'_k` are set to zero and the model functions simplify to .. math:: \operatorname{Re}[C(t)] = \sum_{k=1}^{N_r} a_k e^{b_k t} \cos(c_{k} t) , \\ \operatorname{Im}[C(t)] = \sum_{k=1}^{N_i} a'_k e^{b'_k t} \sin(c'_{k} t) . The simplified version offers faster fits, however it fails for anomalous spectral densities with :math:`\operatorname{Im}[C(0)] \neq 0` as :math:`\sin(0) = 0`. Parameters ---------- tlist : array_like The time range on which to perform the fit. target_rmse : optional, float Desired normalized root mean squared error (default `2e-5`). Can be set to `None` to perform only one fit using the maximum number of modes (`Nr_max`, `Ni_max`). Nr_max : optional, int The maximum number of modes to use for the fit of the real part (default 10). Ni_max : optional, int The maximum number of modes to use for the fit of the imaginary part (default 10). guess : optional, list of float Initial guesses for the parameters :math:`a_k`, :math:`b_k`, etc. The same initial guesses are used for all values of k, and for the real and imaginary parts. If `full_ansatz` is True, `guess` is a list of size 4, otherwise, it is a list of size 3. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. lower : optional, list of float Lower bounds for the parameters :math:`a_k`, :math:`b_k`, etc. The same lower bounds are used for all values of k, and for the real and imaginary parts. If `full_ansatz` is True, `lower` is a list of size 4, otherwise, it is a list of size 3. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. upper : optional, list of float Upper bounds for the parameters :math:`a_k`, :math:`b_k`, etc. The same upper bounds are used for all values of k, and for the real and imaginary parts. If `full_ansatz` is True, `upper` is a list of size 4, otherwise, it is a list of size 3. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. sigma : optional, float or list of float Adds an uncertainty to the correlation function of the environment, i.e., adds a leeway to the fit. This parameter is useful to adjust if the correlation function is very small in parts of the time range. For more details, see the documentation of ``scipy.optimize.curve_fit``. maxfev : optional, int Number of times the parameters of the fit are allowed to vary during the optimization (per fit). full_ansatz : optional, bool (default False) If this is set to False, the parameters :math:`d_k` are all set to zero. The full ansatz, including :math:`d_k`, usually leads to significantly slower fits, and some manual tuning of the `guesses`, `lower` and `upper` is usually needed. On the other hand, the full ansatz can lead to better fits with fewer exponents, especially for anomalous spectral densities with :math:`\operatorname{Im}[C(0)] \neq 0` for which the simplified ansatz will always give :math:`\operatorname{Im}[C(0)] = 0`. When using the full ansatz with default values for the guesses and bounds, if the fit takes too long, we recommend choosing guesses and bounds manually. combine : optional, bool (default True) Whether to combine exponents with the same frequency. See :meth:`combine <.ExponentialBosonicEnvironment.combine>` for details. tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- approx_env : :class:`ExponentialBosonicEnvironment` The approximated environment with multi-exponential correlation function. fit_info : dictionary A dictionary containing the following information about the fit. "Nr" The number of terms used to fit the real part of the correlation function. "Ni" The number of terms used to fit the imaginary part of the correlation function. "fit_time_real" The time the fit of the real part of the correlation function took in seconds. "fit_time_imag" The time the fit of the imaginary part of the correlation function took in seconds. "rmse_real" Normalized mean squared error obtained in the fit of the real part of the correlation function. "rmse_imag" Normalized mean squared error obtained in the fit of the imaginary part of the correlation function. "params_real" The fitted parameters (array of shape Nx3 or Nx4) for the real part of the correlation function. "params_imag" The fitted parameters (array of shape Nx3 or Nx4) for the imaginary part of the correlation function. "summary" A string that summarizes the information about the fit. """ # Process arguments if tag is None and self.tag is not None: tag = (self.tag, "CF Fit") if full_ansatz: num_params = 4 else: num_params = 3 if target_rsme is None: target_rsme = 0 Nr_min, Ni_min = Nr_max, Ni_max else: Nr_min, Ni_min = 1, 1 clist = self.correlation_function(tlist) if guess is None and lower is None and upper is None: guess_re, lower_re, upper_re = _default_guess_cfreal( tlist, np.real(clist), full_ansatz) guess_im, lower_im, upper_im = _default_guess_cfimag( np.imag(clist), full_ansatz) else: guess_re, lower_re, upper_re = guess, lower, upper guess_im, lower_im, upper_im = guess, lower, upper # Fit real part start_real = time() rmse_real, params_real = iterated_fit( _cf_real_fit_model, num_params, tlist, np.real(clist), target_rsme, Nr_min, Nr_max, guess=guess_re, lower=lower_re, upper=upper_re, sigma=sigma, maxfev=maxfev ) end_real = time() fit_time_real = end_real - start_real # Fit imaginary part start_imag = time() rmse_imag, params_imag = iterated_fit( _cf_imag_fit_model, num_params, tlist, np.imag(clist), target_rsme, Ni_min, Ni_max, guess=guess_im, lower=lower_im, upper=upper_im, sigma=sigma, maxfev=maxfev ) end_imag = time() fit_time_imag = end_imag - start_imag # Generate summary Nr = len(params_real) Ni = len(params_imag) full_summary = _cf_fit_summary( params_real, params_imag, fit_time_real, fit_time_imag, Nr, Ni, rmse_real, rmse_imag, n=num_params ) fit_info = {"Nr": Nr, "Ni": Ni, "fit_time_real": fit_time_real, "fit_time_imag": fit_time_imag, "rmse_real": rmse_real, "rmse_imag": rmse_imag, "params_real": params_real, "params_imag": params_imag, "summary": full_summary} # Finally, generate environment and return ckAR = [] vkAR = [] for term in params_real: if full_ansatz: a, b, c, d = term else: a, b, c = term d = 0 ckAR.extend([(a + 1j * d) / 2, (a - 1j * d) / 2]) vkAR.extend([-b - 1j * c, -b + 1j * c]) ckAI = [] vkAI = [] for term in params_imag: if full_ansatz: a, b, c, d = term else: a, b, c = term d = 0 ckAI.extend([-1j * (a + 1j * d) / 2, 1j * (a - 1j * d) / 2]) vkAI.extend([-b - 1j * c, -b + 1j * c]) approx_env = ExponentialBosonicEnvironment( ckAR, vkAR, ckAI, vkAI, combine=combine, T=self.T, tag=tag) return approx_env, fit_info def approx_by_sd_fit( self, wlist: ArrayLike, Nk: int = 1, target_rmse: float = 5e-6, Nmax: int = 10, guess: list[float] = None, lower: list[float] = None, upper: list[float] = None, sigma: float | ArrayLike = None, maxfev: int = None, combine: bool = True, tag: Any = None, ) -> tuple[ExponentialBosonicEnvironment, dict[str, Any]]: r""" Generates an approximation to this environment by fitting its spectral density with a sum of underdamped terms. Each underdamped term effectively acts like an underdamped environment. We use the known exponential decomposition of the underdamped environment, keeping `Nk` Matsubara terms for each. The number of underdamped terms is determined iteratively based on reducing the normalized root mean squared error below a given threshold. Specifically, the spectral density is fit by the following model function: .. math:: J(\omega) = \sum_{k=1}^{N} \frac{2 a_k b_k \omega}{\left(\left( \omega + c_k \right)^2 + b_k^2 \right) \left(\left( \omega - c_k \right)^2 + b_k^2 \right)} Parameters ---------- wlist : array_like The frequency range on which to perform the fit. Nk : optional, int The number of Matsubara terms to keep in each mode (default 1). target_rmse : optional, float Desired normalized root mean squared error (default `5e-6`). Can be set to `None` to perform only one fit using the maximum number of modes (`Nmax`). Nmax : optional, int The maximum number of modes to use for the fit (default 10). guess : optional, list of float Initial guesses for the parameters :math:`a_k`, :math:`b_k` and :math:`c_k`. The same initial guesses are used for all values of k. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. lower : optional, list of float Lower bounds for the parameters :math:`a_k`, :math:`b_k` and :math:`c_k`. The same lower bounds are used for all values of k. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. upper : optional, list of float Upper bounds for the parameters :math:`a_k`, :math:`b_k` and :math:`c_k`. The same upper bounds are used for all values of k. If none of `guess`, `lower` and `upper` are provided, these parameters will be chosen automatically. sigma : optional, float or list of float Adds an uncertainty to the spectral density of the environment, i.e., adds a leeway to the fit. This parameter is useful to adjust if the spectral density is very small in parts of the frequency range. For more details, see the documentation of ``scipy.optimize.curve_fit``. maxfev : optional, int Number of times the parameters of the fit are allowed to vary during the optimization (per fit). combine : optional, bool (default True) Whether to combine exponents with the same frequency. See :meth:`combine <.ExponentialBosonicEnvironment.combine>` for details. tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- approx_env : :class:`ExponentialBosonicEnvironment` The approximated environment with multi-exponential correlation function. fit_info : dictionary A dictionary containing the following information about the fit. "N" The number of underdamped terms used in the fit. "Nk" The number of Matsubara modes included per underdamped term. "fit_time" The time the fit took in seconds. "rmse" Normalized mean squared error obtained in the fit. "params" The fitted parameters (array of shape Nx3). "summary" A string that summarizes the information about the fit. """ # Process arguments if tag is None and self.tag is not None: tag = (self.tag, "SD Fit") if target_rmse is None: target_rmse = 0 Nmin = Nmax else: Nmin = 1 jlist = self.spectral_density(wlist) if guess is None and lower is None and upper is None: guess, lower, upper = _default_guess_sd(wlist, jlist) # Fit start = time() rmse, params = iterated_fit( _sd_fit_model, 3, wlist, jlist, target_rmse, Nmin, Nmax, guess=guess, lower=lower, upper=upper, sigma=sigma, maxfev=maxfev ) end = time() fit_time = end - start # Generate summary N = len(params) summary = _fit_summary( fit_time, rmse, N, "the spectral density", params ) fit_info = { "N": N, "Nk": Nk, "fit_time": fit_time, "rmse": rmse, "params": params, "summary": summary} ckAR, vkAR, ckAI, vkAI = [], [], [], [] # Finally, generate environment and return for a, b, c in params: lam = np.sqrt(a + 0j) gamma = 2 * b w0 = np.sqrt(c**2 + b**2) env = UnderDampedEnvironment(self.T, lam, gamma, w0) coeffs = env._matsubara_params(Nk) ckAR.extend(coeffs[0]) vkAR.extend(coeffs[1]) ckAI.extend(coeffs[2]) vkAI.extend(coeffs[3]) approx_env = ExponentialBosonicEnvironment( ckAR, vkAR, ckAI, vkAI, combine=combine, T=self.T, tag=tag) return approx_env, fit_info class _BosonicEnvironment_fromCF(BosonicEnvironment): def __init__(self, C, tlist, tMax, T, tag, args): super().__init__(T, tag) self._cf = _complex_interpolation( C, tlist, 'correlation function', args) if tlist is not None: self.tMax = max(np.abs(tlist[0]), np.abs(tlist[-1])) else: self.tMax = tMax def correlation_function(self, t, **kwargs): t = np.asarray(t, dtype=float) result = np.zeros_like(t, dtype=complex) positive_mask = (t >= 0) non_positive_mask = np.invert(positive_mask) result[positive_mask] = self._cf(t[positive_mask]) result[non_positive_mask] = np.conj( self._cf(-t[non_positive_mask]) ) return result.item() if t.ndim == 0 else result def spectral_density(self, w): return self._sd_from_ps(w) def power_spectrum(self, w, **kwargs): if self.tMax is None: raise ValueError('The support of the correlation function (tMax) ' 'must be specified for this operation.') return self._ps_from_cf(w, self.tMax) class _BosonicEnvironment_fromPS(BosonicEnvironment): def __init__(self, S, wlist, wMax, T, tag, args): super().__init__(T, tag) self._ps = _real_interpolation(S, wlist, 'power spectrum', args) if wlist is not None: self.wMax = max(np.abs(wlist[0]), np.abs(wlist[-1])) else: self.wMax = wMax def correlation_function(self, t, **kwargs): if self.wMax is None: raise ValueError('The support of the power spectrum (wMax) ' 'must be specified for this operation.') return self._cf_from_ps(t, self.wMax) def spectral_density(self, w): return self._sd_from_ps(w) def power_spectrum(self, w, **kwargs): w = np.asarray(w, dtype=float) ps = self._ps(w) return ps.item() if w.ndim == 0 else self._ps(w) class _BosonicEnvironment_fromSD(BosonicEnvironment): def __init__(self, J, wlist, wMax, T, tag, args): super().__init__(T, tag) self._sd = _real_interpolation(J, wlist, 'spectral density', args) if wlist is not None: self.wMax = max(np.abs(wlist[0]), np.abs(wlist[-1])) else: self.wMax = wMax def correlation_function(self, t, *, eps=1e-10): if self.T is None: raise ValueError('The temperature must be specified for this ' 'operation.') if self.wMax is None: raise ValueError('The support of the spectral density (wMax) ' 'must be specified for this operation.') return self._cf_from_ps(t, self.wMax, eps=eps) def spectral_density(self, w): w = np.asarray(w, dtype=float) result = np.zeros_like(w) positive_mask = (w > 0) result[positive_mask] = self._sd(w[positive_mask]) return result.item() if w.ndim == 0 else result def power_spectrum(self, w, *, eps=1e-10): return self._ps_from_sd(w, eps) class DrudeLorentzEnvironment(BosonicEnvironment): r""" Describes a Drude-Lorentz bosonic environment with the spectral density .. math:: J(\omega) = \frac{2 \lambda \gamma \omega}{\gamma^{2}+\omega^{2}} (see Eq. 15 in [BoFiN23]_). Parameters ---------- T : float Environment temperature. lam : float Coupling strength. gamma : float Spectral density cutoff frequency. Nk : optional, int, defaults to 10 The number of Pade exponents to be used for the calculation of the correlation function. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__( self, T: float, lam: float, gamma: float, *, Nk: int = 10, tag: Any = None ): super().__init__(T, tag) self.lam = lam self.gamma = gamma self.Nk = Nk def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ Calculates the Drude-Lorentz spectral density. Parameters ---------- w : array_like or float Energy of the mode. """ w = np.asarray(w, dtype=float) result = np.zeros_like(w) positive_mask = (w > 0) w_mask = w[positive_mask] result[positive_mask] = ( 2 * self.lam * self.gamma * w_mask / (self.gamma**2 + w_mask**2) ) return result.item() if w.ndim == 0 else result def correlation_function( self, t: float | ArrayLike, Nk: int = None, **kwargs ) -> (float | ArrayLike): """ Calculates the two-time auto-correlation function of the Drude-Lorentz environment. The calculation is performed by summing a large number of exponents of the Pade expansion. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. Nk : int, optional The number of exponents to use. If not provided, then the value that was provided when the class was instantiated is used. """ if self.T == 0: raise ValueError("The Drude-Lorentz correlation function diverges " "at zero temperature.") t = np.asarray(t, dtype=float) abs_t = np.abs(t) Nk = Nk or self.Nk ck_real, vk_real, ck_imag, vk_imag = self._pade_params(Nk) def C(c, v): return np.sum([ck * np.exp(-np.asarray(vk * abs_t)) for ck, vk in zip(c, v)], axis=0) result = C(ck_real, vk_real) + 1j * C(ck_imag, vk_imag) result = np.asarray(result, dtype=complex) result[t < 0] = np.conj(result[t < 0]) return result.item() if t.ndim == 0 else result def power_spectrum( self, w: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Calculates the power spectrum of the Drude-Lorentz environment. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ sd_derivative = 2 * self.lam / self.gamma return self._ps_from_sd(w, None, sd_derivative) @overload def approx_by_matsubara( self, Nk: int, combine: bool = ..., compute_delta: Literal[False] = False, tag: Any = ... ) -> ExponentialBosonicEnvironment: ... @overload def approx_by_matsubara( self, Nk: int, combine: bool = ..., compute_delta: Literal[True] = True, tag: Any = ... ) -> tuple[ExponentialBosonicEnvironment, float]: ... def approx_by_matsubara( self, Nk, combine=True, compute_delta=False, tag=None ): """ Generates an approximation to this environment by truncating its Matsubara expansion. Parameters ---------- Nk : int Number of Matsubara terms to include. In total, the real part of the correlation function will include `Nk+1` terms and the imaginary part `1` term. combine : bool, default `True` Whether to combine exponents with the same frequency. compute_delta : bool, default `False` Whether to compute and return the approximation discrepancy (see below). tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- approx_env : :class:`ExponentialBosonicEnvironment` The approximated environment with multi-exponential correlation function. delta : float, optional The approximation discrepancy. That is, the difference between the true correlation function of the Drude-Lorentz environment and the sum of the ``Nk`` exponential terms is approximately ``2 * delta * dirac(t)``, where ``dirac(t)`` denotes the Dirac delta function. It can be used to create a "terminator" term to add to the system dynamics to take this discrepancy into account, see :func:`.system_terminator`. """ if self.T == 0: raise ValueError("The Drude-Lorentz correlation function diverges " "at zero temperature.") if tag is None and self.tag is not None: tag = (self.tag, "Matsubara Truncation") lists = self._matsubara_params(Nk) approx_env = ExponentialBosonicEnvironment( *lists, T=self.T, combine=combine, tag=tag) if not compute_delta: return approx_env delta = 2 * self.lam * self.T / self.gamma - 1j * self.lam for exp in approx_env.exponents: delta -= exp.coefficient / exp.exponent return approx_env, delta @overload def approx_by_pade( self, Nk: int, combine: bool = ..., compute_delta: Literal[False] = False, tag: Any = ... ) -> ExponentialBosonicEnvironment: ... @overload def approx_by_pade( self, Nk: int, combine: bool = ..., compute_delta: Literal[True] = True, tag: Any = ... ) -> tuple[ExponentialBosonicEnvironment, float]: ... def approx_by_pade( self, Nk, combine=True, compute_delta=False, tag=None ): """ Generates an approximation to this environment by truncating its Pade expansion. Parameters ---------- Nk : int Number of Pade terms to include. In total, the real part of the correlation function will include `Nk+1` terms and the imaginary part `1` term. combine : bool, default `True` Whether to combine exponents with the same frequency. compute_delta : bool, default `False` Whether to compute and return the approximation discrepancy (see below). tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- approx_env : :class:`ExponentialBosonicEnvironment` The approximated environment with multi-exponential correlation function. delta : float, optional The approximation discrepancy. That is, the difference between the true correlation function of the Drude-Lorentz environment and the sum of the ``Nk`` exponential terms is approximately ``2 * delta * dirac(t)``, where ``dirac(t)`` denotes the Dirac delta function. It can be used to create a "terminator" term to add to the system dynamics to take this discrepancy into account, see :func:`.system_terminator`. """ if self.T == 0: raise ValueError("The Drude-Lorentz correlation function diverges " "at zero temperature.") if tag is None and self.tag is not None: tag = (self.tag, "Pade Truncation") ck_real, vk_real, ck_imag, vk_imag = self._pade_params(Nk) approx_env = ExponentialBosonicEnvironment( ck_real, vk_real, ck_imag, vk_imag, T=self.T, combine=combine, tag=tag ) if not compute_delta: return approx_env delta = 2 * self.lam * self.T / self.gamma - 1j * self.lam for exp in approx_env.exponents: delta -= exp.coefficient / exp.exponent return approx_env, delta def _pade_params(self, Nk): eta_p, gamma_p = self._corr(Nk) ck_real = [np.real(eta) for eta in eta_p] vk_real = [gam for gam in gamma_p] # There is only one term in the expansion of the imaginary part of the # Drude-Lorentz correlation function. ck_imag = [np.imag(eta_p[0])] vk_imag = [gamma_p[0]] return ck_real, vk_real, ck_imag, vk_imag def _matsubara_params(self, Nk): """ Calculate the Matsubara coefficients and frequencies. """ ck_real = [self.lam * self.gamma / np.tan(self.gamma / (2 * self.T))] ck_real.extend([ (8 * self.lam * self.gamma * self.T * np.pi * k * self.T / ((2 * np.pi * k * self.T)**2 - self.gamma**2)) for k in range(1, Nk + 1) ]) vk_real = [self.gamma] vk_real.extend([2 * np.pi * k * self.T for k in range(1, Nk + 1)]) ck_imag = [-self.lam * self.gamma] vk_imag = [self.gamma] return ck_real, vk_real, ck_imag, vk_imag # --- Pade approx calculation --- def _corr(self, Nk): kappa, epsilon = self._kappa_epsilon(Nk) eta_p = [self.lam * self.gamma * (self._cot(self.gamma / (2 * self.T)) - 1.0j)] gamma_p = [self.gamma] for ll in range(1, Nk + 1): eta_p.append( (kappa[ll] * self.T) * 4 * self.lam * self.gamma * (epsilon[ll] * self.T) / ((epsilon[ll]**2 * self.T**2) - self.gamma**2) ) gamma_p.append(epsilon[ll] * self.T) return eta_p, gamma_p def _cot(self, x): return 1. / np.tan(x) def _kappa_epsilon(self, Nk): eps = self._calc_eps(Nk) chi = self._calc_chi(Nk) kappa = [0] prefactor = 0.5 * Nk * (2 * (Nk + 1) + 1) for j in range(Nk): term = prefactor for k in range(Nk - 1): term *= ( (chi[k]**2 - eps[j]**2) / (eps[k]**2 - eps[j]**2 + self._delta(j, k)) ) for k in [Nk - 1]: term /= (eps[k]**2 - eps[j]**2 + self._delta(j, k)) kappa.append(term) epsilon = [0] + eps return kappa, epsilon def _delta(self, i, j): return 1.0 if i == j else 0.0 def _calc_eps(self, Nk): alpha = np.diag([ 1. / np.sqrt((2 * k + 5) * (2 * k + 3)) for k in range(2 * Nk - 1) ], k=1) alpha += alpha.transpose() evals = eigvalsh(alpha) eps = [-2. / val for val in evals[0: Nk]] return eps def _calc_chi(self, Nk): alpha_p = np.diag([ 1. / np.sqrt((2 * k + 7) * (2 * k + 5)) for k in range(2 * Nk - 2) ], k=1) alpha_p += alpha_p.transpose() evals = eigvalsh(alpha_p) chi = [-2. / val for val in evals[0: Nk - 1]] return chi class UnderDampedEnvironment(BosonicEnvironment): r""" Describes an underdamped environment with the spectral density .. math:: J(\omega) = \frac{\lambda^{2} \Gamma \omega}{(\omega_0^{2}- \omega^{2})^{2}+ \Gamma^{2} \omega^{2}} (see Eq. 16 in [BoFiN23]_). Parameters ---------- T : float Environment temperature. lam : float Coupling strength. gamma : float Spectral density cutoff frequency. w0 : float Spectral density resonance frequency. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__( self, T: float, lam: float, gamma: float, w0: float, *, tag: Any = None ): super().__init__(T, tag) self.lam = lam self.gamma = gamma self.w0 = w0 def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ Calculates the underdamped spectral density. Parameters ---------- w : array_like or float Energy of the mode. """ w = np.asarray(w, dtype=float) result = np.zeros_like(w) positive_mask = (w > 0) w_mask = w[positive_mask] result[positive_mask] = ( self.lam**2 * self.gamma * w_mask / ( (w_mask**2 - self.w0**2)**2 + (self.gamma * w_mask)**2 ) ) return result.item() if w.ndim == 0 else result def power_spectrum( self, w: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Calculates the power spectrum of the underdamped environment. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ sd_derivative = self.lam**2 * self.gamma / self.w0**4 return self._ps_from_sd(w, None, sd_derivative) def correlation_function( self, t: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Calculates the two-time auto-correlation function of the underdamped environment. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. """ # we need an wMax so that spectral density is zero for w>wMax, guess: wMax = self.w0 + 25 * self.gamma return self._cf_from_ps(t, wMax) def approx_by_matsubara( self, Nk: int, combine: bool = True, tag: Any = None ) -> ExponentialBosonicEnvironment: """ Generates an approximation to this environment by truncating its Matsubara expansion. Parameters ---------- Nk : int Number of Matsubara terms to include. In total, the real part of the correlation function will include `Nk+2` terms and the imaginary part `2` terms. combine : bool, default `True` Whether to combine exponents with the same frequency. tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- :class:`ExponentialBosonicEnvironment` The approximated environment with multi-exponential correlation function. """ if tag is None and self.tag is not None: tag = (self.tag, "Matsubara Truncation") lists = self._matsubara_params(Nk) result = ExponentialBosonicEnvironment( *lists, T=self.T, combine=combine, tag=tag) return result def _matsubara_params(self, Nk): """ Calculate the Matsubara coefficients and frequencies. """ if Nk > 0 and self.T == 0: warnings.warn("The Matsubara expansion cannot be performed at " "zero temperature. Use other approaches such as " "fitting the correlation function.") Nk = 0 Om = np.sqrt(self.w0**2 - (self.gamma / 2)**2) Gamma = self.gamma / 2 z = np.inf if self.T == 0 else (Om + 1j * Gamma) / (2*self.T) # we set the argument of the hyperbolic tangent to infinity if T=0 ck_real = ([ (self.lam**2 / (4 * Om)) * (1 / np.tanh(z)), (self.lam**2 / (4 * Om)) * (1 / np.tanh(np.conjugate(z))), ]) ck_real.extend([ (-2 * self.lam**2 * self.gamma * self.T) * (2 * np.pi * k * self.T) / ( ((Om + 1j * Gamma)**2 + (2 * np.pi * k * self.T)**2) * ((Om - 1j * Gamma)**2 + (2 * np.pi * k * self.T)**2) ) for k in range(1, Nk + 1) ]) vk_real = [-1j * Om + Gamma, 1j * Om + Gamma] vk_real.extend([ 2 * np.pi * k * self.T for k in range(1, Nk + 1) ]) ck_imag = [ 1j * self.lam**2 / (4 * Om), -1j * self.lam**2 / (4 * Om), ] vk_imag = [-1j * Om + Gamma, 1j * Om + Gamma] return ck_real, vk_real, ck_imag, vk_imag class OhmicEnvironment(BosonicEnvironment): r""" Describes Ohmic environments as well as sub- or super-Ohmic environments (depending on the choice of the parameter `s`). The spectral density is .. math:: J(\omega) = \alpha \frac{\omega^s}{\omega_c^{s-1}} e^{-\omega / \omega_c} . This class requires the `mpmath` module to be installed. Parameters ---------- T : float Temperature of the environment. alpha : float Coupling strength. wc : float Cutoff parameter. s : float Power of omega in the spectral density. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__( self, T: float, alpha: float, wc: float, s: float, *, tag: Any = None ): super().__init__(T, tag) self.alpha = alpha self.wc = wc self.s = s if _mpmath_available is False: warnings.warn( "The mpmath module is required for some operations on " "Ohmic environments, but it is not installed.") def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): r""" Calculates the spectral density of the Ohmic environment. Parameters ---------- w : array_like or float Energy of the mode. """ w = np.asarray(w, dtype=float) result = np.zeros_like(w) positive_mask = (w > 0) w_mask = w[positive_mask] result[positive_mask] = ( self.alpha * w_mask ** self.s / (self.wc ** (self.s - 1)) * np.exp(-np.abs(w_mask) / self.wc) ) return result.item() if w.ndim == 0 else result def power_spectrum( self, w: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Calculates the power spectrum of the Ohmic environment. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ if self.s > 1: sd_derivative = 0 elif self.s == 1: sd_derivative = self.alpha else: sd_derivative = np.inf return self._ps_from_sd(w, None, sd_derivative) def correlation_function( self, t: float | ArrayLike, **kwargs ) -> (float | ArrayLike): r""" Calculates the correlation function of an Ohmic environment using the formula .. math:: C(t)= \frac{1}{\pi} \alpha w_{c}^{1-s} \beta^{-(s+1)} \Gamma(s+1) \left[ \zeta\left(s+1,\frac{1+\beta w_{c} -i w_{c} t}{\beta w_{c}} \right) +\zeta\left(s+1,\frac{1+ i w_{c} t}{\beta w_{c}}\right) \right] , where :math:`\Gamma` is the gamma function, and :math:`\zeta` the Riemann zeta function. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. """ t = np.asarray(t, dtype=float) t_was_array = t.ndim > 0 if not t_was_array: t = np.array([t], dtype=float) if self.T != 0: corr = (self.alpha * self.wc ** (1 - self.s) / np.pi * mp.gamma(self.s + 1) * self.T ** (self.s + 1)) z1_u = ((1 + self.wc / self.T - 1j * self.wc * t) / (self.wc / self.T)) z2_u = (1 + 1j * self.wc * t) / (self.wc / self.T) result = np.asarray( [corr * (mp.zeta(self.s + 1, u1) + mp.zeta(self.s + 1, u2)) for u1, u2 in zip(z1_u, z2_u)], dtype=np.cdouble ) else: corr = (self.alpha * self.wc**(self.s + 1) / np.pi * mp.gamma(self.s + 1) * (1 + 1j * self.wc * t) ** (-self.s - 1)) result = np.asarray(corr, dtype=np.cdouble) if t_was_array: return result return result[0] class CFExponent: """ Represents a single exponent (naively, an excitation mode) within an exponential decomposition of the correlation function of a environment. Parameters ---------- type : {"R", "I", "RI", "+", "-"} or one of `CFExponent.types` The type of exponent. "R" and "I" are bosonic exponents that appear in the real and imaginary parts of the correlation expansion, respectively. "RI" is a combined bosonic exponent that appears in both the real and imaginary parts of the correlation expansion. The combined exponent has a single ``vk``. The ``ck`` is the coefficient in the real expansion and ``ck2`` is the coefficient in the imaginary expansion. "+" and "-" are fermionic exponents. ck : complex The coefficient of the excitation term. vk : complex The frequency of the exponent of the excitation term. ck2 : optional, complex For exponents of type "RI" this is the coefficient of the term in the imaginary expansion (and ``ck`` is the coefficient in the real expansion). tag : optional, str, tuple or any other object A label for the exponent (often the name of the environment). It defaults to None. Attributes ---------- fermionic : bool True if the type of the exponent is a Fermionic type (i.e. either "+" or "-") and False otherwise. coefficient : complex The coefficient of this excitation term in the total correlation function (including real and imaginary part). exponent : complex The frequency of the exponent of the excitation term. (Alias for `vk`.) All of the parameters are also available as attributes. """ types = enum.Enum("ExponentType", ["R", "I", "RI", "+", "-"]) def _check_ck2(self, type, ck2): if type == self.types["RI"]: if ck2 is None: raise ValueError("RI exponents require ck2") else: if ck2 is not None: raise ValueError( "Second co-efficient (ck2) should only be specified for" " RI exponents" ) def _type_is_fermionic(self, type): return type in (self.types["+"], self.types["-"]) def __init__( self, type: str | CFExponent.ExponentType, ck: complex, vk: complex, ck2: complex = None, tag: Any = None ): if not isinstance(type, self.types): type = self.types[type] self._check_ck2(type, ck2) self.type = type self.ck = ck self.vk = vk self.ck2 = ck2 self.tag = tag self.fermionic = self._type_is_fermionic(type) def __repr__(self): return ( f"<{self.__class__.__name__} type={self.type.name}" f" ck={self.ck!r} vk={self.vk!r} ck2={self.ck2!r}" f" fermionic={self.fermionic!r}" f" tag={self.tag!r}>" ) @property def coefficient(self) -> complex: coeff = 0 if self.type != self.types['I']: coeff += self.ck else: coeff += 1j * self.ck if self.type == self.types['RI']: coeff += 1j * self.ck2 return coeff @property def exponent(self) -> complex: return self.vk def _can_combine(self, other, rtol, atol): if type(self) is not type(other): return False if self.fermionic or other.fermionic: return False if not np.isclose(self.vk, other.vk, rtol=rtol, atol=atol): return False return True def _combine(self, other, **init_kwargs): # Assumes can combine was checked cls = type(self) if self.type == other.type and self.type != self.types['RI']: # Both R or both I return cls(type=self.type, ck=(self.ck + other.ck), vk=self.vk, tag=self.tag, **init_kwargs) # Result will be RI real_part_coefficient = 0 imag_part_coefficient = 0 for exp in [self, other]: if exp.type == self.types['RI'] or exp.type == self.types['R']: real_part_coefficient += exp.ck if exp.type == self.types['I']: imag_part_coefficient += exp.ck if exp.type == self.types['RI']: imag_part_coefficient += exp.ck2 return cls(type=self.types['RI'], ck=real_part_coefficient, vk=self.vk, ck2=imag_part_coefficient, tag=self.tag, **init_kwargs) class ExponentialBosonicEnvironment(BosonicEnvironment): """ Bosonic environment that is specified through an exponential decomposition of its correlation function. The list of coefficients and exponents in the decomposition may either be passed through the four lists `ck_real`, `vk_real`, `ck_imag`, `vk_imag`, or as a list of bosonic :class:`CFExponent` objects. Parameters ---------- ck_real : list of complex The coefficients of the expansion terms for the real part of the correlation function. The corresponding frequencies are passed as vk_real. vk_real : list of complex The frequencies (exponents) of the expansion terms for the real part of the correlation function. The corresponding coefficients are passed as ck_real. ck_imag : list of complex The coefficients of the expansion terms in the imaginary part of the correlation function. The corresponding frequencies are passed as vk_imag. vk_imag : list of complex The frequencies (exponents) of the expansion terms for the imaginary part of the correlation function. The corresponding coefficients are passed as ck_imag. exponents : list of :class:`CFExponent` The expansion coefficients and exponents of both the real and the imaginary parts of the correlation function as :class:`CFExponent` objects. combine : bool, default True Whether to combine exponents with the same frequency. See :meth:`combine` for details. T: optional, float The temperature of the environment. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ _make_exponent = CFExponent def _check_cks_and_vks(self, ck_real, vk_real, ck_imag, vk_imag): # all None: returns False # all provided and lengths match: returns True # otherwise: raises ValueError lists = [ck_real, vk_real, ck_imag, vk_imag] if all(x is None for x in lists): return False if any(x is None for x in lists): raise ValueError( "If any of the exponent lists ck_real, vk_real, ck_imag, " "vk_imag is provided, all must be provided." ) if len(ck_real) != len(vk_real) or len(ck_imag) != len(vk_imag): raise ValueError( "The exponent lists ck_real and vk_real, and ck_imag and " "vk_imag must be the same length." ) return True def __init__( self, ck_real: ArrayLike = None, vk_real: ArrayLike = None, ck_imag: ArrayLike = None, vk_imag: ArrayLike = None, *, exponents: Sequence[CFExponent] = None, combine: bool = True, T: float = None, tag: Any = None ): super().__init__(T, tag) lists_provided = self._check_cks_and_vks( ck_real, vk_real, ck_imag, vk_imag) if exponents is None and not lists_provided: raise ValueError( "Either the parameter `exponents` or the parameters " "`ck_real`, `vk_real`, `ck_imag`, `vk_imag` must be provided." ) if exponents is not None and any(exp.fermionic for exp in exponents): raise ValueError( "Fermionic exponent passed to exponential bosonic environment." ) exponents = exponents or [] if lists_provided: exponents.extend(self._make_exponent("R", ck, vk, tag=tag) for ck, vk in zip(ck_real, vk_real)) exponents.extend(self._make_exponent("I", ck, vk, tag=tag) for ck, vk in zip(ck_imag, vk_imag)) if combine: exponents = self.combine(exponents) self.exponents = exponents @classmethod def combine( cls, exponents: Sequence[CFExponent], rtol: float = 1e-5, atol: float = 1e-7 ) -> Sequence[CFExponent]: """ Group bosonic exponents with the same frequency and return a single exponent for each frequency present. Parameters ---------- exponents : list of :class:`CFExponent` The list of exponents to combine. rtol : float, default 1e-5 The relative tolerance to use to when comparing frequencies. atol : float, default 1e-7 The absolute tolerance to use to when comparing frequencies. Returns ------- list of :class:`CFExponent` The new reduced list of exponents. """ remaining = exponents[:] new_exponents = [] while remaining: new_exponent = remaining.pop(0) for other_exp in remaining[:]: if new_exponent._can_combine(other_exp, rtol, atol): new_exponent = new_exponent._combine(other_exp) remaining.remove(other_exp) new_exponents.append(new_exponent) return new_exponents def correlation_function( self, t: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Computes the correlation function represented by this exponential decomposition. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. """ t = np.asarray(t, dtype=float) corr = np.zeros_like(t, dtype=complex) for exp in self.exponents: corr += exp.coefficient * np.exp(-exp.exponent * np.abs(t)) corr[t < 0] = np.conj(corr[t < 0]) return corr.item() if t.ndim == 0 else corr def power_spectrum( self, w: float | ArrayLike, **kwargs ) -> (float | ArrayLike): """ Calculates the power spectrum corresponding to the multi-exponential correlation function. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ w = np.asarray(w, dtype=float) S = np.zeros_like(w) for exp in self.exponents: S += 2 * np.real( exp.coefficient / (exp.exponent - 1j * w) ) return S.item() if w.ndim == 0 else S def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ Calculates the spectral density corresponding to the multi-exponential correlation function. Parameters ---------- w : array_like or float Energy of the mode. """ return self._sd_from_ps(w) def system_terminator(Q: Qobj, delta: float) -> Qobj: """ Constructs the terminator for a given approximation discrepancy. Parameters ---------- Q : :class:`Qobj` The system coupling operator. delta : float The approximation discrepancy of approximating an environment with a finite number of exponentials, see for example :meth:`.DrudeLorentzEnvironment.approx_by_matsubara`. Returns ------- terminator : :class:`Qobj` A superoperator acting on the system Hilbert space. Liouvillian term representing the contribution to the system-environment dynamics of all neglected expansion terms. It should be used by adding it to the system Liouvillian (i.e. ``liouvillian(H_sys)``). """ op = 2 * spre(Q) * spost(Q.dag()) - spre(Q.dag() * Q) - spost(Q.dag() * Q) return delta * op # --- utility functions --- def _real_interpolation(fun, xlist, name, args=None): args = args or {} if callable(fun): return lambda w: fun(w, **args) else: if xlist is None or len(xlist) != len(fun): raise ValueError("A list of x-values with the same length must be " f"provided for the discretized function ({name})") return CubicSpline(xlist, fun) def _complex_interpolation(fun, xlist, name, args=None): args = args or {} if callable(fun): return lambda t: fun(t, **args) else: real_interp = _real_interpolation(np.real(fun), xlist, name) imag_interp = _real_interpolation(np.imag(fun), xlist, name) return lambda x: real_interp(x) + 1j * imag_interp(x) def _fft(f, wMax, tMax): r""" Calculates the Fast Fourier transform of the given function. We calculate Fourier transformations via FFT because numerical integration is often noisy in the scenarios we are interested in. Given a (mathematical) function `f(t)`, this function approximates its Fourier transform .. math:: g(\omega) = \int_{-\infty}^\infty dt\, e^{-i\omega t}\, f(t) . The function f is sampled on the interval `[-tMax, tMax]`. The sampling discretization is chosen as `dt = pi / (4*wMax)` (Shannon-Nyquist + some leeway). However, `dt` is always chosen small enough to have at least 500 samples on the interval `[-tMax, tMax]`. Parameters ---------- wMax: float Maximum frequency of interest tMax: float Support of the function f (i.e., f(t) is essentially zero for `|t| > tMax`). Returns ------- The fourier transform of the provided function as an interpolated function. """ # Code adapted from https://stackoverflow.com/a/24077914 numSamples = int( max(500, np.ceil(2 * tMax * 4 * wMax / np.pi + 1)) ) t, dt = np.linspace(-tMax, tMax, numSamples, retstep=True) f_values = f(t) # Compute Fourier transform by numpy's FFT function g = np.fft.fft(f_values) # frequency normalization factor is 2 * np.pi / dt w = np.fft.fftfreq(numSamples) * 2 * np.pi / dt # In order to get a discretisation of the continuous Fourier transform # we need to multiply g by a phase factor g *= dt * np.exp(1j * w * tMax) return _complex_interpolation( np.fft.fftshift(g), np.fft.fftshift(w), 'FFT' ) def _cf_real_fit_model(tlist, a, b, c, d=0): return np.real((a + 1j * d) * np.exp((b + 1j * c) * np.abs(tlist))) def _cf_imag_fit_model(tlist, a, b, c, d=0): return np.sign(tlist) * np.imag( (a + 1j * d) * np.exp((b + 1j * c) * np.abs(tlist)) ) def _default_guess_cfreal(tlist, clist, full_ansatz): corr_abs = np.abs(clist) corr_max = np.max(corr_abs) tc = 2 / np.max(tlist) # Checks if constant array, and assigns zero if (clist == clist[0]).all(): if full_ansatz: return [[0] * 4]*3 return [[0] * 3]*3 if full_ansatz: lower = [-100 * corr_max, -np.inf, -np.inf, -100 * corr_max] guess = [corr_max, -100*corr_max, 0, 0] upper = [100*corr_max, 0, np.inf, 100*corr_max] else: lower = [-20 * corr_max, -np.inf, 0] guess = [corr_max, -tc, 0] upper = [20 * corr_max, 0.1, np.inf] return guess, lower, upper def _default_guess_cfimag(clist, full_ansatz): corr_max = np.max(np.abs(clist)) # Checks if constant array, and assigns zero if (clist == clist[0]).all(): if full_ansatz: return [[0] * 4]*3 return [[0] * 3]*3 if full_ansatz: lower = [-100 * corr_max, -np.inf, -np.inf, -100 * corr_max] guess = [0, -10 * corr_max, 0, 0] upper = [100 * corr_max, 0, np.inf, 100 * corr_max] else: lower = [-20 * corr_max, -np.inf, 0] guess = [-corr_max, -10 * corr_max, 1] upper = [10 * corr_max, 0, np.inf] return guess, lower, upper def _sd_fit_model(wlist, a, b, c): return ( 2 * a * b * wlist / ((wlist + c)**2 + b**2) / ((wlist - c)**2 + b**2) ) def _default_guess_sd(wlist, jlist): sd_abs = np.abs(jlist) sd_max = np.max(sd_abs) wc = wlist[np.argmax(sd_abs)] if sd_max == 0: return [0] * 3 lower = [-100 * sd_max, 0.1 * wc, 0.1 * wc] guess = [sd_max, wc, wc] upper = [100 * sd_max, 100 * wc, 100 * wc] return guess, lower, upper def _fit_summary(time, rmse, N, label, params, columns=['a', 'b', 'c']): # Generates summary of fit by nonlinear least squares if len(columns) == 3: summary = (f"Result of fitting {label} " f"with {N} terms: \n \n {'Parameters': <10}|" f"{columns[0]: ^10}|{columns[1]: ^10}|{columns[2]: >5} \n ") for k in range(N): summary += ( f"{k+1: <10}|{params[k][0]: ^10.2e}|{params[k][1]:^10.2e}|" f"{params[k][2]:>5.2e}\n ") elif len(columns) == 4: summary = ( f"Result of fitting {label} " f"with {N} terms: \n \n {'Parameters': <10}|" f"{columns[0]: ^10}|{columns[1]: ^10}|{columns[2]: ^10}" f"|{columns[3]: >5} \n ") for k in range(N): summary += ( f"{k+1: <10}|{params[k][0]: ^10.2e}|{params[k][1]:^10.2e}" f"|{params[k][2]:^10.2e}|{params[k][3]:>5.2e}\n ") else: raise ValueError("Unsupported number of columns") summary += (f"\nA normalized RMSE of {rmse: .2e}" f" was obtained for the {label}.\n") summary += f"The current fit took {time: 2f} seconds." return summary def _cf_fit_summary( params_real, params_imag, fit_time_real, fit_time_imag, Nr, Ni, rmse_real, rmse_imag, n=3 ): # Generate nicely formatted summary with two columns for CF fit columns = ["a", "b", "c"] if n == 4: columns.append("d") summary_real = _fit_summary( fit_time_real, rmse_real, Nr, "the real part of\nthe correlation function", params_real, columns=columns ) summary_imag = _fit_summary( fit_time_imag, rmse_imag, Ni, "the imaginary part\nof the correlation function", params_imag, columns=columns ) full_summary = "Correlation function fit:\n\n" lines_real = summary_real.splitlines() lines_imag = summary_imag.splitlines() max_lines = max(len(lines_real), len(lines_imag)) # Fill the shorter string with blank lines lines_real = ( lines_real[:-1] + (max_lines - len(lines_real)) * [""] + [lines_real[-1]] ) lines_imag = ( lines_imag[:-1] + (max_lines - len(lines_imag)) * [""] + [lines_imag[-1]] ) # Find the maximum line length in each column max_length1 = max(len(line) for line in lines_real) max_length2 = max(len(line) for line in lines_imag) # Print the strings side by side with a vertical bar separator for line1, line2 in zip(lines_real, lines_imag): formatted_line1 = f"{line1:<{max_length1}} |" formatted_line2 = f"{line2:<{max_length2}}" full_summary += formatted_line1 + formatted_line2 + "\n" return full_summary # --- fermionic environments --- class FermionicEnvironment(abc.ABC): r""" The fermionic environment of an open quantum system. It is characterized by its spectral density, temperature and chemical potential or, equivalently, by its power spectra or its two-time auto-correlation functions. This class is included as a counterpart to :class:`BosonicEnvironment`, but it currently does not support all features that the bosonic environment does. In particular, fermionic environments cannot be constructed from manually specified spectral densities, power spectra or correlation functions. The only types of fermionic environment implemented at this time are Lorentzian environments (:class:`LorentzianEnvironment`) and environments with multi-exponential correlation functions (:class:`ExponentialFermionicEnvironment`). Parameters ---------- T : optional, float The temperature of this environment. mu : optional, float The chemical potential of this environment. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__(self, T: float = None, mu: float = None, tag: Any = None): self.T = T self.mu = mu self.tag = tag @abc.abstractmethod def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): r""" The spectral density of this environment. See the Users Guide on :ref:`fermionic environments ` for specifics on the definitions used by QuTiP. Parameters ---------- w : array_like or float The frequencies at which to evaluate the spectral density. """ ... @abc.abstractmethod def correlation_function_plus( self, t: float | ArrayLike ) -> (float | ArrayLike): r""" The "+"-branch of the auto-correlation function of this environment. See the Users Guide on :ref:`fermionic environments ` for specifics on the definitions used by QuTiP. Parameters ---------- t : array_like or float The times at which to evaluate the correlation function. """ ... @abc.abstractmethod def correlation_function_minus( self, t: float | ArrayLike ) -> (float | ArrayLike): r""" The "-"-branch of the auto-correlation function of this environment. See the Users Guide on :ref:`fermionic environments ` for specifics on the definitions used by QuTiP. Parameters ---------- t : array_like or float The times at which to evaluate the correlation function. """ ... @abc.abstractmethod def power_spectrum_plus(self, w: float | ArrayLike) -> (float | ArrayLike): r""" The "+"-branch of the power spectrum of this environment. See the Users Guide on :ref:`fermionic environments ` for specifics on the definitions used by QuTiP. Parameters ---------- w : array_like or float The frequencies at which to evaluate the power spectrum. """ ... @abc.abstractmethod def power_spectrum_minus( self, w: float | ArrayLike ) -> (float | ArrayLike): r""" The "-"-branch of the power spectrum of this environment. See the Users Guide on :ref:`fermionic environments ` for specifics on the definitions used by QuTiP. Parameters ---------- w : array_like or float The frequencies at which to evaluate the power spectrum. """ ... # --- user-defined environment creation @classmethod def from_correlation_functions(cls, **kwargs) -> FermionicEnvironment: r""" User-defined fermionic environments are currently not implemented. """ raise NotImplementedError("User-defined fermionic environments are " "currently not implemented.") @classmethod def from_power_spectra(cls, **kwargs) -> FermionicEnvironment: r""" User-defined fermionic environments are currently not implemented. """ raise NotImplementedError("User-defined fermionic environments are " "currently not implemented.") @classmethod def from_spectral_density(cls, **kwargs) -> FermionicEnvironment: r""" User-defined fermionic environments are currently not implemented. """ raise NotImplementedError("User-defined fermionic environments are " "currently not implemented.") class LorentzianEnvironment(FermionicEnvironment): r""" Describes a Lorentzian fermionic environment with the spectral density .. math:: J(\omega) = \frac{\gamma W^2}{(\omega - \omega_0)^2 + W^2}. (see Eq. 46 in [BoFiN23]_). Parameters ---------- T : float Environment temperature. mu : float Environment chemical potential. gamma : float Coupling strength. W : float The spectral width of the environment. omega0 : optional, float (default equal to ``mu``) The resonance frequency of the environment. Nk : optional, int, defaults to 10 The number of Pade exponents to be used for the calculation of the correlation functions. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def __init__( self, T: float, mu: float, gamma: float, W: float, omega0: float = None, *, Nk: int = 10, tag: Any = None ): super().__init__(T, mu, tag) self.gamma = gamma self.W = W self.Nk = Nk if omega0 is None: self.omega0 = mu else: self.omega0 = omega0 def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ Calculates the Lorentzian spectral density. Parameters ---------- w : array_like or float Energy of the mode. """ w = np.asarray(w, dtype=float) return self.gamma * self.W**2 / ((w - self.omega0)**2 + self.W**2) def correlation_function_plus( self, t: float | ArrayLike, Nk: int = None ) -> (float | ArrayLike): r""" Calculates the "+"-branch of the two-time auto-correlation function of the Lorentzian environment. The calculation is performed by summing a large number of exponents of the Pade expansion. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. Nk : int, optional The number of exponents to use. If not provided, then the value that was provided when the class was instantiated is used. """ Nk = Nk or self.Nk return self._correlation_function(t, Nk, 1) def correlation_function_minus( self, t: float | ArrayLike, Nk: int = None ) -> (float | ArrayLike): r""" Calculates the "-"-branch of the two-time auto-correlation function of the Lorentzian environment. The calculation is performed by summing a large number of exponents of the Pade expansion. Parameters ---------- t : array_like or float The time at which to evaluate the correlation function. Nk : int, optional The number of exponents to use. If not provided, then the value that was provided when the class was instantiated is used. """ Nk = Nk or self.Nk return self._correlation_function(t, Nk, -1) def _correlation_function(self, t, Nk, sigma): if self.T == 0: raise NotImplementedError( "Calculation of zero-temperature Lorentzian correlation " "functions is not implemented yet.") t = np.asarray(t, dtype=float) abs_t = np.abs(t) c, v = self._corr(Nk, sigma) result = np.sum([ck * np.exp(-np.asarray(vk * abs_t)) for ck, vk in zip(c, v)], axis=0) result = np.asarray(result, dtype=complex) result[t < 0] = np.conj(result[t < 0]) return result.item() if t.ndim == 0 else result def power_spectrum_plus(self, w: float | ArrayLike) -> (float | ArrayLike): r""" Calculates the "+"-branch of the power spectrum of the Lorentzian environment. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ return self.spectral_density(w) / (np.exp((w - self.mu) / self.T) + 1) def power_spectrum_minus( self, w: float | ArrayLike ) -> (float | ArrayLike): r""" Calculates the "-"-branch of the power spectrum of the Lorentzian environment. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ return self.spectral_density(w) / (np.exp((self.mu - w) / self.T) + 1) def approx_by_matsubara( self, Nk: int, tag: Any = None ) -> ExponentialFermionicEnvironment: """ Generates an approximation to this environment by truncating its Matsubara expansion. Parameters ---------- Nk : int Number of Matsubara terms to include. In total, the "+" and "-" correlation function branches will include `Nk+1` terms each. tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- The approximated environment with multi-exponential correlation function. """ if self.T == 0: raise NotImplementedError( "Calculation of zero-temperature Lorentzian correlation " "functions is not implemented yet.") if tag is None and self.tag is not None: tag = (self.tag, "Matsubara Truncation") ck_plus, vk_plus = self._matsubara_params(Nk, 1) ck_minus, vk_minus = self._matsubara_params(Nk, -1) return ExponentialFermionicEnvironment( ck_plus, vk_plus, ck_minus, vk_minus, T=self.T, mu=self.mu, tag=tag ) def approx_by_pade( self, Nk: int, tag: Any = None ) -> ExponentialFermionicEnvironment: """ Generates an approximation to this environment by truncating its Pade expansion. Parameters ---------- Nk : int Number of Pade terms to include. In total, the "+" and "-" correlation function branches will include `Nk+1` terms each. tag : optional, str, tuple or any other object An identifier (name) for the approximated environment. If not provided, a tag will be generated from the tag of this environment. Returns ------- The approximated environment with multi-exponential correlation function. """ if self.T == 0: raise NotImplementedError( "Calculation of zero-temperature Lorentzian correlation " "functions is not implemented yet.") if tag is None and self.tag is not None: tag = (self.tag, "Pade Truncation") ck_plus, vk_plus = self._corr(Nk, sigma=1) ck_minus, vk_minus = self._corr(Nk, sigma=-1) return ExponentialFermionicEnvironment( ck_plus, vk_plus, ck_minus, vk_minus, T=self.T, mu=self.mu, tag=tag ) def _matsubara_params(self, Nk, sigma): """ Calculate the Matsubara coefficients and frequencies. """ def f(x): return 1 / (np.exp(x / self.T) + 1) coeff_list = [( self.W * self.gamma / 2 * f(sigma * (self.omega0 - self.mu) + 1j * self.W) )] exp_list = [self.W - sigma * 1j * self.omega0] xk_list = [(2 * k - 1) * np.pi * self.T for k in range(1, Nk + 1)] for xk in xk_list: coeff_list.append( 1j * self.gamma * self.W**2 * self.T / ((sigma * xk - 1j * self.mu + 1j * self.omega0)**2 - self.W**2) ) exp_list.append( xk - sigma * 1j * self.mu ) return coeff_list, exp_list # --- Pade approx calculation --- def _corr(self, Nk, sigma): beta = 1 / self.T kappa, epsilon = self._kappa_epsilon(Nk) def f_approx(x): f = 0.5 for ll in range(1, Nk + 1): f = f - 2 * kappa[ll] * x / (x**2 + epsilon[ll]**2) return f eta_list = [(0.5 * self.gamma * self.W * f_approx(beta * sigma * (self.omega0 - self.mu) + beta * 1j * self.W))] gamma_list = [self.W - sigma * 1.0j * self.omega0] for ll in range(1, Nk + 1): eta_list.append( -1.0j * (kappa[ll] / beta) * self.gamma * self.W**2 / ((self.mu - self.omega0 + sigma * 1j * epsilon[ll] / beta)**2 + self.W**2) ) gamma_list.append(epsilon[ll] / beta - sigma * 1.0j * self.mu) return eta_list, gamma_list def _kappa_epsilon(self, Nk): eps = self._calc_eps(Nk) chi = self._calc_chi(Nk) kappa = [0] prefactor = 0.5 * Nk * (2 * (Nk + 1) - 1) for j in range(Nk): term = prefactor for k in range(Nk - 1): term *= ( (chi[k]**2 - eps[j]**2) / (eps[k]**2 - eps[j]**2 + self._delta(j, k)) ) for k in [Nk - 1]: term /= (eps[k]**2 - eps[j]**2 + self._delta(j, k)) kappa.append(term) epsilon = [0] + eps return kappa, epsilon def _delta(self, i, j): return 1.0 if i == j else 0.0 def _calc_eps(self, Nk): alpha = np.diag([ 1. / np.sqrt((2 * k + 3) * (2 * k + 1)) for k in range(2 * Nk - 1) ], k=1) alpha += alpha.transpose() evals = eigvalsh(alpha) eps = [-2. / val for val in evals[0: Nk]] return eps def _calc_chi(self, Nk): alpha_p = np.diag([ 1. / np.sqrt((2 * k + 5) * (2 * k + 3)) for k in range(2 * Nk - 2) ], k=1) alpha_p += alpha_p.transpose() evals = eigvalsh(alpha_p) chi = [-2. / val for val in evals[0: Nk - 1]] return chi class ExponentialFermionicEnvironment(FermionicEnvironment): """ Fermionic environment that is specified through an exponential decomposition of its correlation function. The list of coefficients and exponents in the decomposition may either be passed through the four lists `ck_plus`, `vk_plus`, `ck_minus`, `vk_minus`, or as a list of fermionic :class:`CFExponent` objects. Alternative constructors :meth:`from_plus_exponents` and :meth:`from_minus_exponents` are available to compute the "-" exponents automatically from the "+" ones, or vice versa. Parameters ---------- ck_plus : list of complex The coefficients of the expansion terms for the ``+`` part of the correlation function. The corresponding frequencies are passed as vk_plus. vk_plus : list of complex The frequencies (exponents) of the expansion terms for the ``+`` part of the correlation function. The corresponding coefficients are passed as ck_plus. ck_minus : list of complex The coefficients of the expansion terms for the ``-`` part of the correlation function. The corresponding frequencies are passed as vk_minus. vk_minus : list of complex The frequencies (exponents) of the expansion terms for the ``-`` part of the correlation function. The corresponding coefficients are passed as ck_minus. exponents : list of :class:`CFExponent` The expansion coefficients and exponents of both parts of the correlation function as :class:`CFExponent` objects. T: optional, float The temperature of the environment. mu: optional, float The chemical potential of the environment. tag : optional, str, tuple or any other object An identifier (name) for this environment. """ def _check_cks_and_vks(self, ck_plus, vk_plus, ck_minus, vk_minus): # all None: returns False # all provided and lengths match: returns True # otherwise: raises ValueError lists = [ck_plus, vk_plus, ck_minus, vk_minus] if all(x is None for x in lists): return False if any(x is None for x in lists): raise ValueError( "If any of the exponent lists ck_plus, vk_plus, ck_minus, " "vk_minus is provided, all must be provided." ) if len(ck_plus) != len(vk_plus) or len(ck_minus) != len(vk_minus): raise ValueError( "The exponent lists ck_plus and vk_plus, and ck_minus and " "vk_minus must be the same length." ) return True def __init__( self, ck_plus: ArrayLike = None, vk_plus: ArrayLike = None, ck_minus: ArrayLike = None, vk_minus: ArrayLike = None, *, exponents: Sequence[CFExponent] = None, T: float = None, mu: float = None, tag: Any = None ): super().__init__(T, mu, tag) lists_provided = self._check_cks_and_vks( ck_plus, vk_plus, ck_minus, vk_minus) if exponents is None and not lists_provided: raise ValueError( "Either the parameter `exponents` or the parameters " "`ck_plus`, `vk_plus`, `ck_minus`, `vk_minus` must be " "provided." ) if (exponents is not None and not all(exp.fermionic for exp in exponents)): raise ValueError( "Bosonic exponent passed to exponential fermionic environment." ) self.exponents = exponents or [] if lists_provided: self.exponents.extend(CFExponent("+", ck, vk, tag=tag) for ck, vk in zip(ck_plus, vk_plus)) self.exponents.extend(CFExponent("-", ck, vk, tag=tag) for ck, vk in zip(ck_minus, vk_minus)) def spectral_density(self, w: float | ArrayLike) -> (float | ArrayLike): """ Computes the spectral density corresponding to the multi-exponential correlation function. Parameters ---------- w : array_like or float Energy of the mode. """ return self.power_spectrum_minus(w) + self.power_spectrum_plus(w) def correlation_function_plus( self, t: float | ArrayLike ) -> (float | ArrayLike): r""" Computes the "+"-branch of the correlation function represented by this exponential decomposition. Parameters ---------- t : array_like or float The times at which to evaluate the correlation function. """ return self._cf(t, CFExponent.types['+']) def correlation_function_minus( self, t: float | ArrayLike ) -> (float | ArrayLike): r""" Computes the "-"-branch of the correlation function represented by this exponential decomposition. Parameters ---------- t : array_like or float The times at which to evaluate the correlation function. """ return self._cf(t, CFExponent.types['-']) def _cf(self, t, type): t = np.asarray(t, dtype=float) corr = np.zeros_like(t, dtype=complex) for exp in self.exponents: if exp.type == type: corr += exp.coefficient * np.exp(-exp.exponent * np.abs(t)) corr[t < 0] = np.conj(corr[t < 0]) return corr.item() if t.ndim == 0 else corr def power_spectrum_plus( self, w: float | ArrayLike ) -> (float | ArrayLike): r""" Calculates the "+"-branch of the power spectrum corresponding to the multi-exponential correlation function. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ return self._ps(w, CFExponent.types['+'], 1) def power_spectrum_minus( self, w: float | ArrayLike ) -> (float | ArrayLike): r""" Calculates the "-"-branch of the power spectrum corresponding to the multi-exponential correlation function. Parameters ---------- w : array_like or float The frequency at which to evaluate the power spectrum. """ return self._ps(w, CFExponent.types['-'], -1) def _ps(self, w, type, sigma): w = np.asarray(w, dtype=float) S = np.zeros_like(w) for exp in self.exponents: if exp.type == type: S += 2 * np.real( exp.coefficient / (exp.exponent + sigma * 1j * w) ) return S.item() if w.ndim == 0 else S qutip-5.1.1/qutip/core/expect.py000066400000000000000000000065501474175217300166350ustar00rootroot00000000000000__all__ = ['expect', 'variance'] import numpy as np from typing import overload, Sequence from .qobj import Qobj from . import data as _data from ..settings import settings @overload def expect(oper: Qobj, state: Qobj) -> complex: ... @overload def expect( oper: Qobj, state: Qobj | Sequence[Qobj], ) -> np.typing.NDArray[complex]: ... @overload def expect( oper: Qobj | Sequence[Qobj], state: Qobj, ) -> list[complex]: ... @overload def expect( oper: Qobj | Sequence[Qobj], state: Qobj | Sequence[Qobj] ) -> list[np.typing.NDArray[complex]]: ... def expect(oper, state): """ Calculate the expectation value for operator(s) and state(s). The expectation of state ``k`` on operator ``A`` is defined as ``k.dag() @ A @ k``, and for density matrix ``R`` on operator ``A`` it is ``trace(A @ R)``. Parameters ---------- oper : qobj / list of Qobj A single or a `list` of operators for expectation value. state : qobj / list of Qobj A single or a `list` of quantum states or density matrices. Returns ------- expt : float / complex / list / array Expectation value(s). ``real`` if ``oper`` is Hermitian, ``complex`` otherwise. If multiple ``oper`` are passed, a list of array. A (nested) array of expectaction values if ``state`` or ``oper`` are arrays. Examples -------- >>> expect(num(4), basis(4, 3)) == 3 # doctest: +NORMALIZE_WHITESPACE True """ if isinstance(state, Qobj) and isinstance(oper, Qobj): return _single_qobj_expect(oper, state) elif isinstance(oper, Sequence): return [expect(op, state) for op in oper] elif isinstance(state, Sequence): dtype = np.complex128 if oper.isherm and all(op.isherm or op.isket for op in state): dtype = np.float64 return np.array([_single_qobj_expect(oper, x) for x in state], dtype=dtype) raise TypeError('Arguments must be quantum objects') def _single_qobj_expect(oper, state): """ Private function used by expect to calculate expectation values of Qobjs. """ if not oper.isoper or not (state.isket or state.isoper): raise TypeError('invalid operand types') if oper.dims[1] != state.dims[0]: msg = ( "incompatible dimensions " + str(oper.dims[1]) + " and " + str(state.dims[0]) ) raise ValueError(msg) out = _data.expect(oper.data, state.data) # This ensures that expect can return something that is not a number such # as a `tensorflow.Tensor` in qutip-tensorflow. if ( settings.core["auto_real_casting"] and oper.isherm and (state.isket or state.isherm) ): out = out.real return out @overload def variance(oper: Qobj, state: Qobj) -> complex: ... @overload def variance(oper: Qobj, state: list[Qobj]) -> np.typing.NDArray[complex]: ... def variance(oper, state): """ Variance of an operator for the given state vector or density matrix. Parameters ---------- oper : Qobj Operator for expectation value. state : Qobj / list of Qobj A single or ``list`` of quantum states or density matrices.. Returns ------- var : float Variance of operator 'oper' for given state. """ return expect(oper**2, state) - expect(oper, state)**2 qutip-5.1.1/qutip/core/gates.py000066400000000000000000000527531474175217300164560ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations from itertools import product from functools import partial, reduce from operator import mul import numpy as np import scipy.sparse as sp from . import Qobj, qeye, sigmax, fock_dm, qdiags, qeye_like from .dimensions import Dimensions from .. import settings from . import data as _data from ..typing import LayerType __all__ = [ "rx", "ry", "rz", "sqrtnot", "snot", "phasegate", "qrot", "cy_gate", "cz_gate", "s_gate", "t_gate", "cs_gate", "ct_gate", "cphase", "cnot", "csign", "berkeley", "swapalpha", "swap", "iswap", "sqrtswap", "sqrtiswap", "fredkin", "molmer_sorensen", "toffoli", "hadamard_transform", "qubit_clifford_group", "globalphase", ] _DIMS_2_QB = Dimensions([[2, 2], [2, 2]]) _DIMS_3_QB = Dimensions([[2, 2, 2], [2, 2, 2]]) def cy_gate(*, dtype: LayerType = None) -> Qobj: """Controlled Y gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, -1j], [0, 0, 1j, 0]], dims=_DIMS_2_QB, isherm=True, isunitary=True, ).to(dtype) def cz_gate(*, dtype: LayerType = None) -> Qobj: """Controlled Z gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([1, 1, 1, -1], dims=_DIMS_2_QB, dtype=dtype) def s_gate(*, dtype: LayerType = None) -> Qobj: """Single-qubit rotation also called Phase gate or the Z90 gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing a 90 degree rotation around the z-axis. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([1, 1j], dtype=dtype) def cs_gate(*, dtype: LayerType = None) -> Qobj: """Controlled S gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([1, 1, 1, 1j], dims=_DIMS_2_QB, dtype=dtype) def t_gate(*, dtype: LayerType = None) -> Qobj: """Single-qubit rotation related to the S gate by the relationship S=T*T. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing a phase shift of pi/4. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([1, np.exp(1j * np.pi / 4)], dtype=dtype) def ct_gate(*, dtype: LayerType = None) -> Qobj: """Controlled T gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : :class:`.Qobj` Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags( [1, 1, 1, np.exp(1j * np.pi / 4)], dims=_DIMS_2_QB, dtype=dtype, ) def rx(phi: float, *, dtype: LayerType = None) -> Qobj: """Single-qubit rotation for operator sigmax with angle phi. Parameters ---------- phi : float Rotation angle dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : qobj Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return Qobj( [ [np.cos(phi / 2), -1j * np.sin(phi / 2)], [-1j * np.sin(phi / 2), np.cos(phi / 2)], ], isherm=(phi % (2 * np.pi) <= settings.core["atol"]), isunitary=True, ).to(dtype) def ry(phi: float, *, dtype: LayerType = None) -> Qobj: """Single-qubit rotation for operator sigmay with angle phi. Parameters ---------- phi : float Rotation angle dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : qobj Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return Qobj( [ [np.cos(phi / 2), -np.sin(phi / 2)], [np.sin(phi / 2), np.cos(phi / 2)], ], isherm=(phi % (2 * np.pi) <= settings.core["atol"]), isunitary=True, ).to(dtype) def rz(phi: float, *, dtype: LayerType = None) -> Qobj: """Single-qubit rotation for operator sigmaz with angle phi. Parameters ---------- phi : float Rotation angle dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : qobj Quantum object for operator describing the rotation. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([np.exp(-1j * phi / 2), np.exp(1j * phi / 2)], dtype=dtype) def sqrtnot(*, dtype: LayerType = None) -> Qobj: """Single-qubit square root NOT gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- result : qobj Quantum object for operator describing the square root NOT gate. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return Qobj( [[0.5 + 0.5j, 0.5 - 0.5j], [0.5 - 0.5j, 0.5 + 0.5j]], isherm=False, isunitary=True, ).to(dtype) def snot(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the SNOT (Hadamard) gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- snot_gate : qobj Quantum object representation of SNOT gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [[np.sqrt(0.5), np.sqrt(0.5)], [np.sqrt(0.5), -np.sqrt(0.5)]], isherm=True, isunitary=True, ).to(dtype) def phasegate(theta: float, *, dtype: LayerType = None) -> Qobj: """ Returns quantum object representing the phase shift gate. Parameters ---------- theta : float Phase rotation angle. dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- phase_gate : qobj Quantum object representation of phase shift gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags([1, np.exp(1.0j * theta)], dtype=dtype) def qrot(theta: float, phi: float, *, dtype: LayerType = None) -> Qobj: """ Single qubit rotation driving by Rabi oscillation with 0 detune. Parameters ---------- phi : float The inital phase of the rabi pulse. theta : float The duration of the rabi pulse. dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- qrot_gate : :class:`.Qobj` Quantum object representation of physical qubit rotation under a rabi pulse. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return Qobj( [ [np.cos(theta / 2), -1j * np.exp(-1j * phi) * np.sin(theta / 2)], [-1j * np.exp(1j * phi) * np.sin(theta / 2), np.cos(theta / 2)], ], isherm=(theta % (2 * np.pi) <= settings.core["atol"]), isunitary=True, ).to(dtype) # # 2 Qubit Gates # def cphase(theta: float, *, dtype: LayerType = None) -> Qobj: """ Returns quantum object representing the controlled phase shift gate. Parameters ---------- theta : float Phase rotation angle. dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- U : qobj Quantum object representation of controlled phase gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qdiags( [1, 1, 1, np.exp(1.0j * theta)], dims=_DIMS_2_QB, dtype=dtype ) def cnot(*, dtype: LayerType = None) -> Qobj: """ Quantum object representing the CNOT gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- cnot_gate : qobj Quantum object representation of CNOT gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], dims=_DIMS_2_QB, isherm=True, isunitary=True, ).to(dtype) def csign(*, dtype: LayerType = None) -> Qobj: """ Quantum object representing the CSIGN gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- csign_gate : qobj Quantum object representation of CSIGN gate """ return cz_gate(dtype=dtype) def berkeley(*, dtype: LayerType = None) -> Qobj: """ Quantum object representing the Berkeley gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- berkeley_gate : qobj Quantum object representation of Berkeley gate """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return Qobj( [ [np.cos(np.pi / 8), 0, 0, 1.0j * np.sin(np.pi / 8)], [0, np.cos(3 * np.pi / 8), 1.0j * np.sin(3 * np.pi / 8), 0], [0, 1.0j * np.sin(3 * np.pi / 8), np.cos(3 * np.pi / 8), 0], [1.0j * np.sin(np.pi / 8), 0, 0, np.cos(np.pi / 8)], ], dims=_DIMS_2_QB, isherm=False, isunitary=True, ).to(dtype) def swapalpha(alpha: float, *, dtype: LayerType = None) -> Qobj: """ Quantum object representing the SWAPalpha gate. Parameters ---------- alpha : float Angle of the SWAPalpha gate. dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- swapalpha_gate : qobj Quantum object representation of SWAPalpha gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR phase = np.exp(1.0j * np.pi * alpha) return Qobj( [ [1, 0, 0, 0], [0, 0.5 * (1 + phase), 0.5 * (1 - phase), 0], [0, 0.5 * (1 - phase), 0.5 * (1 + phase), 0], [0, 0, 0, 1], ], dims=_DIMS_2_QB, isherm=(np.abs(phase.imag) <= settings.core["atol"]), isunitary=True, ).to(dtype) def swap(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the SWAP gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- swap_gate : qobj Quantum object representation of SWAP gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]], dims=_DIMS_2_QB, isherm=True, isunitary=True, ).to(dtype) def iswap(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the iSWAP gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- iswap_gate : qobj Quantum object representation of iSWAP gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0], [0, 0, 0, 1]], dims=_DIMS_2_QB, isherm=False, isunitary=True, ).to(dtype) def sqrtswap(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the square root SWAP gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- sqrtswap_gate : qobj Quantum object representation of square root SWAP gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( np.array( [ [1, 0, 0, 0], [0, 0.5 + 0.5j, 0.5 - 0.5j, 0], [0, 0.5 - 0.5j, 0.5 + 0.5j, 0], [0, 0, 0, 1], ] ), dims=_DIMS_2_QB, isherm=False, isunitary=True, ).to(dtype) def sqrtiswap(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the square root iSWAP gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- sqrtiswap_gate : qobj Quantum object representation of square root iSWAP gate """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( np.array( [ [1, 0, 0, 0], [0, 1 / np.sqrt(2), 1j / np.sqrt(2), 0], [0, 1j / np.sqrt(2), 1 / np.sqrt(2), 0], [0, 0, 0, 1], ] ), dims=_DIMS_2_QB, isherm=False, isunitary=True, ).to(dtype) def molmer_sorensen(theta: float, *, dtype: LayerType = None) -> Qobj: """ Quantum object of a Mølmer–Sørensen gate. Parameters ---------- theta: float The duration of the interaction pulse. target: int The indices of the target qubits. dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- molmer_sorensen_gate: :class:`.Qobj` Quantum object representation of the Mølmer–Sørensen gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [ [np.cos(theta / 2.0), 0, 0, -1.0j * np.sin(theta / 2.0)], [0, np.cos(theta / 2.0), -1.0j * np.sin(theta / 2.0), 0], [0, -1.0j * np.sin(theta / 2.0), np.cos(theta / 2.0), 0], [-1.0j * np.sin(theta / 2.0), 0, 0, np.cos(theta / 2.0)], ], dims=_DIMS_2_QB, isherm=(theta % (2 * np.pi) <= settings.core["atol"]), isunitary=True, ).to(dtype) # # 3 Qubit Gates # def fredkin(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the Fredkin gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- fredkin_gate : qobj Quantum object representation of Fredkin gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [ [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], ], dims=_DIMS_3_QB, isherm=True, isunitary=True, ).to(dtype) def toffoli(*, dtype: LayerType = None) -> Qobj: """Quantum object representing the Toffoli gate. Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- toff_gate : qobj Quantum object representation of Toffoli gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return Qobj( [ [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0], ], dims=_DIMS_3_QB, isherm=True, isunitary=True, ).to(dtype) # # Miscellaneous Gates # def globalphase(theta: float, N: int = 1, *, dtype: LayerType = None) -> Qobj: """ Returns quantum object representing the global phase shift gate. Parameters ---------- theta : float Phase rotation angle. N : int: Number of qubits dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- phase_gate : qobj Quantum object representation of global phase shift gate. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return qeye([2] * N, dtype=dtype) * np.exp(1.0j * theta) # # Operation on Gates # def _hamming_distance(x): """ Calculate the bit-wise Hamming distance of x from 0: That is, the number 1s in the integer x. """ tot = 0 while x: tot += 1 x &= x - 1 return tot def hadamard_transform(N: int = 1, *, dtype: LayerType = None) -> Qobj: """Quantum object representing the N-qubit Hadamard gate. Parameters ---------- N : int: Number of qubits dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- q : qobj Quantum object representation of the N-qubit Hadamard gate. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense data = 2 ** (-N / 2) * np.array( [ [(-1) ** _hamming_distance(i & j) for i in range(2**N)] for j in range(2**N) ] ) return Qobj(data, dims=[[2] * N, [2] * N], isherm=True, isunitary=True).to( dtype ) def _powers(op, N): """ Generator that yields powers of an operator `op`, through to `N`. """ acc = qeye_like(op) yield acc for _ in range(N - 1): acc *= op yield acc def qubit_clifford_group(*, dtype: LayerType = None) -> list[Qobj]: """ Generates the Clifford group on a single qubit, using the presentation of the group given by Ross and Selinger (http://www.mathstat.dal.ca/~selinger/newsynth/). Parameters ---------- dtype : str or type, [keyword only] [optional] Storage representation. Any data-layer known to `qutip.data.to` is accepted. Returns ------- op : list of Qobj Clifford operators, represented as Qobj instances. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense # The Ross-Selinger presentation of the single-qubit Clifford # group expresses each element in the form C_{ijk} = E^i X^j S^k # for gates E, X and S, and for i in range(3), j in range(2) and # k in range(4). # # We start by defining these gates. E is defined in terms of H, # \omega and S, so we define \omega and H first. w = np.exp(1j * 2 * np.pi / 8) H = snot() X = sigmax() S = phasegate(np.pi / 2) E = H @ (S**3) * w**3 # partial(reduce, mul) returns a function that takes products # of its argument, by analogy to sum. Note that by analogy, # sum can be written as partial(reduce, add). # product(...) yields the Cartesian product of its arguments. # Here, each element is a tuple (E**i, X**j, S**k) such that # partial(reduce, mul) acting on the tuple yields E**i * X**j * S**k. gates = [ op.to(dtype) for op in map( partial(reduce, mul), product(_powers(E, 3), _powers(X, 2), _powers(S, 4)), ) ] for gate in gates: gate.isherm gate._isunitary = True return gates qutip-5.1.1/qutip/core/metrics.py000066400000000000000000000501141474175217300170060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This module contains a collection of functions for calculating metrics (distance measures) between states and operators. """ __all__ = ['fidelity', 'tracedist', 'bures_dist', 'bures_angle', 'hellinger_dist', 'hilbert_dist', 'average_gate_fidelity', 'process_fidelity', 'unitarity', 'dnorm'] from .numpy_backend import np from scipy import linalg as la import scipy.sparse as sp from .superop_reps import to_choi, _to_superpauli, to_super, kraus_to_choi from .superoperator import operator_to_vector, vector_to_operator from .operators import qeye, qeye_like from .states import ket2dm from .semidefinite import dnorm_problem, dnorm_sparse_problem from . import data as _data try: import cvxpy except ImportError: cvxpy = None def fidelity(A, B): """ Calculates the fidelity (pseudo-metric) between two density matrices. Notes ----- Uses the definition from Nielsen & Chuang, "Quantum Computation and Quantum Information". It is the square root of the fidelity defined in R. Jozsa, Journal of Modern Optics, 41:12, 2315 (1994), used in :func:`qutip.core.metrics.process_fidelity`. Parameters ---------- A : qobj Density matrix or state vector. B : qobj Density matrix or state vector with same dimensions as A. Returns ------- fid : float Fidelity pseudo-metric between A and B. Examples -------- >>> x = fock_dm(5,3) >>> y = coherent_dm(5,1) >>> np.testing.assert_almost_equal(fidelity(x,y), 0.24104350624628332) """ if A.isket or A.isbra: if B.isket or B.isbra: # The fidelity for pure states reduces to the modulus of their # inner product. return np.abs(A.overlap(B)) # Take advantage of the fact that the density operator for A # is a projector to avoid a sqrtm call. sqrtmA = ket2dm(A) else: if B.isket or B.isbra: # Swap the order so that we can take a more numerically # stable square root of B. return fidelity(B, A) # If we made it here, both A and B are operators, so # we have to take the sqrtm of one of them. sqrtmA = A.sqrtm() if sqrtmA.dims != B.dims: raise TypeError('Density matrices do not have same dimensions.') # We don't actually need the whole matrix here, just the trace # of its square root, so let's just get its eigenenergies instead. # We also truncate negative eigenvalues to avoid nan propagation; # even for positive semidefinite matrices, small negative eigenvalues # can be reported. eig_vals = (sqrtmA * B * sqrtmA).eigenenergies() eig_vals_non_neg = np.where(eig_vals > 0, eig_vals, 0) return np.real(np.sqrt(eig_vals_non_neg).sum()) def _hilbert_space_dims(oper): """ For a quantum channel `oper`, return the dimensions `[dims_out, dims_in]` of the output Hilbert space and the input Hilbert space. - If oper is a unitary, then `oper.dims == [dims_out, dims_in]`. - If oper is a list of Kraus operators, then `oper[0].dims == [dims_out, dims_in]`. - If oper is a superoperator with `oper.superrep == 'super'`: `oper.dims == [[dims_out, dims_out], [dims_in, dims_in]]` - If oper is a superoperator with `oper.superrep == 'choi'`: `oper.dims == [[dims_in, dims_out], [dims_in, dims_out]]` - If oper is a superoperator with `oper.superrep == 'chi', then `dims_out == dims_in` and `oper.dims == [[dims_out, dims_out], [dims_out, dims_out]]`. :param oper: A quantum channel, represented by a unitary, a list of Kraus operators, or a superoperator :return: `[dims_out, dims_in]`, where `dims_out` and `dims_in` are lists of integers """ if isinstance(oper, list): return oper[0].dims elif oper.type == 'oper': # interpret as unitary quantum channel return oper.dims elif oper.type == 'super' and oper.superrep in ['choi', 'chi', 'super']: return [oper.dims[0][1], oper.dims[1][0]] else: raise TypeError('oper is not a valid quantum channel!') def _process_fidelity_to_id(oper): """ Internal function returning the process fidelity of a quantum channel to the identity quantum channel. Parameters ---------- oper : :class:`.Qobj`/list A unitary operator, or a superoperator in supermatrix, Choi or chi-matrix form, or a list of Kraus operators Returns ------- fid : float """ dims_out, dims_in = _hilbert_space_dims(oper) if dims_out != dims_in: raise TypeError('The process fidelity to identity is only defined ' 'for dimension preserving channels.') d = np.prod(dims_in) if isinstance(oper, list): # oper is a list of Kraus operators return np.sum([np.abs(k.tr()) ** 2 for k in oper]) / d ** 2 elif oper.type == 'oper': # interpret as unitary return np.abs(oper.tr()) ** 2 / d ** 2 elif oper.type == 'super': if oper.superrep == 'chi': return oper[0, 0].real / d ** 2 else: # oper.superrep is either 'super' or 'choi': return to_super(oper).tr().real / d ** 2 def _kraus_or_qobj_to_choi(oper): if isinstance(oper, list): return kraus_to_choi(oper) else: return to_choi(oper) def process_fidelity(oper, target=None): """ Returns the process fidelity of a quantum channel to the target channel, or to the identity channel if no target is given. The process fidelity between two channels is defined as the state fidelity between their normalized Choi matrices. Parameters ---------- oper : :class:`.Qobj`/list A unitary operator, or a superoperator in supermatrix, Choi or chi-matrix form, or a list of Kraus operators target : :class:`.Qobj`/list, optional A unitary operator, or a superoperator in supermatrix, Choi or chi-matrix form, or a list of Kraus operators Returns ------- fid : float Process fidelity between oper and target, or between oper and identity. Notes ----- Since Qutip 5.0, this function computes the process fidelity as defined for example in: A. Gilchrist, N.K. Langford, M.A. Nielsen, Phys. Rev. A 71, 062310 (2005). Previously, it computed a function that is now implemented as ``get_fidelity`` in qutip-qtrl. The definition of state fidelity that the process fidelity is based on is the one from R. Jozsa, Journal of Modern Optics, 41:12, 2315 (1994). It is the square of the one implemented in :func:`qutip.core.metrics.fidelity` which follows Nielsen & Chuang, "Quantum Computation and Quantum Information" """ if target is None: return _process_fidelity_to_id(oper) dims_out, dims_in = _hilbert_space_dims(oper) if dims_out != dims_in: raise NotImplementedError('Process fidelity only implemented for ' 'dimension-preserving operators.') dims_out_target, dims_in_target = _hilbert_space_dims(target) if [dims_out, dims_in] != [dims_out_target, dims_in_target]: raise TypeError('Dimensions of oper and target do not match') if not isinstance(target, list) and target.type == 'oper': # interpret target as unitary. if isinstance(oper, list): # oper is a list of Kraus operators return _process_fidelity_to_id([k * target.dag() for k in oper]) elif oper.type == 'oper': return _process_fidelity_to_id(oper * target.dag()) elif oper.type == 'super': oper_super = to_super(oper) target_dag_super = to_super(target.dag()) return _process_fidelity_to_id(oper_super * target_dag_super) else: # target is a list of Kraus operators or a superoperator if not isinstance(oper, list) and oper.type == 'oper': return process_fidelity(target, oper) # reverse order oper_choi = _kraus_or_qobj_to_choi(oper) target_choi = _kraus_or_qobj_to_choi(target) d = np.prod(dims_in) return (fidelity(oper_choi, target_choi)/d)**2 def average_gate_fidelity(oper, target=None): """ Returns the average gate fidelity of a quantum channel to the target channel, or to the identity channel if no target is given. Parameters ---------- oper : :class:`.Qobj`/list A unitary operator, or a superoperator in supermatrix, Choi or chi-matrix form, or a list of Kraus operators target : :class:`.Qobj` A unitary operator Returns ------- fid : float Average gate fidelity between oper and target, or between oper and identity. Notes ----- The average gate fidelity is defined for example in: A. Gilchrist, N.K. Langford, M.A. Nielsen, Phys. Rev. A 71, 062310 (2005). The definition of state fidelity that the average gate fidelity is based on is the one from R. Jozsa, Journal of Modern Optics, 41:12, 2315 (1994). It is the square of the fidelity implemented in :func:`qutip.core.metrics.fidelity` which follows Nielsen & Chuang, "Quantum Computation and Quantum Information" """ dims_out, dims_in = _hilbert_space_dims(oper) if not (target is None or target.type == 'oper'): raise TypeError( 'target must be None or a Qobj representing a unitary.') d = np.prod(dims_in) return (d * process_fidelity(oper, target) + 1) / (d + 1) def tracedist(A, B, sparse=False, tol=0): """ Calculates the trace distance between two density matrices.. See: Nielsen & Chuang, "Quantum Computation and Quantum Information" Parameters ----------!= A : qobj Density matrix or state vector. B : qobj Density matrix or state vector with same dimensions as A. tol : float, default: 0 Tolerance used by sparse eigensolver, if used. (0 = Machine precision) sparse : bool, default: False Use sparse eigensolver. Returns ------- tracedist : float Trace distance between A and B. Examples -------- >>> x=fock_dm(5,3) >>> y=coherent_dm(5,1) >>> np.testing.assert_almost_equal(tracedist(x,y), 0.9705143161472971) """ if A.isket or A.isbra: A = A.proj() if B.isket or B.isbra: B = B.proj() if A.dims != B.dims: raise TypeError("A and B do not have same dimensions.") diff = A - B diff = diff.dag() * diff vals = diff.eigenenergies(sparse=sparse, tol=tol) return np.real(0.5 * np.sum(np.sqrt(np.abs(vals)))) def hilbert_dist(A, B): """ Returns the Hilbert-Schmidt distance between two density matrices A & B. Parameters ---------- A : qobj Density matrix or state vector. B : qobj Density matrix or state vector with same dimensions as A. Returns ------- dist : float Hilbert-Schmidt distance between density matrices. Notes ----- See V. Vedral and M. B. Plenio, Phys. Rev. A 57, 1619 (1998). """ if A.isket or A.isbra: A = A.proj() if B.isket or B.isbra: B = B.proj() if A.dims != B.dims: raise TypeError('A and B do not have same dimensions.') return ((A - B)**2).tr() def bures_dist(A, B): """ Returns the Bures distance between two density matrices A & B. The Bures distance ranges from 0, for states with unit fidelity, to sqrt(2). Parameters ---------- A : qobj Density matrix or state vector. B : qobj Density matrix or state vector with same dimensions as A. Returns ------- dist : float Bures distance between density matrices. """ if A.isket or A.isbra: A = A.proj() if B.isket or B.isbra: B = B.proj() if A.dims != B.dims: raise TypeError('A and B do not have same dimensions.') dist = np.sqrt(2 * (1 - fidelity(A, B))) return dist def bures_angle(A, B): """ Returns the Bures Angle between two density matrices A & B. The Bures angle ranges from 0, for states with unit fidelity, to pi/2. Parameters ---------- A : qobj Density matrix or state vector. B : qobj Density matrix or state vector with same dimensions as A. Returns ------- angle : float Bures angle between density matrices. """ if A.isket or A.isbra: A = A.proj() if B.isket or B.isbra: B = B.proj() if A.dims != B.dims: raise TypeError('A and B do not have same dimensions.') return np.arccos(fidelity(A, B)) def hellinger_dist(A, B, sparse=False, tol=0): """ Calculates the quantum Hellinger distance between two density matrices. Formula: ``hellinger_dist(A, B) = sqrt(2 - 2 * tr(sqrt(A) * sqrt(B)))`` See: D. Spehner, F. Illuminati, M. Orszag, and W. Roga, "Geometric measures of quantum correlations with Bures and Hellinger distances" arXiv:1611.03449 Parameters ---------- A : :class:`.Qobj` Density matrix or state vector. B : :class:`.Qobj` Density matrix or state vector with same dimensions as A. tol : float, default: 0 Tolerance used by sparse eigensolver, if used. (0 = Machine precision) sparse : bool, default: False Use sparse eigensolver. Returns ------- hellinger_dist : float Quantum Hellinger distance between A and B. Ranges from 0 to sqrt(2). Examples -------- >>> x = fock_dm(5,3) >>> y = coherent_dm(5,1) >>> np.allclose(hellinger_dist(x, y), 1.3725145002591095) True """ if A.isket or A.isbra: sqrtmA = ket2dm(A) else: sqrtmA = A.sqrtm(sparse=sparse, tol=tol) if B.isket or B.isbra: sqrtmB = ket2dm(B) else: sqrtmB = B.sqrtm(sparse=sparse, tol=tol) if sqrtmA.dims != sqrtmB.dims: raise TypeError("A and B do not have compatible dimensions.") product = sqrtmA*sqrtmB eigs = product.eigenenergies(sparse=sparse, tol=tol) # np.maximum() is to avoid nan appearing sometimes due to numerical # instabilities causing np.sum(eigs) slightly (~1e-8) larger than 1 when # hellinger_dist(A, B) is called for A=B return np.sqrt(2.0 * np.maximum(0, 1 - np.real(np.sum(eigs)))) def dnorm(A, B=None, solver="CVXOPT", verbose=False, force_solve=False, sparse=True): r""" Calculates the diamond norm of the quantum map q_oper, using the simplified semidefinite program of [Wat13]_. The diamond norm SDP is solved by using `CVXPY `_. If B is provided and both A and B are unitary, then the diamond norm of the difference is calculated more efficiently using the following geometric interpretation: :math:`\|A - B\|_{\diamond}` equals :math:`2 \sqrt(1 - d^2)`, where :math:`d`is the distance between the origin and the convex hull of the eigenvalues of :math:`A B^{\dagger}`. See [AKN98]_ page 18, in the paragraph immediately below the proof of 12.6, as a reference. Parameters ---------- A : Qobj Quantum map to take the diamond norm of. B : Qobj or None If provided, the diamond norm of :math:`A - B` is taken instead. solver : str {"CVXOPT", "SCS"}, default: "CVXOPT" Solver to use with CVXPY. "SCS" tends to be significantly faster, but somewhat less accurate. verbose : bool, default: False If True, prints additional information about the solution. force_solve : bool, default: False If True, forces dnorm to solve the associated SDP, even if a special case is known for the argument. sparse : bool, default: True Whether to use sparse matrices in the convex optimisation problem. Default True. Returns ------- dn : float Diamond norm of q_oper. Raises ------ ImportError If CVXPY cannot be imported. """ if cvxpy is None: # pragma: no cover raise ImportError("dnorm() requires CVXPY to be installed.") if B is not None and A.dims != B.dims: raise TypeError("A and B do not have the same dimensions.") # We follow the strategy of using Watrous' simpler semidefinite # program in its primal form. This is the same strategy used, # for instance, by both pyGSTi and SchattenNorms.jl. (By contrast, # QETLAB uses the dual problem.) # Check if A and B are both unitaries. If so we can use the geometric # interpretation mentioned in D. Aharonov, A. Kitaev, and N. Nisan. (1998). # We find the eigenvalues of AB⁺ and the distance d between the origin # and the complex hull of these. Plugging this into 2√1-d² gives the # diamond norm. if ( not force_solve and A.isunitary and B is not None and B.isunitary ): # Special optimisation for a difference of unitaries. U = A * B.dag() eigs = U.eigenenergies() d = _find_poly_distance(eigs) return 2 * np.sqrt(1 - d**2) # plug d into formula J = to_choi(A) if B is not None: # If B is provided, calculate difference J -= to_choi(B) if not force_solve and J.iscptp: # diamond norm of a CPTP map is 1 (Prop 3.44 Watrous 2018) return 1.0 # Watrous 2012 also points out that the diamond norm of Lambda # is the same as the completely-bounded operator-norm (∞-norm) # of the dual map of Lambda. We can evaluate that norm much more # easily if Lambda is completely positive, since then the largest # eigenvalue is the same as the largest singular value. if not force_solve and J.iscp: S_dual = to_super(J.dual_chan()) vec_eye = operator_to_vector(qeye(S_dual.dims[1][1])) op = vector_to_operator(S_dual * vec_eye) # The 2-norm was not implemented for sparse matrices as of the time # of this writing. Thus, we must yet again go dense. return la.norm(op.full(), 2) # If we're still here, we need to actually solve the problem. # Assume square... dim = int(np.prod(J.dims[0][0])) # Load the parameters with the Choi matrix passed in. J_dat = _data.to('csr', J.data).as_scipy() if not sparse: problem, Jr, Ji = dnorm_problem(dim) # Load the parameters with the Choi matrix passed in. Jr.value = sp.csr_matrix((J_dat.data.real, J_dat.indices, J_dat.indptr), shape=J_dat.shape).toarray() Ji.value = sp.csr_matrix((J_dat.data.imag, J_dat.indices, J_dat.indptr), shape=J_dat.shape).toarray() else: problem = dnorm_sparse_problem(dim, J_dat) problem.solve(solver=solver, verbose=verbose) return problem.value def unitarity(oper): """ Returns the unitarity of a quantum map, defined as the Frobenius norm of the unital block of that map's superoperator representation. Parameters ---------- oper : Qobj Quantum map under consideration. Returns ------- u : float Unitarity of ``oper``. """ Eu = _to_superpauli(oper).full()[1:, 1:] return np.linalg.norm(Eu, 'fro')**2 / len(Eu) def _find_poly_distance(eigenvals) -> float: """ Returns the distance between the origin and the convex hull of eigenvalues. The complex eigenvalues must have unit length (i.e. lie on the circle about the origin). """ phases = np.angle(eigenvals) phase_max = phases.max() phase_min = phases.min() if phase_min > 0: # all eigenvals have pos phase: hull is above x axis return np.cos((phase_max - phase_min) / 2) if phase_max <= 0: # all eigenvals have neg phase: hull is below x axis return np.cos((np.abs(phase_min) - np.abs(phase_max)) / 2) pos_phase_min = np.where(phases > 0, phases, np.inf).min() neg_phase_max = np.where(phases <= 0, phases, -np.inf).max() big_angle = phase_max - phase_min small_angle = pos_phase_min - neg_phase_max if big_angle >= np.pi: if small_angle <= np.pi: # hull contains the origin return 0 else: # hull is left of y axis return np.cos((2 * np.pi - small_angle) / 2) else: # hull is right of y axis return np.cos(big_angle / 2) qutip-5.1.1/qutip/core/numpy_backend.py000066400000000000000000000003721474175217300201600ustar00rootroot00000000000000from ..settings import settings class NumpyBackend: def _qutip_setting_backend(self, np): self._qt_np = np def __getattr__(self, name): return getattr(self._qt_np, name) # Initialize the numpy backend np = NumpyBackend() qutip-5.1.1/qutip/core/operators.py000066400000000000000000001044301474175217300173570ustar00rootroot00000000000000""" This module contains functions for generating Qobj representation of a variety of commonly occuring quantum operators. """ # Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations __all__ = [ 'jmat', 'spin_Jx', 'spin_Jy', 'spin_Jz', 'spin_Jm', 'spin_Jp', 'spin_J_set', 'sigmap', 'sigmam', 'sigmax', 'sigmay', 'sigmaz', 'destroy', 'create', 'fdestroy', 'fcreate', 'qeye', 'identity', 'position', 'momentum', 'num', 'squeeze', 'squeezing', 'displace', 'commutator', 'qutrit_ops', 'qdiags', 'phase', 'qzero', 'charge', 'tunneling', 'qft', 'qzero_like', 'qeye_like', 'swap', ] import numpy as np from typing import Literal, overload from . import data as _data from .qobj import Qobj from .dimensions import Space from .. import settings from ..typing import DimensionLike, SpaceLike, LayerType def qdiags( diagonals: np.typing.ArrayLike | list[np.typing.ArrayLike], offsets: int | list[int] = None, dims: DimensionLike = None, shape: tuple[int, int] = None, *, dtype: LayerType = None, ) -> Qobj: """ Constructs an operator from an array of diagonals. Parameters ---------- diagonals : array_like or sequence of array_like Array of elements to place along the selected diagonals. offsets : int or sequence of ints, optional Sequence for diagonals to be set: - k=0 main diagonal - k>0 kth upper diagonal - k<0 kth lower diagonal dims : list, optional Dimensions for operator shape : list, tuple, optional Shape of operator. If omitted, a square operator large enough to contain the diagonals is generated. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> qdiags(sqrt(range(1, 4)), 1) # doctest: +SKIP Quantum object: dims = [[4], [4]], \ shape = [4, 4], type = oper, isherm = False Qobj data = [[ 0. 1. 0. 0. ] [ 0. 0. 1.41421356 0. ] [ 0. 0. 0. 1.73205081] [ 0. 0. 0. 0. ]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia offsets = [0] if offsets is None else offsets if not isinstance(offsets, list): offsets = [offsets] if len(offsets) == 1 and offsets[0] != 0: isherm = False isunitary = False elif offsets == [0]: isherm = np.all(np.imag(diagonals) <= settings.core["atol"]) isunitary = np.all(np.abs(diagonals) - 1 <= settings.core["atol"]) else: isherm = None isunitary = None data = _data.diag[dtype](diagonals, offsets, shape) return Qobj( data, copy=False, dims=dims, isherm=isherm, isunitary=isunitary ) @overload def jmat( j: float, which: Literal[None], *, dtype: LayerType = None ) -> tuple[Qobj]: ... @overload def jmat( j: float, which: Literal["x", "y", "z", "+", "-"], *, dtype: LayerType = None ) -> Qobj: ... def jmat( j: float, which: Literal["x", "y", "z", "+", "-", None] = None, *, dtype: LayerType = None ) -> Qobj | tuple[Qobj]: """Higher-order spin operators: Parameters ---------- j : float Spin of operator which : str, optional Which operator to return 'x','y','z','+','-'. If not given, then output is ['x','y','z'] dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- jmat : Qobj or tuple of Qobj ``qobj`` for requested spin operator(s). Examples -------- >>> jmat(1) # doctest: +SKIP [ Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 0. 0.70710678 0. ] [ 0.70710678 0. 0.70710678] [ 0. 0.70710678 0. ]] Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.-0.70710678j 0.+0.j ] [ 0.+0.70710678j 0.+0.j 0.-0.70710678j] [ 0.+0.j 0.+0.70710678j 0.+0.j ]] Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 1. 0. 0.] [ 0. 0. 0.] [ 0. 0. -1.]]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR if int(2 * j) != 2 * j or j < 0: raise ValueError('j must be a non-negative integer or half-integer') if not which: return ( jmat(j, 'x', dtype=dtype), jmat(j, 'y', dtype=dtype), jmat(j, 'z', dtype=dtype) ) dims = [[int(2*j + 1)]]*2 if which == '+': return Qobj(_jplus(j, dtype=dtype), dims=dims, isherm=False, isunitary=False, copy=False) if which == '-': return Qobj(_jplus(j, dtype=dtype).adjoint(), dims=dims, isherm=False, isunitary=False, copy=False) if which == 'x': A = _jplus(j, dtype=dtype) return Qobj(_data.add(A, A.adjoint()) * 0.5, dims=dims, isherm=True, isunitary=False, copy=False) if which == 'y': A = _data.mul(_jplus(j, dtype=dtype), -0.5j) return Qobj(_data.add(A, A.adjoint()), dims=dims, isherm=True, isunitary=False, copy=False) if which == 'z': return Qobj(_jz(j, dtype=dtype), dims=dims, isherm=True, isunitary=False, copy=False) raise ValueError('Invalid spin operator: ' + which) def _jplus(j, *, dtype=None): """ Internal functions for generating the data representing the J-plus operator. """ m = np.arange(j, -j - 1, -1, dtype=complex) data = np.sqrt(j * (j + 1) - m * (m + 1))[1:] return _data.diag[dtype](data, 1) def _jz(j, *, dtype=None): """ Internal functions for generating the data representing the J-z operator. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR N = int(2*j + 1) data = np.array([j-k for k in range(N)], dtype=complex) return _data.diag[dtype](data, 0) # # Spin j operators: # def spin_Jx(j: float, *, dtype: LayerType = None) -> Qobj: """Spin-j x operator Parameters ---------- j : float Spin of operator dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- op : Qobj ``qobj`` representation of the operator. """ return jmat(j, 'x', dtype=dtype) def spin_Jy(j: float, *, dtype: LayerType = None) -> Qobj: """Spin-j y operator Parameters ---------- j : float Spin of operator dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- op : Qobj ``qobj`` representation of the operator. """ return jmat(j, 'y', dtype=dtype) def spin_Jz(j: float, *, dtype: LayerType = None) -> Qobj: """Spin-j z operator Parameters ---------- j : float Spin of operator dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- op : Qobj ``qobj`` representation of the operator. """ return jmat(j, 'z', dtype=dtype) def spin_Jm(j: float, *, dtype: LayerType = None) -> Qobj: """Spin-j annihilation operator Parameters ---------- j : float Spin of operator dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- op : Qobj ``qobj`` representation of the operator. """ return jmat(j, '-', dtype=dtype) def spin_Jp(j: float, *, dtype: LayerType = None) -> Qobj: """Spin-j creation operator Parameters ---------- j : float Spin of operator dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- op : Qobj ``qobj`` representation of the operator. """ return jmat(j, '+', dtype=dtype) def spin_J_set(j: float, *, dtype: LayerType = None) -> tuple[Qobj]: """Set of spin-j operators (x, y, z) Parameters ---------- j : float Spin of operators dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- list : tuple of Qobj list of ``qobj`` representating of the spin operator. """ return jmat(j, dtype=dtype) # Pauli spin-1/2 operators. # # These are so common in quantum information that we want them to be # near-instantaneous to initialise, so we cache them at package import, and # just return copies when someone requests one. _SIGMAP = jmat(0.5, '+') _SIGMAM = jmat(0.5, '-') _SIGMAX = 2 * jmat(0.5, 'x') _SIGMAX._isunitary = True _SIGMAY = 2 * jmat(0.5, 'y') _SIGMAY._isunitary = True _SIGMAZ = 2 * jmat(0.5, 'z') _SIGMAZ._isunitary = True def sigmap(*, dtype: LayerType = None) -> Qobj: """Creation operator for Pauli spins. Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> sigmap() # doctest: +SKIP Quantum object: dims = [[2], [2]], \ shape = [2, 2], type = oper, isHerm = False Qobj data = [[ 0. 1.] [ 0. 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return _SIGMAP.to(dtype, True) def sigmam(*, dtype: LayerType = None) -> Qobj: """Annihilation operator for Pauli spins. Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> sigmam() # doctest: +SKIP Quantum object: dims = [[2], [2]], \ shape = [2, 2], type = oper, isHerm = False Qobj data = [[ 0. 0.] [ 1. 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return _SIGMAM.to(dtype, True) def sigmax(*, dtype: LayerType = None) -> Qobj: """Pauli spin 1/2 sigma-x operator Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> sigmax() # doctest: +SKIP Quantum object: dims = [[2], [2]], \ shape = [2, 2], type = oper, isHerm = False Qobj data = [[ 0. 1.] [ 1. 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return _SIGMAX.to(dtype, True) def sigmay(*, dtype: LayerType = None) -> Qobj: """Pauli spin 1/2 sigma-y operator. Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> sigmay() # doctest: +SKIP Quantum object: dims = [[2], [2]], \ shape = [2, 2], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.-1.j] [ 0.+1.j 0.+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return _SIGMAY.to(dtype, True) def sigmaz(*, dtype: LayerType = None) -> Qobj: """Pauli spin 1/2 sigma-z operator. Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Examples -------- >>> sigmaz() # doctest: +SKIP Quantum object: dims = [[2], [2]], \ shape = [2, 2], type = oper, isHerm = True Qobj data = [[ 1. 0.] [ 0. -1.]] """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return _SIGMAZ.to(dtype, True) def destroy(N: int, offset: int = 0, *, dtype: LayerType = None) -> Qobj: """ Destruction (lowering) operator. Parameters ---------- N : int Number of basis states in the Hilbert space. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Qobj for lowering operator. Examples -------- >>> destroy(4) # doctest: +SKIP Quantum object: dims=[[4], [4]], shape=(4, 4), type='oper', isherm=False Qobj data = [[ 0.00000000+0.j 1.00000000+0.j 0.00000000+0.j 0.00000000+0.j] [ 0.00000000+0.j 0.00000000+0.j 1.41421356+0.j 0.00000000+0.j] [ 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j 1.73205081+0.j] [ 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia if not isinstance(N, (int, np.integer)): # raise error if N not integer raise ValueError("Hilbert space dimension must be integer value") data = np.sqrt(np.arange(offset+1, N+offset, dtype=complex)) return qdiags(data, 1, dtype=dtype) def create(N: int, offset: int = 0, *, dtype: LayerType = None) -> Qobj: """ Creation (raising) operator. Parameters ---------- N : int Number of basis states in the Hilbert space. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Qobj for raising operator. Examples -------- >>> create(4) # doctest: +SKIP Quantum object: dims=[[4], [4]], shape=(4, 4), type='oper', isherm=False Qobj data = [[ 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j] [ 1.00000000+0.j 0.00000000+0.j 0.00000000+0.j 0.00000000+0.j] [ 0.00000000+0.j 1.41421356+0.j 0.00000000+0.j 0.00000000+0.j] [ 0.00000000+0.j 0.00000000+0.j 1.73205081+0.j 0.00000000+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia if not isinstance(N, (int, np.integer)): # raise error if N not integer raise ValueError("Hilbert space dimension must be integer value") data = np.sqrt(np.arange(offset+1, N+offset, dtype=complex)) return qdiags(data, -1, dtype=dtype) def fdestroy(n_sites: int, site, dtype: LayerType = None) -> Qobj: """ Fermionic destruction operator. We use the Jordan-Wigner transformation, making use of the Jordan-Wigner ZZ..Z strings, to construct this as follows: .. math:: a_j = \\sigma_z^{\\otimes j} \\otimes (\\frac{\\sigma_x + i \\sigma_y}{2}) \\otimes I^{\\otimes N-j-1} Parameters ---------- n_sites : int Number of sites in Fock space. site : int The site in Fock space to add a fermion to. Corresponds to j in the above JW transform. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Qobj for destruction operator. Examples -------- >>> fdestroy(2) # doctest: +SKIP Quantum object: dims=[[2 2], [2 2]], shape=(4, 4), \ type='oper', isherm=False Qobj data = [[0. 0. 1. 0.] [0. 0. 0. 1.] [0. 0. 0. 0.] [0. 0. 0. 0.]] """ return _f_op(n_sites, site, 'destruction', dtype=dtype) def fcreate(n_sites: int, site, dtype: LayerType = None) -> Qobj: """ Fermionic creation operator. We use the Jordan-Wigner transformation, making use of the Jordan-Wigner ZZ..Z strings, to construct this as follows: .. math:: a_j = \\sigma_z^{\\otimes j} \\otimes (\\frac{\\sigma_x - i \\sigma_y}{2}) \\otimes I^{\\otimes N-j-1} Parameters ---------- n_sites : int Number of sites in Fock space. site : int The site in Fock space to add a fermion to. Corresponds to j in the above JW transform. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Qobj for raising operator. Examples -------- >>> fcreate(2) # doctest: +SKIP Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), \ type = oper, isherm = False Qobj data = [[0. 0. 0. 0.] [0. 0. 0. 0.] [1. 0. 0. 0.] [0. 1. 0. 0.]] """ return _f_op(n_sites, site, 'creation', dtype=dtype) def _f_op(n_sites, site, action, dtype: LayerType = None,): """ Makes fermionic creation and destruction operators. We use the Jordan-Wigner transformation, making use of the Jordan-Wigner ZZ..Z strings, to construct this as follows: .. math:: a_j = \\sigma_z^{\\otimes j} \\otimes (frac{sigma_x \\pm i sigma_y}{2}) \\otimes I^{\\otimes N-j-1} Parameters ---------- action : str The type of operator to build. Can only be 'creation' or 'destruction' n_sites : int Number of sites in Fock space. site : int The site in Fock space to create/destroy a fermion on. Corresponds to j in the above JW transform. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Qobj for destruction operator. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR # get `tensor` and sigma z objects from .tensor import tensor s_z = 2 * jmat(0.5, 'z', dtype=dtype) # sanity check if site < 0: raise ValueError(f'The specified site {site} cannot be \ less than 0.') elif 0 >= n_sites: raise ValueError(f'The specified number of sites {n_sites} \ cannot be equal to or less than 0.') elif site >= n_sites: raise ValueError(f'The specified site {site} is not in \ the range of {n_sites} sites.') # figure out which operator to build if action.lower() == 'creation': operator = create(2, dtype=dtype) elif action.lower() == 'destruction': operator = destroy(2, dtype=dtype) else: raise TypeError("Unknown operator '%s'. `action` must be \ either 'creation' or 'destruction.'" % action) eye = identity(2, dtype=dtype) opers = [s_z] * site + [operator] + [eye] * (n_sites - site - 1) out = tensor(opers).to(dtype) out.isherm = False out._isunitary = False return out def qzero( dimensions: SpaceLike, dims_right: SpaceLike = None, *, dtype: LayerType = None ) -> Qobj: """ Zero operator. Parameters ---------- dimensions : int, list of int, list of list of int, Space Number of basis states in the Hilbert space. If provided as a list of ints, then the dimension is the product over this list, but the ``dims`` property of the new Qobj are set to this list. This can produce either `oper` or `super` depending on the passed `dimensions`. dims_right : int, list of int, list of list of int, Space, optional Number of basis states in the right Hilbert space when the operator is rectangular. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- qzero : qobj Zero operator Qobj. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR dims_left = Space(dimensions) size_left = dims_left.size if dims_right is None: dims_right = dims_left size_right = size_left else: dims_right = Space(dims_right) size_right = dims_right.size dims = [dims_left, dims_right] # A sparse matrix with no data is equal to a zero matrix. return Qobj(_data.zeros[dtype](size_left, size_right), dims=dims, isherm=True, isunitary=False, copy=False) def qzero_like(qobj: Qobj) -> Qobj: """ Zero operator of the same dims and type as the reference. Parameters ---------- qobj : Qobj, QobjEvo Reference quantum object to copy the dims from. Returns ------- qzero : qobj Zero operator Qobj. """ return Qobj( _data.zeros[qobj.dtype](*qobj.shape), dims=qobj._dims, isherm=True, isunitary=False, copy=False ) def qeye(dimensions: SpaceLike, *, dtype: LayerType = None) -> Qobj: """ Identity operator. Parameters ---------- dimensions : (int) or (list of int) or (list of list of int), Space Number of basis states in the Hilbert space. If provided as a list of ints, then the dimension is the product over this list, but the ``dims`` property of the new Qobj are set to this list. This can produce either `oper` or `super` depending on the passed `dimensions`. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Identity operator Qobj. Examples -------- >>> qeye(3) # doctest: +SKIP Quantum object: dims = [[3], [3]], shape = (3, 3), type = oper, \ isherm = True Qobj data = [[ 1. 0. 0.] [ 0. 1. 0.] [ 0. 0. 1.]] >>> qeye([2,2]) # doctest: +SKIP Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, \ isherm = True Qobj data = [[1. 0. 0. 0.] [0. 1. 0. 0.] [0. 0. 1. 0.] [0. 0. 0. 1.]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia dimensions = Space(dimensions) return Qobj(_data.identity[dtype](dimensions.size), dims=[dimensions]*2, isherm=True, isunitary=True, copy=False) # Name alias. identity = qeye def qeye_like(qobj: Qobj) -> Qobj: """ Identity operator with the same dims and type as the reference quantum object. Parameters ---------- qobj : Qobj, QobjEvo Reference quantum object to copy the dims from. Returns ------- oper : qobj Identity operator Qobj. """ if qobj.shape[0] != qobj.shape[1]: raise ValueError( "Can't create an identity matrix like a non square matrix." ) return Qobj( _data.identity[qobj.dtype](qobj.shape[0]), dims=qobj._dims, isherm=True, isunitary=True, copy=False ) def position(N: int, offset: int = 0, *, dtype: LayerType = None) -> Qobj: """ Position operator :math:`x = 1 / sqrt(2) * (a + a.dag())` Parameters ---------- N : int Number of basis states in the Hilbert space. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Position operator as Qobj. """ dtype = dtype or settings.core["default_dtype"] or _data.Dia a = destroy(N, offset=offset, dtype=dtype) position = np.sqrt(0.5) * (a + a.dag()) position.isherm = True position._isunitary = False return position.to(dtype) def momentum(N: int, offset: int = 0, *, dtype: LayerType = None) -> Qobj: """ Momentum operator p=-1j/sqrt(2)*(a-a.dag()) Parameters ---------- N : int Number of basis states in the Hilbert space. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Momentum operator as Qobj. """ dtype = dtype or settings.core["default_dtype"] or _data.Dia a = destroy(N, offset=offset, dtype=dtype) momentum = -1j * np.sqrt(0.5) * (a - a.dag()) momentum.isherm = True momentum._isunitary = False return momentum.to(dtype) def num(N: int, offset: int = 0, *, dtype: LayerType = None) -> Qobj: """ Quantum object for number operator. Parameters ---------- N : int Number of basis states in the Hilbert space. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper: qobj Qobj for number operator. Examples -------- >>> num(4) # doctest: +SKIP Quantum object: dims=[[4], [4]], shape=(4, 4), type='oper', isherm=True Qobj data = [[0 0 0 0] [0 1 0 0] [0 0 2 0] [0 0 0 3]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia data = np.arange(offset, offset + N, dtype=complex) return qdiags(data, 0, dtype=dtype) def squeeze( N: int, z: float, offset: int = 0, *, dtype: LayerType = None, ) -> Qobj: """Single-mode squeezing operator. Parameters ---------- N : int Dimension of hilbert space. z : float/complex Squeezing parameter. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : :class:`.Qobj` Squeezing operator. Examples -------- >>> squeeze(4, 0.25) # doctest: +SKIP Quantum object: dims = [[4], [4]], \ shape = [4, 4], type = oper, isHerm = False Qobj data = [[ 0.98441565+0.j 0.00000000+0.j 0.17585742+0.j 0.00000000+0.j] [ 0.00000000+0.j 0.95349007+0.j 0.00000000+0.j 0.30142443+0.j] [-0.17585742+0.j 0.00000000+0.j 0.98441565+0.j 0.00000000+0.j] [ 0.00000000+0.j -0.30142443+0.j 0.00000000+0.j 0.95349007+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dense asq = destroy(N, offset=offset, dtype=dtype) ** 2 op = 0.5*np.conj(z)*asq - 0.5*z*asq.dag() out = op.expm(dtype=dtype) out.isherm = (N == 2) or (z == 0.) out._isunitary = True return out def squeezing(a1: Qobj, a2: Qobj, z: float) -> Qobj: """Generalized squeezing operator. .. math:: S(z) = \\exp\\left(\\frac{1}{2}\\left(z^*a_1a_2 - za_1^\\dagger a_2^\\dagger\\right)\\right) Parameters ---------- a1 : :class:`.Qobj` Operator 1. a2 : :class:`.Qobj` Operator 2. z : float/complex Squeezing parameter. Returns ------- oper : :class:`.Qobj` Squeezing operator. """ b = 0.5 * (np.conj(z)*(a1 @ a2) - z*(a1.dag() @ a2.dag())) return b.expm() def displace( N: int, alpha: float, offset: int = 0, *, dtype: LayerType = None, ) -> Qobj: """Single-mode displacement operator. Parameters ---------- N : int Number of basis states in the Hilbert space. alpha : float/complex Displacement amplitude. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the operator. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Displacement operator. Examples -------- >>> displace(4,0.25) # doctest: +SKIP Quantum object: dims = [[4], [4]], \ shape = [4, 4], type = oper, isHerm = False Qobj data = [[ 0.96923323+0.j -0.24230859+0.j 0.04282883+0.j -0.00626025+0.j] [ 0.24230859+0.j 0.90866411+0.j -0.33183303+0.j 0.07418172+0.j] [ 0.04282883+0.j 0.33183303+0.j 0.84809499+0.j -0.41083747+0.j] [ 0.00626025+0.j 0.07418172+0.j 0.41083747+0.j 0.90866411+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dense a = destroy(N, offset=offset) out = (alpha * a.dag() - np.conj(alpha) * a).expm(dtype=dtype) out.isherm = (alpha == 0.) out._isunitary = True return out def commutator( A: Qobj, B: Qobj, kind: Literal["normal", "anti"] = "normal" ) -> Qobj: """ Return the commutator of kind `kind` (normal, anti) of the two operators A and B. Parameters ---------- A, B : :obj:`Qobj`, :obj:`QobjEvo` The operators to compute the commutator of. kind: str {"normal", "anti"}, default: "anti" Which kind of commutator to compute. """ if kind == 'normal': return A @ B - B @ A elif kind == 'anti': return A @ B + B @ A else: raise TypeError("Unknown commutator kind '%s'" % kind) def qutrit_ops(*, dtype: LayerType = None) -> list[Qobj]: """ Operators for a three level system (qutrit). Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- opers: array `array` of qutrit operators. """ from .states import qutrit_basis dtype = dtype or settings.core["default_dtype"] or _data.CSR out = [] basis = qutrit_basis(dtype=dtype) for i in range(3): op = basis[i] @ basis[i].dag() op.isherm = True op._isunitary = False out.append(op) for i in range(3): op = basis[i] @ basis[(i+1)%3].dag() op.isherm = False op._isunitary = False out.append(op) return out def phase(N: int, phi0: float = 0, *, dtype: LayerType = None) -> Qobj: """ Single-mode Pegg-Barnett phase operator. Parameters ---------- N : int Number of basis states in the Hilbert space. phi0 : float, default: 0 Reference phase. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Phase operator with respect to reference phase. Notes ----- The Pegg-Barnett phase operator is Hermitian on a truncated Hilbert space. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense phim = phi0 + (2 * np.pi * np.arange(N)) / N # discrete phase angles n = np.arange(N)[:, np.newaxis] states = np.array([np.sqrt(kk) / np.sqrt(N) * np.exp(1j * n * kk) for kk in phim]) ops = np.sum([np.outer(st, st.conj()) for st in states], axis=0) return Qobj( ops, isherm=True, isunitary=False, dims=[[N], [N]], copy=False ).to(dtype) def charge( Nmax: int, Nmin: int = None, frac: float = 1, *, dtype: LayerType = None ) -> Qobj: """ Generate the diagonal charge operator over charge states from Nmin to Nmax. Parameters ---------- Nmax : int Maximum charge state to consider. Nmin : int, default: -Nmax Lowest charge state to consider. frac : float, default: 1 Specify fractional charge if needed. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- C : Qobj Charge operator over [Nmin, Nmax]. Notes ----- .. versionadded:: 3.2 """ dtype = dtype or settings.core["default_dtype"] or _data.Dia if Nmin is None: Nmin = -Nmax diag = frac * np.arange(Nmin, Nmax+1, dtype=float) out = qdiags(diag, 0, dtype=dtype) out._isunitary = (len(diag) <= 2) and np.all(np.abs(diag) == 1.) return out def tunneling(N: int, m: int = 1, *, dtype: LayerType = None) -> Qobj: r""" Tunneling operator with elements of the form :math:`\\sum |N> Qobj: """ Quantum Fourier Transform operator. Parameters ---------- dimensions : (int) or (list of int) or (list of list of int) Number of basis states in the Hilbert space. If provided as a list of ints, then the dimension is the product over this list, but the ``dims`` property of the new Qobj are set to this list. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- QFT: qobj Quantum Fourier transform operator. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense dimensions = Space(dimensions) dims = [dimensions]*2 N2 = dimensions.size phase = 2.0j * np.pi / N2 arr = np.arange(N2) L, M = np.meshgrid(arr, arr) data = np.exp(phase * (L * M)) / np.sqrt(N2) return Qobj(data, isherm=False, isunitary=True, dims=dims).to(dtype) def swap(N: int, M: int, *, dtype: LayerType = None) -> Qobj: """ Operator that exchanges the order of tensored spaces: swap(N, M) @ tensor(ketN, ketM) == tensor(ketM, ketN) parameters ---------- N : int Number of basis states in the first Hilbert space. M : int Number of basis states in the second Hilbert space. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR if N == 1 and M == 1: return qeye([1, 1], dtype=dtype) data = np.ones(N * M) rows = np.arange(N * M + 1) # last entry is nnz cols = np.ravel(M * np.arange(N)[None, :] + np.arange(M)[:, None]) return Qobj( _data.CSR((data, cols, rows), (N * M, N * M)), dims=[[M, N], [N, M]], isherm=(N == M), isunitary=True, ).to(dtype) qutip-5.1.1/qutip/core/options.py000066400000000000000000000153451474175217300170420ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations from ..settings import settings from .numpy_backend import np as qt_np import numpy from typing import overload, Literal, Any import types __all__ = ["CoreOptions"] class QutipOptions: """ Class for basic functionality for qutip's options. Define basic method to wrap an ``options`` dict. Default options are in a class _options dict. Options can also act as properties. The ``_properties`` map options keys to a function to call when the ``QutipOptions`` become the default. """ _options: dict[str, Any] = {} _properties = {} _settings_name = None # Where the default is in settings def __init__(self, **options): self.options = self._options.copy() for key in set(options) & set(self.options): self[key] = options.pop(key) if options: raise KeyError(f"Options {set(options)} are not supported.") def __contains__(self, key: str) -> bool: return key in self.options def __getitem__(self, key: str) -> Any: # Let the dict catch the KeyError return self.options[key] def __setitem__(self, key: str, value: Any) -> None: # Let the dict catch the KeyError self.options[key] = value if ( key in self._properties and self is getattr(settings, self._settings_name) ): self._properties[key](value) def __repr__(self, full: bool = True) -> str: out = [f"<{self.__class__.__name__}("] for key, value in self.options.items(): if full or value != self._options[key]: out += [f" '{key}': {repr(value)},"] out += [")>"] if len(out) - 2: return "\n".join(out) else: return "".join(out) def __enter__(self): self._backup = getattr(settings, self._settings_name) self._set_as_global_default() def __exit__( self, exc_type: type[BaseException] | None, exc_value: BaseException | None, exc_traceback: types.TracebackType | None, ) -> None: self._backup._set_as_global_default() def _set_as_global_default(self): setattr(settings, self._settings_name, self) for key in self._properties: self._properties[key](self.options[key]) class CoreOptions(QutipOptions): """ Options used by the core of qutip such as the tolerance of :obj:`.Qobj` comparison or coefficient's format. Values can be changed in ``qutip.settings.core`` or by using context: ``with CoreOptions(atol=1e-6): ...`` ******** Options: ******** auto_tidyup : bool Whether to tidyup during sparse operations. auto_tidyup_dims : bool [False] Use auto tidyup dims on multiplication, tensor, etc. Without auto_tidyup_dims: ``basis([2, 2]).dims == [[2, 2], [1, 1]]`` With auto_tidyup_dims: ``basis([2, 2]).dims == [[2, 2], [1]]`` atol : float {1e-12} General absolute tolerance. Used in various functions to round off small values. rtol : float {1e-12} General relative tolerance. auto_tidyup_atol : float {1e-14} The absolute tolerance used in automatic tidyup (see the ``auto_tidyup`` parameter above) and the default value of ``atol`` used in :meth:`Qobj.tidyup`. function_coefficient_style : str {"auto"} The signature expected by function coefficients. The options are: - "pythonic": the signature should be ``f(t, ...)`` where ``t`` is the time and the ``...`` are the remaining arguments passed directly into the function. E.g. ``f(t, w, b=5)``. - "dict": the signature shoule be ``f(t, args)`` where ``t`` is the time and ``args`` is a dict containing the remaining arguments. E.g. ``f(t, {"w": w, "b": 5})``. - "auto": select automatically between the two options above based on the signature of the supplied function. If the function signature is exactly ``f(t, args)`` then ``dict`` is used. Otherwise ``pythonic`` is used. default_dtype : Nonetype, str, type {None} When set, functions creating :obj:`.Qobj`, such as :func:"qeye" or :func:"rand_herm", will use the specified data type. Any data-layer known to ``qutip.data.to`` is accepted. When ``None``, these functions will default to a sensible data type. """ _options = { # use auto tidyup "auto_tidyup": True, # use auto tidyup dims on multiplication "auto_tidyup_dims": False, # general absolute tolerance "atol": 1e-12, # general relative tolerance "rtol": 1e-12, # use auto tidyup absolute tolerance "auto_tidyup_atol": 1e-14, # signature style expected by function coefficients "function_coefficient_style": "auto", # Default Qobj dtype for Qobj create function "default_dtype": None, # Expect, trace, etc. will return real for hermitian matrices. # Hermiticity checks can be slow, stop jitting, etc. "auto_real_casting": True, # Default backend is numpy "numpy_backend": numpy } _settings_name = "core" _properties = { "numpy_backend": qt_np._qutip_setting_backend, } @overload def __getitem__( self, key: Literal["auto_tidyup", "auto_tidyup_dims", "auto_real_casting"], ) -> bool: ... @overload def __getitem__( self, key: Literal["atol", "rtol", "auto_tidyup_atol"] ) -> float: ... @overload def __getitem__( self, key: Literal["function_coefficient_style"] ) -> str: ... @overload def __getitem__(self, key: Literal["default_dtype"]) -> str | None: ... def __getitem__(self, key: str) -> Any: # Let the dict catch the KeyError return self.options[key] @overload def __setitem__( self, key: Literal["auto_tidyup", "auto_tidyup_dims", "auto_real_casting"], value: bool, ) -> None: ... @overload def __setitem__( self, key: Literal["atol", "rtol", "auto_tidyup_atol"], value: float ) -> None: ... @overload def __setitem__( self, key: Literal["function_coefficient_style"], value: str ) -> None: ... @overload def __setitem__( self, key: Literal["default_dtype"], value: str | None ) -> None: ... def __setitem__(self, key: str, value: Any) -> None: # Let the dict catch the KeyError super().__setitem__(key, value) # Creating the instance of core options to use everywhere. # settings.core = CoreOptions() CoreOptions()._set_as_global_default() qutip-5.1.1/qutip/core/properties.py000066400000000000000000000017061474175217300175370ustar00rootroot00000000000000from . import Qobj, QobjEvo __all__ = [ 'isbra', 'isket', 'isoper', 'issuper', 'isoperbra', 'isoperket', 'isherm' ] def isbra(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['bra', 'scalar'] def isket(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['ket', 'scalar'] def isoper(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['oper', 'scalar'] def isoperbra(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['operator-bra'] def isoperket(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['operator-ket'] def issuper(x: Qobj | QobjEvo) -> bool: return isinstance(x, (Qobj, QobjEvo)) and x.type in ['super'] def isherm(x: Qobj) -> bool: if not isinstance(x, Qobj): raise TypeError(f"Invalid input type, got {type(x)}, exected Qobj") return x.isherm qutip-5.1.1/qutip/core/qobj.py000066400000000000000000001717531474175217300163100ustar00rootroot00000000000000"""The Quantum Object (Qobj) class, for representing quantum states and operators, and related functions. """ from __future__ import annotations import functools import numbers import warnings from typing import Any, Literal import numpy as np from numpy.typing import ArrayLike import scipy.sparse from .. import __version__ from ..settings import settings from . import data as _data from qutip.typing import LayerType, DimensionLike import qutip from .dimensions import ( enumerate_flat, collapse_dims_super, flatten, unflatten, Dimensions ) __all__ = ['Qobj', 'ptrace'] _NORM_FUNCTION_LOOKUP = { 'tr': _data.norm.trace, 'one': _data.norm.one, 'max': _data.norm.max, 'fro': _data.norm.frobenius, 'l2': _data.norm.l2, } _NORM_ALLOWED_MATRIX = {'tr', 'fro', 'one', 'max'} _NORM_ALLOWED_VECTOR = {'l2', 'max'} _CALL_ALLOWED = { ('super', 'oper'), ('super', 'ket'), ('oper', 'ket'), } def _require_equal_type(method): """ Decorate a binary Qobj method to ensure both operands are Qobj and of the same type and dimensions. Promote numeric scalar to identity matrices of the same type and shape. """ @functools.wraps(method) def out(self, other): if isinstance(other, Qobj): if self._dims != other._dims: msg = ( "incompatible dimensions " + repr(self.dims) + " and " + repr(other.dims) ) raise ValueError(msg) return method(self, other) if other == 0: return method(self, other) if self._dims.issquare and isinstance(other, numbers.Number): scale = complex(other) other = Qobj(_data.identity(self.shape[0], scale, dtype=type(self.data)), dims=self._dims, isherm=(scale.imag == 0), isunitary=(abs(abs(scale)-1) < settings.core['atol']), copy=False) return method(self, other) return NotImplemented return out def _latex_real(x): if not x: return "0" if not 0.001 <= abs(x) < 1000: base, exp = "{:.3e}".format(x).split('e') return base + r"\times10^{{ {:d} }}".format(int(exp)) if abs(x - int(x)) < 0.001: return "{:d}".format(round(x)) return "{:.3f}".format(x) def _latex_complex(x): if abs(x.imag) < 0.001: return _latex_real(x.real) if abs(x.real) < 0.001: return _latex_real(x.imag) + "j" sign = "+" if x.imag > 0 else "-" return "(" + _latex_real(x.real) + sign + _latex_real(abs(x.imag)) + "j)" def _latex_row(row, cols, data): if row is None: bits = (r"\ddots" if col is None else r"\vdots" for col in cols) else: bits = (r"\cdots" if col is None else _latex_complex(data[row, col]) for col in cols) return " & ".join(bits) class Qobj: """ A class for representing quantum objects, such as quantum operators and states. The Qobj class is the QuTiP representation of quantum operators and state vectors. This class also implements math operations +,-,* between Qobj instances (and / by a C-number), as well as a collection of common operator/state operations. The Qobj constructor optionally takes a dimension ``list`` and/or shape ``list`` as arguments. Parameters ---------- arg: array_like, data object or :obj:`.Qobj` Data for vector/matrix representation of the quantum object. dims: list Dimensions of object used for tensor products. copy: bool Flag specifying whether Qobj should get a copy of the input data, or use the original. Attributes ---------- data : object The data object storing the vector / matrix representation of the `Qobj`. dtype : type The data-layer type used for storing the data. The possible types are described in `Qobj.to <./classes.html#qutip.core.qobj.Qobj.to>`__. dims : list List of dimensions keeping track of the tensor structure. shape : list Shape of the underlying `data` array. type : str Type of quantum object: 'bra', 'ket', 'oper', 'operator-ket', 'operator-bra', or 'super'. superrep : str Representation used if `type` is 'super'. One of 'super' (Liouville form), 'choi' (Choi matrix with tr = dimension), or 'chi' (chi-matrix representation). isherm : bool Indicates if quantum object represents Hermitian operator. isunitary : bool Indictaes if quantum object represents unitary operator. iscp : bool Indicates if the quantum object represents a map, and if that map is completely positive (CP). ishp : bool Indicates if the quantum object represents a map, and if that map is hermicity preserving (HP). istp : bool Indicates if the quantum object represents a map, and if that map is trace preserving (TP). iscptp : bool Indicates if the quantum object represents a map that is completely positive and trace preserving (CPTP). isket : bool Indicates if the quantum object represents a ket. isbra : bool Indicates if the quantum object represents a bra. isoper : bool Indicates if the quantum object represents an operator. issuper : bool Indicates if the quantum object represents a superoperator. isoperket : bool Indicates if the quantum object represents an operator in column vector form. isoperbra : bool Indicates if the quantum object represents an operator in row vector form. Methods ------- copy() Create copy of Qobj conj() Conjugate of quantum object. contract() Contract subspaces of the tensor structure which are 1D. cosm() Cosine of quantum object. dag() Adjoint (dagger) of quantum object. data_as(format, copy) Vector / matrix representation of quantum object. diag() Diagonal elements of quantum object. dnorm() Diamond norm of quantum operator. dual_chan() Dual channel of quantum object representing a CP map. eigenenergies(sparse=False, sort='low', eigvals=0, tol=0, maxiter=100000) Returns eigenenergies (eigenvalues) of a quantum object. eigenstates(sparse=False, sort='low', eigvals=0, tol=0, maxiter=100000) Returns eigenenergies and eigenstates of quantum object. expm() Matrix exponential of quantum object. full(order='C') Returns dense array of quantum object `data` attribute. groundstate(sparse=False, tol=0, maxiter=100000) Returns eigenvalue and eigenket for the groundstate of a quantum object. inv() Return a Qobj corresponding to the matrix inverse of the operator. logm() Matrix logarithm of quantum operator. matrix_element(bra, ket) Returns the matrix element of operator between `bra` and `ket` vectors. norm(norm='tr', sparse=False, tol=0, maxiter=100000) Returns norm of a ket or an operator. overlap(other) Overlap between two state vectors or two operators. permute(order) Returns composite qobj with indices reordered. proj() Computes the projector for a ket or bra vector. ptrace(sel) Returns quantum object for selected dimensions after performing partial trace. purity() Calculates the purity of a quantum object. sinm() Sine of quantum object. sqrtm() Matrix square root of quantum object. tidyup(atol=1e-12) Removes small elements from quantum object. tr() Trace of quantum object. trans() Transpose of quantum object. transform(inpt, inverse=False) Performs a basis transformation defined by `inpt` matrix. trunc_neg(method='clip') Removes negative eigenvalues and returns a new Qobj that is a valid density operator. unit(norm='tr', sparse=False, tol=0, maxiter=100000) Returns normalized quantum object. """ # Disable ufuncs from acting directly on Qobj. __array_ufunc__ = None def _initialize_data(self, arg, dims, copy): if isinstance(arg, _data.Data): self._data = arg.copy() if copy else arg self._dims = Dimensions(dims or [[arg.shape[0]], [arg.shape[1]]]) elif isinstance(arg, Qobj): self._data = arg.data.copy() if copy else arg.data self._dims = Dimensions(dims or arg._dims) if self._isherm is None and arg._isherm is not None: self._isherm = arg._isherm if self._isunitary is None and arg._isunitary is not None: self._isunitary = arg._isunitary else: self._data = _data.create(arg, copy=copy) self._dims = Dimensions( dims or [[self._data.shape[0]], [self._data.shape[1]]] ) if self._dims.shape != self._data.shape: raise ValueError('Provided dimensions do not match the data: ' + f"{self._dims.shape} vs {self._data.shape}") def __init__( self, arg: ArrayLike | Any = None, dims: DimensionLike = None, copy: bool = True, superrep: str = None, isherm: bool = None, isunitary: bool = None ): self._isherm = isherm self._isunitary = isunitary self._initialize_data(arg, dims, copy) if superrep is not None: self.superrep = superrep def copy(self) -> Qobj: """Create identical copy""" return Qobj(arg=self._data, dims=self._dims, isherm=self._isherm, isunitary=self._isunitary, copy=True) @property def dims(self) -> list[list[int]] | list[list[list[int]]]: return self._dims.as_list() @dims.setter def dims(self, dims: list[list[int]] | list[list[list[int]]] | Dimensions): dims = Dimensions(dims, rep=self.superrep) if dims.shape != self._data.shape: raise ValueError('Provided dimensions do not match the data: ' + f"{dims.shape} vs {self._data.shape}") self._dims = dims @property def type(self) -> str: return self._dims.type @property def superrep(self) -> str: return self._dims.superrep @superrep.setter def superrep(self, super_rep: str): self._dims = self._dims.replace_superrep(super_rep) @property def data(self) -> _data.Data: return self._data @data.setter def data(self, data: _data.Data): if not isinstance(data, _data.Data): raise TypeError('Qobj data must be a data-layer format.') if self._dims.shape != data.shape: raise ValueError('Provided data do not match the dimensions: ' + f"{self._dims.shape} vs {data.shape}") self._data = data @property def dtype(self): return type(self._data) def to(self, data_type: LayerType, copy: bool=False) -> Qobj: """ Convert the underlying data store of this `Qobj` into a different storage representation. The different storage representations available are the "data-layer types" which are known to :obj:`qutip.core.data.to`. By default, these are :class:`~qutip.core.data.CSR`, :class:`~qutip.core.data.Dense` and :class:`~qutip.core.data.Dia`, which respectively construct a compressed sparse row matrix, diagonal matrix and a dense one. Certain algorithms and operations may be faster or more accurate when using a more appropriate data store. Parameters ---------- data_type : type, str The data-layer type or its string alias that the data of this :class:`Qobj` should be converted to. copy : Bool If the data store is already in the format requested, whether the function should return returns `self` or a copy. Returns ------- Qobj A :class:`Qobj` with the data stored in the requested format. """ data_type = _data.to.parse(data_type) if type(self._data) is data_type and copy: return self.copy() elif type(self._data) is data_type: return self return Qobj( _data.to(data_type, self._data), dims=self._dims, isherm=self._isherm, isunitary=self._isunitary, copy=False ) @_require_equal_type def __add__(self, other: Qobj | complex) -> Qobj: if other == 0: return self.copy() return Qobj(_data.add(self._data, other._data), dims=self._dims, isherm=(self._isherm and other._isherm) or None, copy=False) def __radd__(self, other: Qobj | complex) -> Qobj: return self.__add__(other) @_require_equal_type def __sub__(self, other: Qobj | complex) -> Qobj: if other == 0: return self.copy() return Qobj(_data.sub(self._data, other._data), dims=self._dims, isherm=(self._isherm and other._isherm) or None, copy=False) def __rsub__(self, other: Qobj | complex) -> Qobj: return self.__neg__().__add__(other) def __mul__(self, other: complex) -> Qobj: """ If other is a Qobj, we dispatch to __matmul__. If not, we check that other is a valid complex scalar, i.e., we can do complex(other). Otherwise, we return NotImplemented. """ if isinstance(other, Qobj): return self.__matmul__(other) # We send other to mul instead of complex(other) to be more flexible. # The dispatcher can then decide how to handle other and return # TypeError if it does not know what to do with the type of other. try: out = _data.mul(self._data, other) except TypeError: return NotImplemented # Infer isherm and isunitary if possible try: multiplier = complex(other) isherm = (self._isherm and multiplier.imag == 0) or None isunitary = (abs(abs(multiplier) - 1) < settings.core['atol'] if self._isunitary else None) except TypeError: isherm = None isunitary = None return Qobj(out, dims=self._dims, isherm=isherm, isunitary=isunitary, copy=False) def __rmul__(self, other: complex) -> Qobj: # Shouldn't be here unless `other.__mul__` has already been tried, so # we _shouldn't_ check that `other` is `Qobj`. return self.__mul__(other) def __matmul__(self, other: Qobj) -> Qobj: if not isinstance(other, Qobj): try: other = Qobj(other) except TypeError: return NotImplemented new_dims = self._dims @ other._dims if new_dims.type == 'scalar': return _data.inner(self._data, other._data) return Qobj( _data.matmul(self._data, other._data), dims=new_dims, isunitary=self._isunitary and other._isunitary, copy=False ) def __truediv__(self, other: complex) -> Qobj: return self.__mul__(1 / other) def __neg__(self) -> Qobj: return Qobj(_data.neg(self._data), dims=self._dims, isherm=self._isherm, isunitary=self._isunitary, copy=False) def __getitem__(self, ind): # TODO: should we require that data-layer types implement this? This # isn't the right way of handling it, for sure. if isinstance(self._data, _data.CSR): data = self._data.as_scipy() elif isinstance(self._data, _data.Dense): data = self._data.as_ndarray() else: data = self._data try: out = data[ind] return out.toarray() if scipy.sparse.issparse(out) else out except TypeError: pass return data.to_array()[ind] def __eq__(self, other) -> bool: if self is other: return True if not isinstance(other, Qobj) or self._dims != other._dims: return False # isequal uses both atol and rtol from settings.core return _data.isequal(self._data, other._data) def __pow__(self, n: int, m=None) -> Qobj: # calculates powers of Qobj if ( self.type not in ('oper', 'super') or self._dims[0] != self._dims[1] or m is not None or not isinstance(n, numbers.Integral) or n < 0 ): return NotImplemented return Qobj(_data.pow(self._data, n), dims=self._dims, isherm=self._isherm, isunitary=self._isunitary, copy=False) def _str_header(self): out = ", ".join([ "Quantum object: dims=" + str(self.dims), "shape=" + str(self._data.shape), "type=" + repr(self.type), "dtype=" + self.dtype.__name__, ]) if self.type in ('oper', 'super'): out += ", isherm=" + str(self.isherm) if self.issuper and self.superrep != 'super': out += ", superrep=" + repr(self.superrep) return out def __str__(self): if self.data.shape[0] * self.data.shape[0] > 100_000_000: # If the system is huge, don't attempt to convert to a dense matrix # and then to string, because it is pointless and is likely going # to produce memory errors. Instead print the sparse data string # representation. data = _data.to(_data.CSR, self.data).as_scipy() elif _data.iszero(_data.sub(self.data.conj(), self.data)): data = np.real(self.full()) else: data = self.full() return self._str_header() + "\nQobj data =\n" + str(data) def __repr__(self): # give complete information on Qobj without print statement in # command-line we cant realistically serialize a Qobj into a string, # so we simply return the informal __str__ representation instead.) return self.__str__() def __call__(self, other: Qobj) -> Qobj: """ Acts this Qobj on another Qobj either by left-multiplication, or by vectorization and devectorization, as appropriate. """ if not isinstance(other, Qobj): raise TypeError("Only defined for quantum objects.") if (self.type, other.type) not in _CALL_ALLOWED: raise TypeError(self.type + " cannot act on " + other.type) if self.issuper: if other.isket: other = other.proj() return qutip.vector_to_operator(self @ qutip.operator_to_vector(other)) return self.__matmul__(other) def __getstate__(self): # defines what happens when Qobj object gets pickled self.__dict__.update({'qutip_version': __version__[:5]}) return self.__dict__ def __setstate__(self, state): # defines what happens when loading a pickled Qobj if 'qutip_version' in state.keys(): del state['qutip_version'] (self.__dict__).update(state) def _repr_latex_(self): """ Generate a LaTeX representation of the Qobj instance. Can be used for formatted output in ipython notebook. """ half_length = 5 n_rows, n_cols = self.data.shape # Choose which rows and columns we're going to output, or None if that # element should be truncated. rows = list(range(min((half_length, n_rows)))) if n_rows <= half_length * 2: rows += list(range(half_length, min((2*half_length, n_rows)))) else: rows.append(None) rows += list(range(n_rows - half_length, n_rows)) cols = list(range(min((half_length, n_cols)))) if n_cols <= half_length * 2: cols += list(range(half_length, min((2*half_length, n_cols)))) else: cols.append(None) cols += list(range(n_cols - half_length, n_cols)) # Make the data array. data = r'$$\left(\begin{array}{cc}' data += r"\\".join(_latex_row(row, cols, self.data.to_array()) for row in rows) data += r'\end{array}\right)$$' return self._str_header() + data def __and__(self, other: Qobj) -> Qobj: """ Syntax shortcut for tensor: A & B ==> tensor(A, B) """ return qutip.tensor(self, other) def dag(self) -> Qobj: """Get the Hermitian adjoint of the quantum object.""" if self._isherm: return self.copy() return Qobj(_data.adjoint(self._data), dims=Dimensions(self._dims[0], self._dims[1]), isherm=self._isherm, isunitary=self._isunitary, copy=False) def conj(self) -> Qobj: """Get the element-wise conjugation of the quantum object.""" return Qobj(_data.conj(self._data), dims=self._dims, isherm=self._isherm, isunitary=self._isunitary, copy=False) def trans(self) -> Qobj: """Get the matrix transpose of the quantum operator. Returns ------- oper : :class:`.Qobj` Transpose of input operator. """ return Qobj(_data.transpose(self._data), dims=Dimensions(self._dims[0], self._dims[1]), isherm=self._isherm, isunitary=self._isunitary, copy=False) def dual_chan(self) -> Qobj: """Dual channel of quantum object representing a completely positive map. """ # Uses the technique of Johnston and Kribs (arXiv:1102.0948), which # is only valid for completely positive maps. if not self.iscp: raise ValueError("Dual channels are only implemented for CP maps.") J = qutip.to_choi(self) tensor_idxs = enumerate_flat(J.dims) J_dual = qutip.tensor_swap(J, *( list(zip(tensor_idxs[0][1], tensor_idxs[0][0])) + list(zip(tensor_idxs[1][1], tensor_idxs[1][0])) )).trans() J_dual.superrep = 'choi' return J_dual def norm( self, norm: Literal["l2", "max", "fro", "tr", "one"] = None, kwargs: dict[str, Any] = None ) -> float: """ Norm of a quantum object. Default norm is L2-norm for kets and trace-norm for operators. Other ket and operator norms may be specified using the `norm` parameter. Parameters ---------- norm : str Which type of norm to use. Allowed values for vectors are 'l2' and 'max'. Allowed values for matrices are 'tr' for the trace norm, 'fro' for the Frobenius norm, 'one' and 'max'. kwargs : dict Additional keyword arguments to pass on to the relevant norm solver. See details for each norm function in :mod:`.data.norm`. Returns ------- norm : float The requested norm of the operator or state quantum object. """ if self.type in ('oper', 'super'): norm = norm or 'tr' if norm not in _NORM_ALLOWED_MATRIX: raise ValueError( "matrix norm must be in " + repr(_NORM_ALLOWED_MATRIX) ) else: norm = norm or 'l2' if norm not in _NORM_ALLOWED_VECTOR: raise ValueError( "vector norm must be in " + repr(_NORM_ALLOWED_VECTOR) ) kwargs = kwargs or {} return _NORM_FUNCTION_LOOKUP[norm](self._data, **kwargs) def proj(self) -> Qobj: """Form the projector from a given ket or bra vector. Parameters ---------- Q : :class:`.Qobj` Input bra or ket vector Returns ------- P : :class:`.Qobj` Projection operator. """ if not (self.isket or self.isbra): raise TypeError("projection is only defined for bras and kets") dims = ([self._dims[0], self._dims[0]] if self.isket else [self._dims[1], self._dims[1]]) return Qobj(_data.project(self._data), dims=dims, isherm=True, copy=False) def tr(self) -> complex: """Trace of a quantum object. Returns ------- trace : float Returns the trace of the quantum object. """ out = _data.trace(self._data) # This ensures that trace can return something that is not a number such # as a `tensorflow.Tensor` in qutip-tensorflow. if settings.core["auto_real_casting"] and self.isherm: out = out.real return out def purity(self) -> complex: """Calculate purity of a quantum object. Returns ------- state_purity : float Returns the purity of a quantum object. For a pure state, the purity is 1. For a mixed state of dimension `d`, 1/d<=purity<1. """ if self.type in ("super", "operator-ket", "operator-bra"): raise TypeError('purity is only defined for states.') if self.isket or self.isbra: return _data.norm.l2(self._data)**2 return _data.trace(_data.matmul(self._data, self._data)).real def full( self, order: Literal['C', 'F'] = 'C', squeeze: bool = False ) -> np.ndarray: """Dense array from quantum object. Parameters ---------- order : str {'C', 'F'} Return array in C (default) or Fortran ordering. squeeze : bool {False, True} Squeeze output array. Returns ------- data : array Array of complex data from quantum objects `data` attribute. """ out = np.asarray(self.data.to_array(), order=order) return out.squeeze() if squeeze else out def data_as(self, format: str = None, copy: bool = True) -> Any: """Matrix from quantum object. Parameters ---------- format : str, default: None Type of the output, "ndarray" for ``Dense``, "csr_matrix" for ``CSR``. A ValueError will be raised if the format is not supported. copy : bool {False, True} Whether to return a copy Returns ------- data : numpy.ndarray, scipy.sparse.matrix_csr, etc. Matrix in the type of the underlying libraries. """ return _data.extract(self._data, format, copy) def diag(self) -> np.ndarray: """Diagonal elements of quantum object. Returns ------- diags : array Returns array of ``real`` values if operators is Hermitian, otherwise ``complex`` values are returned. """ # TODO: add a `diagonal` method to the data layer? out = _data.to(_data.CSR, self.data).as_scipy().diagonal() if settings.core["auto_real_casting"] and self.isherm: out = np.real(out) return out def expm(self, dtype: LayerType = None) -> Qobj: """Matrix exponential of quantum operator. Input operator must be square. Parameters ---------- dtype : type The data-layer type that should be output. Returns ------- oper : :class:`.Qobj` Exponentiated quantum operator. Raises ------ TypeError Quantum operator is not square. """ if not self._dims.issquare: raise TypeError("expm is only valid for square operators") if dtype is None and isinstance(self.data, (_data.CSR, _data.Dia)): dtype = _data.Dense return Qobj(_data.expm(self._data, dtype=dtype), dims=self._dims, isherm=self._isherm, copy=False) def logm(self) -> Qobj: """Matrix logarithm of quantum operator. Input operator must be square. Returns ------- oper : :class:`.Qobj` Logarithm of the quantum operator. Raises ------ TypeError Quantum operator is not square. """ if not self._dims.issquare: raise TypeError("expm is only valid for square operators") return Qobj(_data.logm(self._data), dims=self._dims, isherm=self._isherm, copy=False) def check_herm(self) -> bool: """Check if the quantum object is hermitian. Returns ------- isherm : bool Returns the new value of isherm property. """ self._isherm = None return self.isherm def sqrtm( self, sparse: bool = False, tol: float = 0, maxiter: int = 100000 ) -> Qobj: """ Sqrt of a quantum operator. Operator must be square. Parameters ---------- sparse : bool Use sparse eigenvalue/vector solver. tol : float Tolerance used by sparse solver (0 = machine precision). maxiter : int Maximum number of iterations used by sparse solver. Returns ------- oper : :class:`.Qobj` Matrix square root of operator. Raises ------ TypeError Quantum object is not square. Notes ----- The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it. """ if self._dims[0] != self._dims[1]: raise TypeError('sqrt only valid on square matrices') return Qobj(_data.sqrtm(self._data), dims=self._dims, copy=False) def cosm(self) -> Qobj: """Cosine of a quantum operator. Operator must be square. Returns ------- oper : :class:`.Qobj` Matrix cosine of operator. Raises ------ TypeError Quantum object is not square. Notes ----- Uses the Q.expm() method. """ if self._dims[0] != self._dims[1]: raise TypeError('invalid operand for matrix cosine') return 0.5 * ((1j * self).expm() + (-1j * self).expm()) def sinm(self) -> Qobj: """Sine of a quantum operator. Operator must be square. Returns ------- oper : :class:`.Qobj` Matrix sine of operator. Raises ------ TypeError Quantum object is not square. Notes ----- Uses the Q.expm() method. """ if self._dims[0] != self._dims[1]: raise TypeError('invalid operand for matrix sine') return -0.5j * ((1j * self).expm() - (-1j * self).expm()) def inv(self, sparse: bool = False) -> Qobj: """Matrix inverse of a quantum operator Operator must be square. Returns ------- oper : :class:`.Qobj` Matrix inverse of operator. Raises ------ TypeError Quantum object is not square. """ if self.data.shape[0] != self.data.shape[1]: raise TypeError('Invalid operand for matrix inverse') if isinstance(self.data, _data.CSR) and not sparse: data = _data.to(_data.Dense, self.data) else: data = self.data return Qobj(_data.inv(data), dims=[self._dims[1], self._dims[0]], copy=False) def unit( self, inplace: bool = False, norm: Literal["l2", "max", "fro", "tr", "one"] = None, kwargs: dict[str, Any] = None ) -> Qobj: """ Operator or state normalized to unity. Uses norm from Qobj.norm(). Parameters ---------- inplace : bool Do an in-place normalization norm : str Requested norm for states / operators. kwargs : dict Additional key-word arguments to be passed on to the relevant norm function (see :meth:`.norm` for more details). Returns ------- obj : :class:`.Qobj` Normalized quantum object. Will be the `self` object if in place. """ norm_ = self.norm(norm=norm, kwargs=kwargs) if inplace: self.data = _data.mul(self.data, 1 / norm_) self._isherm = self._isherm if norm_.imag == 0 else None self._isunitary = (self._isunitary if abs(norm_) - 1 < settings.core['atol'] else None) out = self else: out = self / norm_ return out def ptrace(self, sel: int | list[int], dtype: LayerType = None) -> Qobj: """ Take the partial trace of the quantum object leaving the selected subspaces. In other words, trace out all subspaces which are _not_ passed. This is typically a function which acts on operators; bras and kets will be promoted to density matrices before the operation takes place since the partial trace is inherently undefined on pure states. For operators which are currently being represented as states in the superoperator formalism (i.e. the object has type `operator-ket` or `operator-bra`), the partial trace is applied as if the operator were in the conventional form. This means that for any operator `x`, ``operator_to_vector(x).ptrace(0) == operator_to_vector(x.ptrace(0))`` and similar for `operator-bra`. The story is different for full superoperators. In the formalism that QuTiP uses, if an operator has dimensions (`dims`) of `[[2, 3], [2, 3]]` then it can be represented as a state on a Hilbert space of dimensions `[2, 3, 2, 3]`, and a superoperator would be an operator which acts on this joint space. This function performs the partial trace on superoperators by letting the selected components refer to elements of the _joint_ _space_, and then returns a regular operator (of type `oper`). Parameters ---------- sel : int or iterable of int An ``int`` or ``list`` of components to keep after partial trace. The selected subspaces will _not_ be reordered, no matter order they are supplied to `ptrace`. Returns ------- oper : :class:`.Qobj` Quantum object representing partial trace with selected components remaining. """ try: sel = sorted(sel) except TypeError: if not isinstance(sel, numbers.Integral): raise TypeError( "selection must be an integer or list of integers" ) from None sel = [sel] if self.isoperket: dims = self.dims[0] data = qutip.vector_to_operator(self).data elif self.isoperbra: dims = self.dims[1] data = qutip.vector_to_operator(self.dag()).data elif self.issuper or self.isoper: dims = self.dims data = self.data else: dims = [self.dims[0] if self.isket else self.dims[1]] * 2 data = _data.project(self.data) if dims[0] != dims[1]: raise ValueError("partial trace is not defined on non-square maps") dims = flatten(dims[0]) new_data = _data.ptrace(data, dims, sel, dtype=dtype) new_dims = [[dims[x] for x in sel]] * 2 if sel else None out = Qobj(new_data, dims=new_dims, copy=False) if self.isoperket: return qutip.operator_to_vector(out) if self.isoperbra: return qutip.operator_to_vector(out).dag() return out def contract(self, inplace: bool = False) -> Qobj: """ Contract subspaces of the tensor structure which are 1D. Not defined on superoperators. If all dimensions are scalar, a Qobj of dimension [[1], [1]] is returned, i.e. _multiple_ scalar dimensions are contracted, but one is left. Parameters ---------- inplace: bool, optional If ``True``, modify the dimensions in place. If ``False``, return a copied object. Returns ------- out: :class:`.Qobj` Quantum object with dimensions contracted. Will be ``self`` if ``inplace`` is ``True``. """ if self.isket: sub = [x for x in self.dims[0] if x > 1] or [1] dims = [sub, [1]*len(sub)] elif self.isbra: sub = [x for x in self.dims[1] if x > 1] or [1] dims = [[1]*len(sub), sub] elif self.isoper or self.isoperket or self.isoperbra: if self.isoper: oper_dims = self.dims elif self.isoperket: oper_dims = self.dims[0] else: oper_dims = self.dims[1] if len(oper_dims[0]) != len(oper_dims[1]): raise ValueError("cannot parse Qobj dimensions: " + repr(self.dims)) dims_ = [ (x, y) for x, y in zip(oper_dims[0], oper_dims[1]) if x > 1 or y > 1 ] or [(1, 1)] dims = [[x for x, _ in dims_], [y for _, y in dims_]] if self.isoperket: dims = [dims, [1]] elif self.isoperbra: dims = [[1], dims] else: raise TypeError("not defined for superoperators") if inplace: self.dims = dims return self return Qobj(self.data.copy(), dims=dims, copy=False) def permute(self, order: list) -> Qobj: """ Permute the tensor structure of a quantum object. For example, ``qutip.tensor(x, y).permute([1, 0])`` will give the same result as ``qutip.tensor(y, x)`` and ``qutip.tensor(a, b, c).permute([1, 2, 0])`` will be the same as ``qutip.tensor(b, c, a)`` For regular objects (bras, kets and operators) we expect ``order`` to be a flat list of integers, which specifies the new order of the tensor product. For superoperators, we expect ``order`` to be something like ``[[0, 2], [1, 3]]`` which tells us to permute according to [0, 2, 1, 3], and then group indices according to the length of each sublist. As another example, permuting a superoperator with dimensions of ``[[[1, 2, 3], [1, 2, 3]], [[1, 2, 3], [1, 2, 3]]]`` by an ``order`` ``[[0, 3], [1, 4], [2, 5]]`` should give a new object with dimensions ``[[[1, 1], [2, 2], [3, 3]], [[1, 1], [2, 2], [3, 3]]]``. Parameters ---------- order : list List of indices specifying the new tensor order. Returns ------- P : :class:`.Qobj` Permuted quantum object. """ if self.type in ('bra', 'ket', 'oper'): structure = self.dims[1] if self.isbra else self.dims[0] new_structure = [structure[x] for x in order] if self.isbra: dims = [self.dims[0], new_structure] elif self.isket: dims = [new_structure, self.dims[1]] else: if self._dims[0] != self._dims[1]: raise TypeError("undefined for non-square operators") dims = [new_structure, new_structure] data = _data.permute.dimensions(self.data, structure, order) return Qobj(data, dims=dims, isherm=self._isherm, isunitary=self._isunitary, copy=False) # If we've got here, we're some form of superoperator, so we work with # the flattened structure. flat_order = flatten(order) flat_structure = flatten(self.dims[1] if self.isoperbra else self.dims[0]) new_structure = unflatten([flat_structure[x] for x in flat_order], enumerate_flat(order)) if self.isoperbra: dims = [self.dims[0], new_structure] elif self.isoperket: dims = [new_structure, self.dims[1]] else: if self._dims[0] != self._dims[1]: raise TypeError("undefined for non-square operators") dims = [new_structure, new_structure] data = _data.permute.dimensions(self.data, flat_structure, flat_order) return Qobj(data, dims=dims, superrep=self.superrep, copy=False) def tidyup(self, atol: float = None) -> Qobj: """ Removes small elements from the quantum object. Parameters ---------- atol : float Absolute tolerance used by tidyup. Default is set via qutip global settings parameters. Returns ------- oper : :class:`.Qobj` Quantum object with small elements removed. """ atol = atol or settings.core['auto_tidyup_atol'] self.data = _data.tidyup(self.data, atol) return self def transform( self, inpt: list[Qobj] | ArrayLike, inverse: bool = False ) -> Qobj: """Basis transform defined by input array. Input array can be a ``matrix`` defining the transformation, or a ``list`` of kets that defines the new basis. Parameters ---------- inpt : array_like A ``matrix`` or ``list`` of kets defining the transformation. inverse : bool Whether to return inverse transformation. Returns ------- oper : :class:`.Qobj` Operator in new basis. Notes ----- This function is still in development. """ if isinstance(inpt, list) or (isinstance(inpt, np.ndarray) and inpt.ndim == 1): if len(inpt) != max(self.shape): raise TypeError( 'Invalid size of ket list for basis transformation') base = np.hstack([psi.full() for psi in inpt]) S = _data.adjoint(_data.create(base)) elif isinstance(inpt, Qobj) and inpt.isoper: S = inpt.data elif isinstance(inpt, np.ndarray): S = _data.create(inpt).conj() else: raise TypeError('Invalid operand for basis transformation') # transform data if inverse: if self.isket: data = _data.matmul(S.adjoint(), self.data) elif self.isbra: data = _data.matmul(self.data, S) else: data = _data.matmul(_data.matmul(S.adjoint(), self.data), S) else: if self.isket: data = _data.matmul(S, self.data) elif self.isbra: data = _data.matmul(self.data, S.adjoint()) else: data = _data.matmul(_data.matmul(S, self.data), S.adjoint()) return Qobj(data, dims=self.dims, isherm=self._isherm, superrep=self.superrep, copy=False) def trunc_neg(self, method: Literal["clip", "sgs"] = "clip") -> Qobj: """Truncates negative eigenvalues and renormalizes. Returns a new Qobj by removing the negative eigenvalues of this instance, then renormalizing to obtain a valid density operator. Parameters ---------- method : str Algorithm to use to remove negative eigenvalues. "clip" simply discards negative eigenvalues, then renormalizes. "sgs" uses the SGS algorithm (doi:10/bb76) to find the positive operator that is nearest in the Shatten 2-norm. Returns ------- oper : :class:`.Qobj` A valid density operator. """ if not self.isherm: raise ValueError("Must be a Hermitian operator to remove negative " "eigenvalues.") if method not in ('clip', 'sgs'): raise ValueError("Method {} not recognized.".format(method)) eigvals, eigstates = self.eigenstates() if all(eigval >= 0 for eigval in eigvals): # All positive, so just renormalize. return self.unit() idx_nonzero = eigvals != 0 eigvals = eigvals[idx_nonzero] eigstates = eigstates[idx_nonzero] if method == 'clip': eigvals[eigvals < 0] = 0 elif method == 'sgs': eigvals = eigvals[::-1] eigstates = eigstates[::-1] acc = 0.0 n_eigs = len(eigvals) for idx in reversed(range(n_eigs)): if eigvals[idx] + acc / (idx + 1) >= 0: break acc += eigvals[idx] eigvals[idx] = 0.0 eigvals[:idx+1] += acc / (idx + 1) out_data = _data.zeros(*self.shape) for value, state in zip(eigvals, eigstates): if value: # add in 3-argument form is fused-add-multiply out_data = _data.add(out_data, _data.project(state.data), value) out_data = _data.mul(out_data, 1/_data.norm.trace(out_data)) return Qobj(out_data, dims=self._dims, isherm=True, copy=False) def matrix_element(self, bra: Qobj, ket: Qobj) -> Qobj: """Calculates a matrix element. Gives the matrix element for the quantum object sandwiched between a `bra` and `ket` vector. Parameters ---------- bra : :class:`.Qobj` Quantum object of type 'bra' or 'ket' ket : :class:`.Qobj` Quantum object of type 'ket'. Returns ------- elem : complex Complex valued matrix element. Notes ----- It is slightly more computationally efficient to use a ket vector for the 'bra' input. """ if not self.isoper: raise TypeError("Can only get matrix elements for an operator.") if bra.type not in ('bra', 'ket') or ket.type not in ('bra', 'ket'): msg = "Can only calculate matrix elements between a bra and a ket." raise TypeError(msg) left, op, right = bra.data, self.data, ket.data if ket.isbra: right = right.adjoint() return _data.inner_op(left, op, right, bra.isket) def overlap(self, other: Qobj) -> complex: """ Overlap between two state vectors or two operators. Gives the overlap (inner product) between the current bra or ket Qobj and and another bra or ket Qobj. It gives the Hilbert-Schmidt overlap when one of the Qobj is an operator/density matrix. Parameters ---------- other : :class:`.Qobj` Quantum object for a state vector of type 'ket', 'bra' or density matrix. Returns ------- overlap : complex Complex valued overlap. Raises ------ TypeError Can only calculate overlap between a bra, ket and density matrix quantum objects. """ if not isinstance(other, Qobj): raise TypeError("".join([ "cannot calculate overlap with non-quantum object ", repr(other), ])) if ( self.type not in ('ket', 'bra', 'oper') or other.type not in ('ket', 'bra', 'oper') ): msg = "only bras, kets and density matrices have defined overlaps" raise TypeError(msg) left, right = self._data.adjoint(), other.data if self.isoper or other.isoper: if not self.isoper: left = _data.project(left) if not other.isoper: right = _data.project(right) return _data.trace(_data.matmul(left, right)) if other.isbra: right = right.adjoint() out = _data.inner(left, right, self.isket) if self.isket and other.isbra: # In this particular case, we've basically doing # conj(other.overlap(self)) # so we take care to conjugate the output. out = np.conj(out) return out def eigenstates( self, sparse: bool = False, sort: Literal["low", "high"] = 'low', eigvals: int = 0, tol: float = 0, maxiter: int = 100000, phase_fix: int = None ) -> tuple[np.ndarray, list[Qobj]]: """Eigenstates and eigenenergies. Eigenstates and eigenenergies are defined for operators and superoperators only. Parameters ---------- sparse : bool Use sparse Eigensolver sort : str Sort eigenvalues (and vectors) 'low' to high, or 'high' to low. eigvals : int Number of requested eigenvalues. Default is all eigenvalues. tol : float Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low. maxiter : int Maximum number of iterations performed by sparse solver (if used). phase_fix : int, None If not None, set the phase of each kets so that ket[phase_fix,0] is real positive. Returns ------- eigvals : array Array of eigenvalues for operator. eigvecs : array Array of quantum operators representing the oprator eigenkets. Order of eigenkets is determined by order of eigenvalues. Notes ----- The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it. """ if isinstance(self.data, _data.CSR) and sparse: evals, evecs = _data.eigs_csr(self.data, isherm=self._isherm, sort=sort, eigvals=eigvals, tol=tol, maxiter=maxiter) elif isinstance(self.data, (_data.CSR, _data.Dia)): evals, evecs = _data.eigs(_data.to(_data.Dense, self.data), isherm=self._isherm, sort=sort, eigvals=eigvals) else: evals, evecs = _data.eigs(self.data, isherm=self._isherm, sort=sort, eigvals=eigvals) if self.type == 'super': new_dims = [self._dims[0], [1]] else: new_dims = [self._dims[0], [1]*len(self.dims[0])] ekets = np.empty((evecs.shape[1],), dtype=object) ekets[:] = [Qobj(vec, dims=new_dims, copy=False) for vec in _data.split_columns(evecs, False)] norms = np.array([ket.norm() for ket in ekets]) if phase_fix is None: phase = np.array([1] * len(ekets)) else: phase = np.array([np.abs(ket[phase_fix, 0]) / ket[phase_fix, 0] if ket[phase_fix, 0] else 1 for ket in ekets]) return evals, ekets / norms * phase def eigenenergies( self, sparse: bool = False, sort: Literal["low", "high"] = 'low', eigvals: int = 0, tol: float = 0, maxiter: int = 100000, ) -> np.ndarray: """Eigenenergies of a quantum object. Eigenenergies (eigenvalues) are defined for operators or superoperators only. Parameters ---------- sparse : bool Use sparse Eigensolver sort : str Sort eigenvalues 'low' to high, or 'high' to low. eigvals : int Number of requested eigenvalues. Default is all eigenvalues. tol : float Tolerance used by sparse Eigensolver (0=machine precision). The sparse solver may not converge if the tolerance is set too low. maxiter : int Maximum number of iterations performed by sparse solver (if used). Returns ------- eigvals : array Array of eigenvalues for operator. Notes ----- The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it. """ # TODO: consider another way of handling the dispatch here. if isinstance(self.data, _data.CSR) and sparse: return _data.eigs_csr(self.data, vecs=False, isherm=self._isherm, sort=sort, eigvals=eigvals, tol=tol, maxiter=maxiter) elif isinstance(self.data, (_data.CSR, _data.Dia)): return _data.eigs(_data.to(_data.Dense, self.data), vecs=False, isherm=self._isherm, sort=sort, eigvals=eigvals) return _data.eigs(self.data, vecs=False, isherm=self._isherm, sort=sort, eigvals=eigvals) def groundstate( self, sparse: bool = False, tol: float = 0, maxiter: int = 100000, safe: bool = True ) -> tuple[float, Qobj]: """Ground state Eigenvalue and Eigenvector. Defined for quantum operators or superoperators only. Parameters ---------- sparse : bool Use sparse Eigensolver tol : float Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low. maxiter : int Maximum number of iterations performed by sparse solver (if used). safe : bool (default=True) Check for degenerate ground state Returns ------- eigval : float Eigenvalue for the ground state of quantum operator. eigvec : :class:`.Qobj` Eigenket for the ground state of quantum operator. Notes ----- The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it. """ eigvals = 2 if safe else 1 evals, evecs = self.eigenstates(sparse=sparse, eigvals=eigvals, tol=tol, maxiter=maxiter) if safe: tol = tol or settings.core['atol'] # This tol should be less strick than the tol for the eigensolver # so it's numerical errors are not seens as degenerate states. if (evals[1]-evals[0]) <= 10 * tol: warnings.warn("Ground state may be degenerate.", UserWarning) return evals[0], evecs[0] def dnorm(self, B: Qobj = None) -> float: """Calculates the diamond norm, or the diamond distance to another operator. Parameters ---------- B : :class:`.Qobj` or None If B is not None, the diamond distance d(A, B) = dnorm(A - B) between this operator and B is returned instead of the diamond norm. Returns ------- d : float Either the diamond norm of this operator, or the diamond distance from this operator to B. """ return qutip.dnorm(self, B) @property def ishp(self) -> bool: # FIXME: this needs to be cached in the same ways as isherm. if self.type in ["super", "oper"]: try: J = qutip.to_choi(self) return J.isherm except: return False else: return False @property def iscp(self) -> bool: # FIXME: this needs to be cached in the same ways as isherm. if self.type not in ["super", "oper"]: return False # We can test with either Choi or chi, since the basis # transformation between them is unitary and hence preserves # the CP and TP conditions. J = self if self.superrep in ('choi', 'chi') else qutip.to_choi(self) # If J isn't hermitian, then that could indicate either that J is not # normal, or is normal, but has complex eigenvalues. In either case, # it makes no sense to then demand that the eigenvalues be # non-negative. return J.isherm and np.all(J.eigenenergies() >= -settings.core['atol']) @property def istp(self) -> bool: if self.type not in ['super', 'oper']: return False # Normalize to a super of type choi or chi. # We can test with either Choi or chi, since the basis # transformation between them is unitary and hence # preserves the CP and TP conditions. if self.issuper and self.superrep in ('choi', 'chi'): qobj = self else: qobj = qutip.to_choi(self) # Possibly collapse dims. if any([len(index) > 1 for super_index in qobj.dims for index in super_index]): qobj = Qobj(qobj.data, dims=collapse_dims_super(qobj.dims), superrep=qobj.superrep, copy=False) # We use the condition from John Watrous' lecture notes, # Tr_1(J(Phi)) = identity_2. # See: https://cs.uwaterloo.ca/~watrous/LectureNotes.html, # Theory of Quantum Information (Fall 2011), theorem 5.4. tr_oper = qobj.ptrace([0]) return np.allclose(tr_oper.full(), np.eye(tr_oper.shape[0]), atol=settings.core['atol']) @property def iscptp(self) -> bool: if not (self.issuper or self.isoper): return False reps = ('choi', 'chi') q_oper = qutip.to_choi(self) if self.superrep not in reps else self return q_oper.iscp and q_oper.istp @property def isherm(self) -> bool: if self._isherm is not None: return self._isherm self._isherm = _data.isherm(self._data) return self._isherm @isherm.setter def isherm(self, isherm: bool): self._isherm = isherm def _calculate_isunitary(self): """ Checks whether qobj is a unitary matrix """ if not self.isoper or self._data.shape[0] != self._data.shape[1]: return False cmp = _data.matmul(self._data, self._data.adjoint()) iden = _data.identity_like(cmp) return _data.iszero(_data.sub(cmp, iden), tol=settings.core['atol']) @property def isunitary(self) -> bool: if self._isunitary is not None: return self._isunitary self._isunitary = self._calculate_isunitary() return self._isunitary @property def shape(self) -> tuple[int, int]: """Return the shape of the Qobj data.""" return self._data.shape @property def isoper(self) -> bool: """Indicates if the Qobj represents an operator.""" return self._dims.type in ['oper', 'scalar'] @property def isbra(self) -> bool: """Indicates if the Qobj represents a bra state.""" return self._dims.type in ['bra', 'scalar'] @property def isket(self) -> bool: """Indicates if the Qobj represents a ket state.""" return self._dims.type in ['ket', 'scalar'] @property def issuper(self) -> bool: """Indicates if the Qobj represents a superoperator.""" return self._dims.type == 'super' @property def isoperket(self) -> bool: """Indicates if the Qobj represents a operator-ket state.""" return self._dims.type == 'operator-ket' @property def isoperbra(self) -> bool: """Indicates if the Qobj represents a operator-bra state.""" return self._dims.type == 'operator-bra' def ptrace(Q: Qobj, sel: int | list[int]) -> Qobj: """ Partial trace of the Qobj with selected components remaining. Parameters ---------- Q : :class:`.Qobj` Composite quantum object. sel : int/list An ``int`` or ``list`` of components to keep after partial trace. Returns ------- oper : :class:`.Qobj` Quantum object representing partial trace with selected components remaining. Notes ----- This function is for legacy compatibility only. It is recommended to use the ``ptrace()`` Qobj method. """ if not isinstance(Q, Qobj): raise TypeError("Input is not a quantum object") return Q.ptrace(sel) qutip-5.1.1/qutip/core/semidefinite.py000066400000000000000000000114601474175217300200060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This module implements internal-use functions for semidefinite programming. """ import collections import functools import numpy as np import scipy.sparse as sp # Conditionally import CVXPY try: import cvxpy __all__ = ["dnorm_problem", "dnorm_sparse_problem"] except ImportError: cvxpy = None __all__ = [] from .operators import swap Complex = collections.namedtuple("Complex", ["re", "im"]) def _complex_var(rows=1, cols=1, name=None): return Complex( re=cvxpy.Variable((rows, cols), name=(name + "_re") if name else None), im=cvxpy.Variable((rows, cols), name=(name + "_im") if name else None), ) def _make_constraints(*rhos): """ Create constraints to ensure definied density operators. """ # rhos traces are 1 constraints = [cvxpy.trace(rho.re) == 1 for rho in rhos] # rhos are Hermitian for rho in rhos: constraints += [rho.re == rho.re.T] + [rho.im == -rho.im.T] # Non negative constraints += [ cvxpy.bmat([[rho.re, -rho.im], [rho.im, rho.re]]) >> 0 for rho in rhos ] return constraints def _arr_to_complex(A): if np.iscomplex(A).any(): return Complex(re=A.real, im=A.imag) return Complex(re=A, im=np.zeros_like(A)) def _kron(A, B): if isinstance(A, np.ndarray): A = _arr_to_complex(A) if isinstance(B, np.ndarray): B = _arr_to_complex(B) return Complex( re=(cvxpy.kron(A.re, B.re) - cvxpy.kron(A.im, B.im)), im=(cvxpy.kron(A.im, B.re) + cvxpy.kron(A.re, B.im)), ) def _conj(W, A): U, V = W.re, W.im A, B = A.re, A.im return Complex( re=(U @ A @ U.T - U @ B @ V.T - V @ A @ V.T - V @ B @ U.T), im=(U @ A @ V.T + U @ B @ U.T + V @ A @ U.T - V @ B @ V.T), ) @functools.lru_cache def initialize_constraints_on_dnorm_problem(dim): # Start assembling constraints and variables. constraints = [] # Make a complex variable for X. X = _complex_var(dim**2, dim**2, "X") # Make complex variables for rho0 and rho1. rho0 = _complex_var(dim, dim, "rho0") rho1 = _complex_var(dim, dim, "rho1") constraints += _make_constraints(rho0, rho1) # Finally, add the tricky positive semidefinite constraint. # Since we're using column-stacking, but Watrous used row-stacking, # we need to swap the order in Rho0 and Rho1. This is not straightforward, # as CVXPY requires that the constant be the first argument. To solve this, # We conjugate by SWAP. W = swap(dim, dim).full() W = Complex(re=W.real, im=W.imag) Rho0 = _conj(W, _kron(np.eye(dim), rho0)) Rho1 = _conj(W, _kron(np.eye(dim), rho1)) Y = cvxpy.bmat( [ [Rho0.re, X.re, -Rho0.im, -X.im], [X.re.T, Rho1.re, X.im.T, -Rho1.im], [Rho0.im, X.im, Rho0.re, X.re], [-X.im.T, Rho1.im, X.re.T, Rho1.re], ] ) constraints += [Y >> 0] return X, constraints def dnorm_problem(dim): """ Creade the cvxpy ``Problem`` for the dnorm metric using dense arrays """ X, constraints = initialize_constraints_on_dnorm_problem(dim) Jr = cvxpy.Parameter((dim**2, dim**2)) Ji = cvxpy.Parameter((dim**2, dim**2)) # The objective, however, depends on J. objective = cvxpy.Maximize(cvxpy.trace(Jr.T @ X.re + Ji.T @ X.im)) problem = cvxpy.Problem(objective, constraints) return problem, Jr, Ji def dnorm_sparse_problem(dim, J_dat): """ Creade the cvxpy ``Problem`` for the dnorm metric using sparse arrays """ X, constraints = initialize_constraints_on_dnorm_problem(dim) J_val = J_dat.tocoo() def adapt_sparse_params(A_val, dim): # This detour is needed as pointed out in cvxgrp/cvxpy#1159, as cvxpy # can not solve with parameters that aresparse matrices directly. # Solutions have to be made through calling cvxpy.reshape on # the original sparse matrix. side_size = dim**2 A_nnz = cvxpy.Parameter(A_val.nnz) A_data = np.ones(A_nnz.size) A_rows = A_val.row * side_size + A_val.col A_cols = np.arange(A_nnz.size) # We are pushing the data on the location of the nonzero elements # to the nonzero rows of A_indexer A_Indexer = sp.coo_matrix( (A_data, (A_rows, A_cols)), shape=(side_size**2, A_nnz.size) ) # We get finaly the sparse matrix A which we wanted A = cvxpy.reshape(A_Indexer @ A_nnz, (side_size, side_size), order="C") A_nnz.value = A_val.data return A Jr_val = J_val.real Jr = adapt_sparse_params(Jr_val, dim) Ji_val = J_val.imag Ji = adapt_sparse_params(Ji_val, dim) # The objective, however, depends on J. objective = cvxpy.Maximize(cvxpy.trace(Jr.T @ X.re + Ji.T @ X.im)) problem = cvxpy.Problem(objective, constraints) return problem qutip-5.1.1/qutip/core/states.py000066400000000000000000001136011474175217300166440ustar00rootroot00000000000000# Required for Sphinx to follow autodoc_type_aliases from __future__ import annotations __all__ = ['basis', 'qutrit_basis', 'coherent', 'coherent_dm', 'fock_dm', 'fock', 'thermal_dm', 'maximally_mixed_dm', 'ket2dm', 'projection', 'qstate', 'ket', 'bra', 'state_number_enumerate', 'state_number_index', 'state_index_number', 'state_number_qobj', 'phase_basis', 'zero_ket', 'spin_state', 'spin_coherent', 'bell_state', 'singlet_state', 'triplet_states', 'w_state', 'ghz_state'] import itertools import numbers import warnings from collections.abc import Iterator from typing import Literal import numpy as np import scipy.sparse as sp from . import data as _data from .qobj import Qobj from .operators import jmat, displace, qdiags from .tensor import tensor from .dimensions import Space from .. import settings from ..typing import SpaceLike, LayerType def _promote_to_zero_list(arg, length): """ Ensure `arg` is a list of length `length`. If `arg` is None it is promoted to `[0]*length`. All other inputs are checked that they match the correct form. Returns ------- list_ : list A list of integers of length `length`. """ if arg is None: arg = [0]*length elif not isinstance(arg, list): arg = [arg] if not len(arg) == length: raise ValueError("All list inputs must be the same length.") if all(isinstance(x, numbers.Integral) for x in arg): return arg raise TypeError("Dimensions must be an integer or list of integers.") def _to_space(dimensions): """ Convert `dimensions` to a :class:`.Space`. Returns ------- space : :class:`.Space` """ if isinstance(dimensions, Space): return dimensions elif isinstance(dimensions, list): return Space(dimensions) else: return Space([dimensions]) def basis( dimensions: SpaceLike, n: int | list[int] = None, offset: int | list[int] = None, *, dtype: LayerType = None, ) -> Qobj: """Generates the vector representation of a Fock state. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. n : int or list of ints, optional (default 0 for all dimensions) Integer corresponding to desired number state, defaults to 0 for all dimensions if omitted. The shape must match ``dimensions``, e.g. if ``dimensions`` is a list, then ``n`` must either be omitted or a list of equal length. offset : int or list of ints, optional (default 0 for all dimensions) The lowest number state that is included in the finite number state representation of the state in the relevant dimension. dtype : type or str, optional storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : :class:`.Qobj` Qobj representing the requested number state ``|n>``. Examples -------- >>> basis(5,2) # doctest: +SKIP Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[ 0.+0.j] [ 0.+0.j] [ 1.+0.j] [ 0.+0.j] [ 0.+0.j]] >>> basis([2,2,2], [0,1,0]) # doctest: +SKIP Quantum object: dims = [[2, 2, 2], [1, 1, 1]], shape = (8, 1), type = ket Qobj data = [[0.] [0.] [1.] [0.] [0.] [0.] [0.] [0.]] Notes ----- A subtle incompatibility with the quantum optics toolbox: In QuTiP:: basis(N, 0) = ground state but in the qotoolbox:: basis(N, 1) = ground state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense # Promote all parameters to Space to simplify later logic. dimensions = _to_space(dimensions) size = dimensions.size if n is None: location = 0 elif offset: if not isinstance(offset, list): offset = [offset] if not isinstance(n, list): n = [n] if len(n) != len(dimensions.as_list()) or len(offset) != len(n): raise ValueError("All list inputs must be the same length.") n_off = [m-off for m, off in zip(n, offset)] try: location = dimensions.dims2idx(n_off) except IndexError: raise ValueError("All basis indices must be integers in the range " "`offset <= n < dimension+offset`.") else: if not isinstance(n, list): n = [n] if len(n) != len(dimensions.as_list()): raise ValueError("All list inputs must be the same length.") try: location = dimensions.dims2idx(n) except IndexError: raise ValueError("All basis indices must be integers in the range " "`0 <= n < dimension`.") data = _data.one_element[dtype]((size, 1), (location, 0), 1) return Qobj(data, dims=[dimensions, dimensions.scalar_like()], isherm=False, isunitary=False, copy=False) def qutrit_basis(*, dtype: LayerType = None) -> list[Qobj]: """Basis states for a three level system (qutrit) dtype : type or str, optional storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- qstates : array Array of qutrit basis vectors """ dtype = dtype or settings.core["default_dtype"] or _data.Dense out = [ basis(3, 0, dtype=dtype), basis(3, 1, dtype=dtype), basis(3, 2, dtype=dtype), ] return out _COHERENT_METHODS = ('operator', 'analytic') def coherent( N: int, alpha: float, offset: int = 0, method: str = None, *, dtype: LayerType = None, ) -> Qobj: """Generates a coherent state with eigenvalue alpha. Constructed using displacement operator on vacuum state. Parameters ---------- N : int Number of Fock states in Hilbert space. alpha : float/complex Eigenvalue of coherent state. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the state. Using a non-zero offset will make the default method 'analytic'. method : string {'operator', 'analytic'}, optional Method for generating coherent state. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : qobj Qobj quantum object for coherent state Examples -------- >>> coherent(5,0.25j) # doctest: +SKIP Quantum object: dims = [[5], [1]], shape = [5, 1], type = ket Qobj data = [[ 9.69233235e-01+0.j ] [ 0.00000000e+00+0.24230831j] [ -4.28344935e-02+0.j ] [ 0.00000000e+00-0.00618204j] [ 7.80904967e-04+0.j ]] Notes ----- Select method 'operator' (default) or 'analytic'. With the 'operator' method, the coherent state is generated by displacing the vacuum state using the displacement operator defined in the truncated Hilbert space of size 'N'. This method guarantees that the resulting state is normalized. With 'analytic' method the coherent state is generated using the analytical formula for the coherent state coefficients in the Fock basis. This method does not guarantee that the state is normalized if truncated to a small number of Fock states, but would in that case give more accurate coefficients. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense if offset < 0: raise ValueError('Offset must be non-negative') if method is None: method = "operator" if offset == 0 else "analytic" if method == "operator": if offset != 0: raise ValueError( "The method 'operator' does not support offset != 0. Please" " select another method or set the offset to zero." ) return (displace(N, alpha, dtype=dtype) @ basis(N, 0)).to(dtype) elif method == "analytic": sqrtn = np.sqrt(np.arange(offset, offset+N, dtype=complex)) sqrtn[0] = 1 # Get rid of divide by zero warning data = alpha / sqrtn if offset == 0: data[0] = np.exp(-abs(alpha)**2 / 2.0) else: s = np.prod(np.sqrt(np.arange(1, offset + 1))) # sqrt factorial data[0] = np.exp(-abs(alpha)**2 * 0.5) * alpha**offset / s np.cumprod(data, out=sqrtn) # Reuse sqrtn array return Qobj(sqrtn, dims=[[N], [1]], copy=False).to(dtype) raise TypeError( "The method option can only take values in " + repr(_COHERENT_METHODS) ) def coherent_dm( N: int, alpha: float, offset: int = 0, method: str = None, *, dtype: LayerType = None, ) -> Qobj: """Density matrix representation of a coherent state. Constructed via outer product of :func:`coherent` Parameters ---------- N : int Number of basis states in Hilbert space. alpha : float/complex Eigenvalue for coherent state. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the state. method : string {'operator', 'analytic'}, optional Method for generating coherent density matrix. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- dm : qobj Density matrix representation of coherent state. Examples -------- >>> coherent_dm(3,0.25j) # doctest: +SKIP Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 0.93941695+0.j 0.00000000-0.23480733j -0.04216943+0.j ] [ 0.00000000+0.23480733j 0.05869011+0.j 0.00000000-0.01054025j] [-0.04216943+0.j 0.00000000+0.01054025j 0.00189294+0.j\ ]] Notes ----- Select method 'operator' (default) or 'analytic'. With the 'operator' method, the coherent density matrix is generated by displacing the vacuum state using the displacement operator defined in the truncated Hilbert space of size 'N'. This method guarantees that the resulting density matrix is normalized. With 'analytic' method the coherent density matrix is generated using the analytical formula for the coherent state coefficients in the Fock basis. This method does not guarantee that the state is normalized if truncated to a small number of Fock states, but would in that case give more accurate coefficients. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return coherent( N, alpha, offset=offset, method=method, dtype=dtype ).proj().to(dtype) def fock_dm( dimensions: int | list[int] | Space, n: int | list[int] = None, offset: int | list[int] = None, *, dtype: LayerType = None, ) -> Qobj: """Density matrix representation of a Fock state Constructed via outer product of :func:`basis`. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. n : int or list of ints, default: 0 for all dimensions Integer corresponding to desired number state, defaults to 0 for all dimensions if omitted. The shape must match ``dimensions``, e.g. if ``dimensions`` is a list, then ``n`` must either be omitted or a list of equal length. offset : int or list of ints, default: 0 for all dimensions The lowest number state that is included in the finite number state representation of the state in the relevant dimension. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- dm : qobj Density matrix representation of Fock state. Examples -------- >>> fock_dm(3,1) # doctest: +SKIP Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 0.+0.j 0.+0.j]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dia return basis(dimensions, n, offset=offset, dtype=dtype).proj().to(dtype) def fock( dimensions: SpaceLike, n: int | list[int] = None, offset: int | list[int] = None, *, dtype: LayerType = None, ) -> Qobj: """Bosonic Fock (number) state. Same as :func:`basis`. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. n : int or list of ints, default: 0 for all dimensions Integer corresponding to desired number state, defaults to 0 for all dimensions if omitted. The shape must match ``dimensions``, e.g. if ``dimensions`` is a list, then ``n`` must either be omitted or a list of equal length. offset : int or list of ints, default: 0 for all dimensions The lowest number state that is included in the finite number state representation of the state in the relevant dimension. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- Requested number state :math:`\\left|n\\right>`. Examples -------- >>> fock(4,3) # doctest: +SKIP Quantum object: dims = [[4], [1]], shape = [4, 1], type = ket Qobj data = [[ 0.+0.j] [ 0.+0.j] [ 0.+0.j] [ 1.+0.j]] """ return basis(dimensions, n, offset=offset, dtype=dtype) def thermal_dm( N: int, n: float, method: Literal['operator', 'analytic'] = 'operator', *, dtype: LayerType = None, ) -> Qobj: """Density matrix for a thermal state of n particles Parameters ---------- N : int Number of basis states in Hilbert space. n : float Expectation value for number of particles in thermal state. method : string {'operator', 'analytic'}, default: 'operator' ``string`` that sets the method used to generate the thermal state probabilities dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- dm : qobj Thermal state density matrix. Examples -------- >>> thermal_dm(5, 1) # doctest: +SKIP Quantum object: dims = [[5], [5]], \ shape = [5, 5], type = oper, isHerm = True Qobj data = [[ 0.51612903 0. 0. 0. 0. ] [ 0. 0.25806452 0. 0. 0. ] [ 0. 0. 0.12903226 0. 0. ] [ 0. 0. 0. 0.06451613 0. ] [ 0. 0. 0. 0. 0.03225806]] >>> thermal_dm(5, 1, 'analytic') # doctest: +SKIP Quantum object: dims = [[5], [5]], \ shape = [5, 5], type = oper, isHerm = True Qobj data = [[ 0.5 0. 0. 0. 0. ] [ 0. 0.25 0. 0. 0. ] [ 0. 0. 0.125 0. 0. ] [ 0. 0. 0. 0.0625 0. ] [ 0. 0. 0. 0. 0.03125]] Notes ----- The 'operator' method (default) generates the thermal state using the truncated number operator ``num(N)``. This is the method that should be used in computations. The 'analytic' method uses the analytic coefficients derived in an infinite Hilbert space. The analytic form is not necessarily normalized, if truncated too aggressively. """ dtype = dtype or settings.core["default_dtype"] or _data.Dia if n == 0: return fock_dm(N, 0, dtype=dtype) else: i = np.arange(N) if method == 'operator': beta = np.log(1.0 / n + 1.0) diags = np.exp(-beta * i) diags = diags / np.sum(diags) # populates diagonal terms using truncated operator expression elif method == 'analytic': # populates diagonal terms using analytic values diags = (1.0 + n) ** (-1.0) * (n / (1.0 + n)) ** (i) else: raise ValueError("The method option can only take " "values 'operator' or 'analytic'") out = qdiags(diags, 0, dims=[[N], [N]], shape=(N, N), dtype=dtype) out._isherm = True return out def maximally_mixed_dm( dimensions: SpaceLike, *, dtype: LayerType = None ) -> Qobj: """ Returns the maximally mixed density matrix for a Hilbert space of dimension N. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- dm : :obj:`.Qobj` Thermal state density matrix. """ dtype = dtype or settings.core["default_dtype"] or _data.Dia dimensions = _to_space(dimensions) N = dimensions.size return Qobj(_data.identity[dtype](N, scale=1/N), dims=[dimensions, dimensions], isherm=True, isunitary=(N == 1), copy=False) def ket2dm(Q: Qobj) -> Qobj: """ Takes input ket or bra vector and returns density matrix formed by outer product. This is completely identical to calling ``Q.proj()``. Parameters ---------- Q : :obj:`.Qobj` Ket or bra type quantum object. Returns ------- dm : :obj:`.Qobj` Density matrix formed by outer product of `Q`. Examples -------- >>> x=basis(3,2) >>> ket2dm(x) # doctest: +SKIP Quantum object: dims = [[3], [3]], \ shape = [3, 3], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j] [ 0.+0.j 0.+0.j 0.+0.j] [ 0.+0.j 0.+0.j 1.+0.j]] """ if Q.isket or Q.isbra: return Q.proj() raise TypeError("Input is not a ket or bra vector.") def projection( dimensions: int | list[int], n: int | list[int], m: int | list[int], offset: int | list[int] = None, *, dtype: LayerType = None, ) -> Qobj: r""" The projection operator that projects state :math:`\lvert m\rangle` on state :math:`\lvert n\rangle`. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. n, m : int The number states in the projection. offset : int, default: 0 The lowest number state that is included in the finite number state representation of the projector. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- oper : qobj Requested projection operator. """ dtype = dtype or settings.core["default_dtype"] or _data.CSR return ( basis(dimensions, n, offset=offset, dtype=dtype) @ basis(dimensions, m, offset=offset, dtype=dtype).dag() ).to(dtype) def qstate(string: str, *, dtype: LayerType = None) -> Qobj: r"""Creates a tensor product for a set of qubits in either the 'up' :math:`\lvert0\rangle` or 'down' :math:`\lvert1\rangle` state. Parameters ---------- string : str String containing 'u' or 'd' for each qubit (ex. 'ududd') Returns ------- qstate : qobj Qobj for tensor product corresponding to input string. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Notes ----- Look at ket and bra for more general functions creating multiparticle states. Examples -------- >>> qstate('udu') # doctest: +SKIP Quantum object: dims = [[2, 2, 2], [1, 1, 1]], shape = [8, 1], type = ket Qobj data = [[ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 1.] [ 0.] [ 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dense n = len(string) if n != (string.count('u') + string.count('d')): raise TypeError('String input to QSTATE must consist ' + 'of "u" and "d" elements only') return basis([2]*n, [1 if x == 'u' else 0 for x in string], dtype=dtype) # # different qubit notation dictionary # _qubit_dict = { 'g': 0, # ground state 'e': 1, # excited state 'u': 0, # spin up 'd': 1, # spin down 'H': 0, # horizontal polarization 'V': 1, # vertical polarization } def _character_to_qudit(x: int | str) -> int: """ Converts a character representing a one-particle state into int. """ return _qubit_dict[x] if x in _qubit_dict else int(x) def ket( seq: list[int | str] | str, dim: int | list[int] = 2, *, dtype: LayerType = None, ) -> Qobj: """ Produces a multiparticle ket state for a list or string, where each element stands for state of the respective particle. Parameters ---------- seq : str / list of ints or characters Each element defines state of the respective particle. (e.g. [1,1,0,1] or a string "1101"). For qubits it is also possible to use the following conventions: - 'g'/'e' (ground and excited state) - 'u'/'d' (spin up and down) - 'H'/'V' (horizontal and vertical polarization) Note: for dimension > 9 you need to use a list. dim : int or list of ints, default: 2 Space dimension for each particle: int if there are the same, list if they are different. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- ket : qobj Examples -------- >>> ket("10") # doctest: +SKIP Quantum object: dims = [[2, 2], [1, 1]], shape = [4, 1], type = ket Qobj data = [[ 0.] [ 0.] [ 1.] [ 0.]] >>> ket("Hue") # doctest: +SKIP Quantum object: dims = [[2, 2, 2], [1, 1, 1]], shape = [8, 1], type = ket Qobj data = [[ 0.] [ 1.] [ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 0.]] >>> ket("12", 3) # doctest: +SKIP Quantum object: dims = [[3, 3], [1, 1]], shape = [9, 1], type = ket Qobj data = [[ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 1.] [ 0.] [ 0.] [ 0.]] >>> ket("31", [5, 2]) # doctest: +SKIP Quantum object: dims = [[5, 2], [1, 1]], shape = [10, 1], type = ket Qobj data = [[ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 1.] [ 0.] [ 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dense ns = [_character_to_qudit(x) for x in seq] dim = [dim]*len(ns) if isinstance(dim, numbers.Integral) else dim return basis(dim, ns, dtype=dtype) def bra( seq: list[int | str] | str, dim: int | list[int] = 2, *, dtype: LayerType = None, ) -> Qobj: """ Produces a multiparticle bra state for a list or string, where each element stands for state of the respective particle. Parameters ---------- seq : str / list of ints or characters Each element defines state of the respective particle. (e.g. [1,1,0,1] or a string "1101"). For qubits it is also possible to use the following conventions: - 'g'/'e' (ground and excited state) - 'u'/'d' (spin up and down) - 'H'/'V' (horizontal and vertical polarization) Note: for dimension > 9 you need to use a list. dim : int (default: 2) / list of ints Space dimension for each particle: int if there are the same, list if they are different. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- bra : qobj Examples -------- >>> bra("10") # doctest: +SKIP Quantum object: dims = [[1, 1], [2, 2]], shape = [1, 4], type = bra Qobj data = [[ 0. 0. 1. 0.]] >>> bra("Hue") # doctest: +SKIP Quantum object: dims = [[1, 1, 1], [2, 2, 2]], shape = [1, 8], type = bra Qobj data = [[ 0. 1. 0. 0. 0. 0. 0. 0.]] >>> bra("12", 3) # doctest: +SKIP Quantum object: dims = [[1, 1], [3, 3]], shape = [1, 9], type = bra Qobj data = [[ 0. 0. 0. 0. 0. 1. 0. 0. 0.]] >>> bra("31", [5, 2]) # doctest: +SKIP Quantum object: dims = [[1, 1], [5, 2]], shape = [1, 10], type = bra Qobj data = [[ 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]] """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return ket(seq, dim=dim, dtype=dtype).dag() def state_number_enumerate( dims: list[int], excitations: int = None ) -> Iterator[tuple]: """ An iterator that enumerates all the state number tuples (quantum numbers of the form (n1, n2, n3, ...)) for a system with dimensions given by dims. Example: >>> for state in state_number_enumerate([2,2]): # doctest: +SKIP >>> print(state) # doctest: +SKIP ( 0 0 ) ( 0 1 ) ( 1 0 ) ( 1 1 ) Parameters ---------- dims : list The quantum state dimensions array, as it would appear in a Qobj. excitations : integer, optional Restrict state space to states with excitation numbers below or equal to this value. Returns ------- state_number : tuple Successive state number tuples that can be used in loops and other iterations, using standard state enumeration *by definition*. """ if excitations is None: # in this case, state numbers are a direct product yield from itertools.product(*(range(d) for d in dims)) return # From here on, excitations is not None # General idea of algorithm: add excitations one by one in last mode (idx = # len(dims)-1), and carry over to the next index when the limit is reached. # Keep track of the number of excitations while doing so to avoid having to # do explicit sums over the states. state = (0,)*len(dims) nexc = 0 while True: yield state idx = len(dims) - 1 state = state[:idx] + (state[idx]+1,) nexc += 1 while nexc > excitations or state[idx] >= dims[idx]: # remove all excitations in mode idx, add one in idx-1 idx -= 1 if idx < 0: return nexc -= state[idx+1] - 1 state = state[:idx] + (state[idx]+1, 0) + state[idx+2:] def state_number_index( dims: list[int], state: list[int], ) -> int: """ Return the index of a quantum state corresponding to state, given a system with dimensions given by dims. Example: >>> state_number_index([2, 2, 2], [1, 1, 0]) 6 Parameters ---------- dims : list The quantum state dimensions array, as it would appear in a Qobj. state : list State number array. Returns ------- idx : int The index of the state given by `state` in standard enumeration ordering. """ return np.ravel_multi_index(state, dims) def state_index_number( dims: list[int], index: int, ) -> tuple: """ Return a quantum number representation given a state index, for a system of composite structure defined by dims. Example: >>> state_index_number([2, 2, 2], 6) [1, 1, 0] Parameters ---------- dims : list or array The quantum state dimensions array, as it would appear in a Qobj. index : integer The index of the state in standard enumeration ordering. Returns ------- state : tuple The state number tuple corresponding to index `index` in standard enumeration ordering. """ return np.unravel_index(index, dims) def state_number_qobj( dims: SpaceLike, state: int | list[int] = None, *, dtype: LayerType = None, ) -> Qobj: """ Return a Qobj representation of a quantum state specified by the state array `state`. .. note:: Deprecated in QuTiP 5.0, use :func:`basis` instead. Example: >>> state_number_qobj([2, 2, 2], [1, 0, 1]) # doctest: +SKIP Quantum object: dims = [[2, 2, 2], [1, 1, 1]], \ shape = [8, 1], type = ket Qobj data = [[ 0.] [ 0.] [ 0.] [ 0.] [ 0.] [ 1.] [ 0.] [ 0.]] Parameters ---------- dims : list or array The quantum state dimensions array, as it would appear in a Qobj. state : list State number array. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : :class:`.Qobj` The state as a :class:`.Qobj` instance. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense warnings.warn("basis() is a drop-in replacement for this", DeprecationWarning) return basis(dims, state, dtype=dtype) def phase_basis( N: int, m: int, phi0: float = 0, *, dtype: LayerType = None, ) -> Qobj: """ Basis vector for the mth phase of the Pegg-Barnett phase operator. Parameters ---------- N : int Number of basis states in Hilbert space. m : int Integer corresponding to the mth discrete phase ``phi_m = phi0 + 2 * pi * m / N`` phi0 : float, default: 0 Reference phase angle. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : qobj Ket vector for mth Pegg-Barnett phase operator basis state. Notes ----- The Pegg-Barnett basis states form a complete set over the truncated Hilbert space. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense phim = phi0 + (2.0 * np.pi * m) / N n = np.arange(N)[:, np.newaxis] data = np.exp(1.0j * n * phim) / np.sqrt(N) return Qobj(data, dims=[[N], [1]], copy=False).to(dtype) def zero_ket(dimensions: SpaceLike, *, dtype: LayerType = None) -> Qobj: """ Creates the zero ket vector with shape Nx1 and dimensions `dims`. Parameters ---------- dimensions : int or list of ints, Space Number of basis states in Hilbert space. If a list, then the resultant object will be a tensor product over spaces with those dimensions. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- zero_ket : qobj Zero ket on given Hilbert space. """ dtype = dtype or settings.core["default_dtype"] or _data.Dense dimensions = _to_space(dimensions) N = dimensions.size return Qobj(_data.zeros[dtype](N, 1), dims=[dimensions, dimensions.scalar_like()], copy=False) def spin_state( j: float, m: float, type: Literal["ket", "bra", "dm"] = "ket", *, dtype: LayerType = None, ) -> Qobj: r"""Generates the spin state :math:`\lvert j, m\rangle`, i.e. the eigenstate of the spin-j Sz operator with eigenvalue m. Parameters ---------- j : float The spin of the state (). m : float Eigenvalue of the spin-j Sz operator. type : string {'ket', 'bra', 'dm'}, default: 'ket' Type of state to generate. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : qobj Qobj quantum object for spin state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense J = 2*j + 1 if type == 'ket': return basis(int(J), int(j - m), dtype=dtype) elif type == 'bra': return basis(int(J), int(j - m), dtype=dtype).dag() elif type == 'dm': return fock_dm(int(J), int(j - m), dtype=dtype) else: raise ValueError(f"Invalid value keyword argument type='{type}'") def spin_coherent( j: float, theta: float, phi: float, type: Literal["ket", "bra", "dm"] = "ket", *, dtype: LayerType = None, ) -> Qobj: r"""Generate the coherent spin state :math:`\lvert \theta, \phi\rangle`. Parameters ---------- j : float The spin of the state. theta : float Angle from z axis. phi : float Angle from x axis. type : string {'ket', 'bra', 'dm'}, default: 'ket' Type of state to generate. dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- state : qobj Qobj quantum object for spin coherent state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense if type not in ['ket', 'bra', 'dm']: raise ValueError("Invalid value keyword argument 'type'") Sp = jmat(j, '+') Sm = jmat(j, '-') psi = (0.5 * theta * np.exp(1j * phi) * Sm - 0.5 * theta * np.exp(-1j * phi) * Sp).expm() * \ spin_state(j, j) if type == 'bra': psi = psi.dag() elif type == 'dm': psi = ket2dm(psi) return psi.to(dtype) _BELL_STATES = { '00': np.sqrt(0.5) * (basis([2, 2], [0, 0]) + basis([2, 2], [1, 1])), '01': np.sqrt(0.5) * (basis([2, 2], [0, 0]) - basis([2, 2], [1, 1])), '10': np.sqrt(0.5) * (basis([2, 2], [0, 1]) + basis([2, 2], [1, 0])), '11': np.sqrt(0.5) * (basis([2, 2], [0, 1]) - basis([2, 2], [1, 0])), } def bell_state( state: Literal["00", "01", "10", "11"] = "00", *, dtype: LayerType = None, ) -> Qobj: r""" Returns the selected Bell state: .. math:: \begin{aligned} \lvert B_{00}\rangle &= \frac1{\sqrt2}(\lvert00\rangle+\lvert11\rangle)\\ \lvert B_{01}\rangle &= \frac1{\sqrt2}(\lvert00\rangle-\lvert11\rangle)\\ \lvert B_{10}\rangle &= \frac1{\sqrt2}(\lvert01\rangle+\lvert10\rangle)\\ \lvert B_{11}\rangle &= \frac1{\sqrt2}(\lvert01\rangle-\lvert10\rangle)\\ \end{aligned} Parameters ---------- state : str ['00', '01', '10', '11'] Which bell state to return dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- Bell_state : qobj Bell state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return _BELL_STATES[state].copy().to(dtype) def singlet_state(*, dtype: LayerType = None) -> Qobj: r""" Returns the two particle singlet-state: .. math:: \lvert S\rangle = \frac1{\sqrt2}(\lvert01\rangle-\lvert10\rangle) that is identical to the fourth bell state. Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- Bell_state : qobj :math:`\lvert B_{11}\rangle` Bell state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return bell_state('11').to(dtype) def triplet_states(*, dtype: LayerType = None) -> list[Qobj]: r""" Returns a list of the two particle triplet-states: .. math:: \lvert T_1\rangle = \lvert11\rangle \lvert T_2\rangle = \frac1{\sqrt2}(\lvert01\rangle + \lvert10\rangle) \lvert T_3\rangle = \lvert00\rangle Parameters ---------- dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- trip_states : list 2 particle triplet states """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return [ basis([2, 2], [1, 1], dtype=dtype), ( np.sqrt(0.5) * ( basis([2, 2], [0, 1], dtype=dtype) + basis([2, 2], [1, 0], dtype=dtype) ) ).to(dtype), basis([2, 2], [0, 0], dtype=dtype), ] def w_state(N_qubit: int, *, dtype: LayerType = None) -> Qobj: """ Returns the N-qubit W-state: ``[ |100..0> + |010..0> + |001..0> + ... |000..1> ] / sqrt(n)`` Parameters ---------- N_qubit : int Number of qubits in state dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- W : :obj:`.Qobj` N-qubit W-state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense inds = np.zeros(N_qubit, dtype=int) inds[0] = 1 state = basis([2]*N_qubit, list(inds), dtype=dtype) for kk in range(1, N_qubit): state += basis([2] * N_qubit, list(np.roll(inds, kk)), dtype=dtype) return (np.sqrt(1 / N_qubit) * state).to(dtype) def ghz_state(N_qubit: int, *, dtype: LayerType = None) -> Qobj: """ Returns the N-qubit GHZ-state: ``[ |00...00> + |11...11> ] / sqrt(2)`` Parameters ---------- N_qubit : int Number of qubits in state dtype : type or str, optional Storage representation. Any data-layer known to ``qutip.data.to`` is accepted. Returns ------- G : qobj N-qubit GHZ-state """ dtype = dtype or settings.core["default_dtype"] or _data.Dense return ( np.sqrt(0.5) * ( basis([2] * N_qubit, [0] * N_qubit, dtype=dtype) + basis([2] * N_qubit, [1] * N_qubit, dtype=dtype) ) ).to(dtype) qutip-5.1.1/qutip/core/subsystem_apply.py000066400000000000000000000167111474175217300206100ustar00rootroot00000000000000# # This code was contributed by Ben Criger. Resemblance to # partial_transpose is intentional, and meant to enhance legibility. # __all__ = ['subsystem_apply'] import itertools import numpy as np from . import Qobj, qeye, to_kraus, tensor from . import data as _data def subsystem_apply( state: Qobj, channel: Qobj, mask: list[bool], reference: bool=False )-> Qobj: """ Returns the result of applying the propagator `channel` to the subsystems indicated in `mask`, which comprise the density operator `state`. Parameters ---------- state : :class:`.Qobj` A density matrix or ket. channel : :class:`.Qobj` A propagator, either an `oper` or `super`. mask : *list* / *array* A mask that selects which subsystems should be subjected to the channel. reference : bool Decides whether explicit Kraus map should be used to evaluate action of channel. Returns ------- rho_out: :class:`.Qobj` A density matrix with the selected subsystems transformed according to the specified channel. """ # TODO: Include sparse/dense methods a la partial_transpose. if not (state.isket or state.isoper): raise ValueError("input state must be a ket or oper") if not (channel.issuper or channel.isoper): raise ValueError("input channel must be a super or oper") # Since there's only one channel, all affected subsystems must have # the same dimensions: aff_subs_dim_ar = np.transpose(np.array(state.dims))[np.array(mask)] if any((aff_subs_dim_ar[j] != aff_subs_dim_ar[0]).any() for j in range(len(aff_subs_dim_ar))): raise ValueError("affected subsystems must have the same dimension") # If the map is on the Hilbert space, it must have the same dimension # as the affected subsystem. If it is on the Liouville space, it must # exist on a space as large as the square of the Hilbert dimension. required_shape = ([x**2 for x in aff_subs_dim_ar[0]] if channel.issuper else aff_subs_dim_ar[0]) if tuple(required_shape) != channel.shape: raise ValueError( "superoperator dimension must be the subsystem dimension squared" ) mask = np.asarray(mask) if reference: return _subsystem_apply_reference(state, channel, mask) if state.isoper: return _subsystem_apply_dm(state, channel, mask) return _subsystem_apply_ket(state, channel, mask) def _subsystem_apply_ket(state, channel, mask): # TODO Write more efficient code for single-matrix map on pure states # TODO Write more efficient code for single-subsystem map . . . return _subsystem_apply_dm(state.proj(), channel, mask) def _subsystem_apply_dm(state, channel, mask): """ Applies a channel to every subsystem indicated by a mask, by repeatedly applying the channel to each affected subsystem. """ # Initialize Output Matrix rho_out = state # checked affected subsystems print arange(len(state.dims[0]))[mask] for subsystem in np.arange(len(state.dims[0]))[mask]: rho_out = _one_subsystem_apply(rho_out, channel, subsystem) return rho_out def _one_subsystem_apply(state, channel, idx): """ Applies a channel to a state on one subsystem, by breaking it into blocks and applying a reduced channel to each block. """ subs_dim_ar = np.array(state.dims).T # Calculate number of blocks n_blks = 1 for mul_idx in range(idx): n_blks = n_blks * subs_dim_ar[mul_idx][0] blk_sz = state.shape[0] // n_blks # Apply channel to top subsystem of each block in matrix full_data_matrix = state.full() for blk_r in range(n_blks): for blk_c in range(n_blks): # Apply channel to high-level blocks of matrix: blk_rx = blk_r * blk_sz blk_cx = blk_c * blk_sz full_data_matrix[blk_rx : blk_rx+blk_sz, blk_cx : blk_cx+blk_sz] =\ _block_apply(full_data_matrix[blk_rx : blk_rx+blk_sz, blk_cx : blk_cx+blk_sz], channel) return Qobj(full_data_matrix, dims=state.dims) def _block_apply(block, channel): return (_top_apply_U(block, channel) if channel.isoper else _top_apply_S(block, channel)) def _top_apply_U(block, channel): """ Uses scalar-matrix multiplication to efficiently apply a channel to the leftmost register in the tensor product, given a unitary matrix for a channel. """ split_mat = _block_split(block, *channel.shape) temp_split_mat = np.zeros(np.shape(split_mat)).astype(complex) for dm_row_idx in range(channel.shape[0]): for dm_col_idx in range(channel.shape[1]): for op_row_idx in range(channel.shape[0]): for op_col_idx in range(channel.shape[1]): temp_split_mat[dm_row_idx][dm_col_idx] += ( channel[dm_row_idx, op_col_idx] * channel[dm_col_idx, op_row_idx].conjugate() * split_mat[op_col_idx][op_row_idx] ) return _block_join(temp_split_mat) def _top_apply_S(block, channel): # If the channel is a super-operator, perform second block decomposition; # block-size matches Hilbert space of affected subsystem: # FIXME use state shape? n_v = int(np.sqrt(channel.shape[0])) n_h = int(np.sqrt(channel.shape[1])) column = _block_col(block, n_v, n_h) chan_mat = channel.full() temp_col = np.zeros(np.shape(column)).astype(complex) for i, row in enumerate(chan_mat): temp_col[i] = sum(s * mat for s, mat in zip(row.T, column)) return _block_stack(temp_col, n_v, n_h) def _block_split(mat_in, n_v, n_h): """ Returns a 4D array of matrices, splitting mat_in into n_v * n_h square sub-arrays. """ return [np.hsplit(x, n_h) for x in np.vsplit(mat_in, n_v)] def _block_join(mat_in): return np.hstack(np.hstack(mat_in)) def _block_col(mat_in, n_v, n_h): """ Returns a 3D array of matrices, splitting mat_in into n_v * n_h square sub-arrays. """ rows, cols = np.shape(mat_in) return np.reshape( np.array(_block_split(mat_in, n_v, n_h)).transpose(1, 0, 2, 3), (n_v * n_h, rows // n_v, cols // n_h) ) def _block_stack(arr_in, n_v, n_h): """ Inverse of _block_split """ rs, cs = np.shape(arr_in)[-2:] temp = list(map(np.transpose, arr_in)) # print shape(arr_in) temp = np.reshape(temp, (n_v, n_h, rs, cs)) return np.hstack(np.hstack(temp)).T def _subsystem_apply_reference(state, channel, mask): state = state.proj() if state.isket else state if channel.isoper: full_oper = tensor([channel if mask_ else qeye(size) for size, mask_ in zip(state.dims[0], mask)]) return full_oper @ state @ full_oper.dag() kraus_list = to_kraus(channel) # Kraus operators to be padded with identities: k_qubit_kraus_list = itertools.product(kraus_list, repeat=np.sum(mask)) rho_out = Qobj(_data.csr.zeros(*state.shape), dims=state.dims) for operator_iter in k_qubit_kraus_list: operator_iter = iter(operator_iter) op_iter_list = [next(operator_iter) if mask[j] else qeye(state.dims[0][j]) for j in range(len(state.dims[0]))] full_oper = tensor(list(map(Qobj, op_iter_list))) rho_out = rho_out + full_oper * state * full_oper.dag() return rho_out qutip-5.1.1/qutip/core/superop_reps.py000066400000000000000000000435371474175217300201010ustar00rootroot00000000000000# -*- coding: utf-8 -*- # # This module was initially contributed by Ben Criger. # """ This module implements transformations between superoperator representations, including supermatrix, Kraus, Choi and Chi (process) matrix formalisms. """ __all__ = [ 'kraus_to_choi', 'kraus_to_super', 'to_choi', 'to_chi', 'to_super', 'to_kraus', 'to_stinespring', ] import itertools import numbers import numpy as np import scipy.linalg from . import data as _data from .superoperator import stack_columns, unstack_columns, sprepost from .tensor import tensor from .dimensions import flatten from .qobj import Qobj from .operators import identity, sigmax, sigmay, sigmaz from .states import basis # TODO: revisit when creation routines have dispatching. _SINGLE_QUBIT_PAULI_BASIS = ( identity(2).to(_data.CSR), sigmax().to(_data.CSR), sigmay().to(_data.CSR), sigmaz().to(_data.CSR), ) def _superpauli_basis(nq=1): dims = [[[2] * nq] * 2] * 2 nnz = 8**nq data = _data.csr.empty(4**nq, 4**nq, nnz) sci = data.as_scipy(full=True) ptr, ptr_inc = 0, 2**nq # Construct the Pauli basis by vertically stacking rows in sparse format. # The CSR format is much more efficient at handling row-stacking, so we # actually have to do a little dance through adjoint/transpose to get it # into the right format. for i, paulis in enumerate(itertools.product(_SINGLE_QUBIT_PAULI_BASIS, repeat=nq)): basis = paulis[0].data for pauli in paulis[1:]: basis = _data.kron_csr(basis, pauli.data) basis_ket_sci = _data.column_stack_csr(basis).transpose().as_scipy() sci.data[ptr : ptr+ptr_inc] = basis_ket_sci.data sci.indices[ptr : ptr+ptr_inc] = basis_ket_sci.indices sci.indptr[i] = ptr ptr += ptr_inc sci.indptr[-1] = nnz return Qobj(data.adjoint(), dims=dims, superrep='super', isherm=False, isunitary=False, copy=False) def _int_log_two(x): return int(x).bit_length() - 1 def _is_power_of_two(x): return isinstance(x, numbers.Integral) and x == 2**_int_log_two(x) def _nq(dims): dim = np.prod(dims[0][0]) nq = _int_log_two(dim) if 2 ** nq != dim: raise ValueError("{} is not an integer power of 2.".format(dim)) return nq def isqubitdims(dims: list[list[int]] | list[list[list[int]]]) -> bool: """ Checks whether all entries in a dims list are integer powers of 2. Parameters ---------- dims : nested list of ints Dimensions to be checked. Returns ------- isqubitdims : bool True if and only if every member of the flattened dims list is an integer power of 2. """ return all(_is_power_of_two(dim) for dim in flatten(dims)) def _to_superpauli(q_oper): """ Convert a superoperator to the Pauli basis (assuming qubit dimensions). This is an internal function, as QuTiP does not currently have a way to mark that superoperators are represented in the Pauli basis as opposed to the column-stacking basis; a Pauli-basis ``type='super'`` would thus break other conversion functions. """ # Ensure we start with a column-stacking-basis superoperator. sqobj = to_super(q_oper) if not isqubitdims(sqobj.dims): raise ValueError("Pauli basis is only defined for qubits.") nq = _int_log_two(sqobj.shape[0]) // 2 B = _superpauli_basis(nq) * 2**(-0.5 * nq) # To do this, we have to hack a bit and force the dims to match, # since the superpauli_basis function makes different assumptions # about indices than we need here. B.dims = sqobj.dims return B.dag() @ sqobj @ B def _choi_to_kraus(q_oper, tol=1e-9): """ Takes a Choi matrix and returns a list of Kraus operators. TODO: Create a new class structure for quantum channels, perhaps as a strict sub-class of Qobj. """ vals, vecs = q_oper.eigenstates() dims = [q_oper.dims[0][1], q_oper.dims[0][0]] shape = (np.prod(q_oper.dims[0][1]), np.prod(q_oper.dims[0][0])) return [Qobj(_data.mul(unstack_columns(vec.data, shape=shape), np.sqrt(val)), dims=dims, copy='False') for val, vec in zip(vals, vecs) if abs(val) >= tol] # Individual conversions from Kraus operators are public because the output # list of Kraus operators is not itself a quantum object. def kraus_to_choi(kraus_ops: list[Qobj]) -> Qobj: r""" Convert a list of Kraus operators into Choi representation of the channel. Essentially, kraus operators are a decomposition of a Choi matrix, and its reconstruction from them should go as :math:`E = \sum_{i} |K_i\rangle\rangle \langle\langle K_i|`, where we use vector representation of Kraus operators. Parameters ---------- kraus_ops : list[Qobj] The list of Kraus operators to be converted to Choi representation. Returns ------- choi : Qobj A quantum object representing the same map as ``kraus_ops``, such that ``choi.superrep == "choi"``. """ len_op = np.prod(kraus_ops[0].shape) # If Kraus ops have dims [M, N] in qutip notation (act on [N, N] density # matrix and produce [M, M] d.m.), Choi matrix Hilbert space will # be [[M, N], [M, N]] because Choi Hilbert space # is (output space) x (input space). choi_dims = [kraus_ops[0].dims] * 2 # transform a list of Qobj matrices list[sum_ij k_ij |i>> = sum_I k_I |I>> kraus_vectors = np.asarray([ np.reshape(kraus_op.full(), len_op, order="F") for kraus_op in kraus_ops ]) # sum_{I} |k_I|^2 |I>>< Qobj: """ Convert a list of Kraus operators to a superoperator. Parameters ---------- kraus_list : list of Qobj The list of Kraus super operators to convert. sparse: bool Prevents dense intermediates if true. """ if sparse: return sum(sprepost(k, k.dag()) for k in kraus_list) else: return to_super(kraus_to_choi(kraus_list)) def _super_tofrom_choi(q_oper): """ We exploit that the basis transformation between Choi and supermatrix representations squares to the identity, so that if we munge Qobj.type, we can use the same function. """ if not q_oper.issuper: raise ValueError("needs to be a superoperator") if q_oper.superrep not in ('super', 'choi'): raise ValueError("operator is not in super or choi format") data = q_oper.data.to_array() dims = q_oper.dims new_dims = [[dims[1][1], dims[0][1]], [dims[1][0], dims[0][0]]] d0 = np.prod(flatten(new_dims[0])) d1 = np.prod(flatten(new_dims[1])) s0 = np.prod(dims[0][0]) s1 = np.prod(dims[1][1]) data = ( data.reshape([s0, s1, s0, s1]).transpose(3, 1, 2, 0).reshape([d0, d1]) ) return Qobj(data, dims=new_dims, superrep='super' if q_oper.superrep == 'choi' else 'choi', copy=False) def _choi_to_chi(q_oper): """ Converts a Choi matrix to a Chi matrix in the Pauli basis. NOTE: this is only supported for qubits right now. Need to extend to Heisenberg-Weyl for other subsystem dimensions. """ nq = _nq(q_oper.dims) B = _superpauli_basis(nq).data return Qobj(_data.matmul(_data.matmul(B.adjoint(), q_oper.data), B), dims=q_oper.dims, superrep='chi', copy=False) def _chi_to_choi(q_oper): """ Converts a Chi matrix to a Choi matrix. NOTE: this is only supported for qubits right now. Need to extend to Heisenberg-Weyl for other subsystem dimensions. """ nq = _nq(q_oper.dims) B = _superpauli_basis(nq).data # The Chi matrix has tr(chi) == d², so we need to divide out # by that to get back to the Choi form. return Qobj(_data.mul( _data.matmul(_data.matmul(B, q_oper.data), B.adjoint()), 1 / q_oper.shape[0] ), dims=q_oper.dims, superrep='choi', copy=False) def _svd_u_to_kraus(U, S, d, dK, indims, outdims): """ Given a partial isometry U and a vector of square-roots of singular values S obtained from a SVD, produces the Kraus operators represented by U. Returns ------- Ks : list of Qobj Quantum objects represnting each of the Kraus operators. """ # We use U * S since S is 1-index, such that this is equivalent to # U . diag(S), but easier to write down. data = np.array(U * S).reshape((d, d, dK), order='F').transpose((2, 0, 1)) return [ Qobj(x, dims=[outdims, indims], copy=False) for x in data ] def _generalized_kraus(q_oper, threshold=1e-10): # TODO: document! # TODO: use this to generalize to_kraus to the case where U != V. # This is critical for non-CP maps, as appear in (for example) # diamond norm differences between two CP maps. if not q_oper.issuper or q_oper.superrep != "choi": raise ValueError("".join([ "Expected a Choi matrix, got a ", repr(q_oper.type), " (superrep ", repr(q_oper.superrep), ")." ])) # Remember the shape of the underlying space, # as we'll need this to make Kraus operators later. dL, dR = int(np.sqrt(q_oper.shape[0])), int(np.sqrt(q_oper.shape[1])) # Also remember the dims breakout. out_dims, in_dims = q_oper.dims out_left, out_right = out_dims in_left, in_right = in_dims # Find the SVD. U, S, V = scipy.linalg.svd(q_oper.full()) # Truncate away the zero singular values, up to a threshold. nonzero_idxs = S > threshold dK = nonzero_idxs.sum() U = np.array(U)[:, nonzero_idxs] # We also want S to be a single index array, which np.matrix # doesn't allow for. This is stripped by calling array() on it. S = np.sqrt(np.array(S)[nonzero_idxs]) # Since NumPy returns V and not V+, we need to take the dagger # to get back to quantum info notation for Stinespring pairs. V = np.array(V.conj().T)[:, nonzero_idxs] # Next, we convert each of U and V into Kraus operators. # Finally, we want the Kraus index to be left-most so that we # can map over it when making Qobjs. # FIXME: does not preserve dims! kU = _svd_u_to_kraus(U, S, dL, dK, out_right, out_left) kV = _svd_u_to_kraus(V, S, dL, dK, in_right, in_left) return kU, kV def _choi_to_stinespring(q_oper, threshold=1e-10): # TODO: document! kU, kV = _generalized_kraus(q_oper, threshold=threshold) assert len(kU) == len(kV) dK = len(kU) dL = kU[0].shape[0] dR = kV[0].shape[1] # Also remember the dims breakout. out_dims, in_dims = q_oper.dims out_left, out_right = out_dims in_left, in_right = in_dims A = Qobj(_data.zeros(dK * dL, dL), dims=[out_left + [dK], out_right + [1]], isherm=True, isunitary=False, copy=False) B = Qobj(_data.zeros(dK * dR, dR), dims=[in_left + [dK], in_right + [1]], isherm=True, isunitary=False, copy=False) for idx_kraus, (KL, KR) in enumerate(zip(kU, kV)): A += tensor(KL, basis(dK, idx_kraus)) B += tensor(KR, basis(dK, idx_kraus)) # There is no input (right) Kraus index, so strip that off. A.dims = [out_left + [dK], out_right] B.dims = [in_left + [dK], in_right] return A, B def to_choi(q_oper: Qobj) -> Qobj: """ Converts a Qobj representing a quantum map to the Choi representation, such that the trace of the returned operator is equal to the dimension of the system. Parameters ---------- q_oper : Qobj Superoperator to be converted to Choi representation. If ``q_oper`` is ``type="oper"``, then it is taken to act by conjugation, such that ``to_choi(A) == to_choi(sprepost(A, A.dag()))``. Returns ------- choi : Qobj A quantum object representing the same map as ``q_oper``, such that ``choi.superrep == "choi"``. Raises ------ TypeError: If the given quantum object is not a map, or cannot be converted to Choi representation. """ if q_oper.type == 'super': if q_oper.superrep == 'choi': return q_oper if q_oper.superrep == 'super': return _super_tofrom_choi(q_oper) if q_oper.superrep == 'chi': return _chi_to_choi(q_oper) else: raise TypeError(q_oper.superrep) elif q_oper.type == 'oper': return _super_tofrom_choi(sprepost(q_oper, q_oper.dag())) else: raise TypeError( "Conversion of Qobj with type = {0.type} " "and superrep = {0.choi} to Choi not supported.".format(q_oper) ) def to_chi(q_oper: Qobj) -> Qobj: """ Converts a Qobj representing a quantum map to a representation as a chi (process) matrix in the Pauli basis, such that the trace of the returned operator is equal to the dimension of the system. Parameters ---------- q_oper : Qobj Superoperator to be converted to Chi representation. If ``q_oper`` is ``type="oper"``, then it is taken to act by conjugation, such that ``to_chi(A) == to_chi(sprepost(A, A.dag()))``. Returns ------- chi : Qobj A quantum object representing the same map as ``q_oper``, such that ``chi.superrep == "chi"``. Raises ------ TypeError: If the given quantum object is not a map, or cannot be converted to Chi representation. """ if q_oper.type == 'super': if q_oper.superrep == 'chi': return q_oper elif q_oper.superrep == 'choi': return _choi_to_chi(q_oper) elif q_oper.superrep == 'super': return _choi_to_chi(to_choi(q_oper)) else: raise TypeError(q_oper.superrep) elif q_oper.type == 'oper': return to_chi(sprepost(q_oper, q_oper.dag())) else: raise TypeError( "Conversion of Qobj with type = {0.type} " "and superrep = {0.choi} to Choi not supported.".format(q_oper) ) def to_super(q_oper: Qobj) -> Qobj: """ Converts a Qobj representing a quantum map to the supermatrix (Liouville) representation. Parameters ---------- q_oper : Qobj Superoperator to be converted to supermatrix representation. If ``q_oper`` is ``type="oper"``, then it is taken to act by conjugation, such that ``to_super(A) == sprepost(A, A.dag())``. Returns ------- superop : Qobj A quantum object representing the same map as ``q_oper``, such that ``superop.superrep == "super"``. Raises ------ TypeError If the given quantum object is not a map, or cannot be converted to supermatrix representation. """ if q_oper.type == 'super': if q_oper.superrep == "super": return q_oper elif q_oper.superrep == 'choi': return _super_tofrom_choi(q_oper) elif q_oper.superrep == 'chi': return to_super(to_choi(q_oper)) else: raise ValueError( "Unrecognized superrep '{}'.".format(q_oper.superrep)) elif q_oper.type == 'oper': # Assume unitary return sprepost(q_oper, q_oper.dag()) else: raise TypeError( "Conversion of Qobj with type = {0.type} " "and superrep = {0.superrep} to supermatrix not " "supported.".format(q_oper) ) def to_kraus(q_oper: Qobj, tol: float=1e-9) -> list[Qobj]: """ Converts a Qobj representing a quantum map to a list of quantum objects, each representing an operator in the Kraus decomposition of the given map. Parameters ---------- q_oper : Qobj Superoperator to be converted to Kraus representation. If ``q_oper`` is ``type="oper"``, then it is taken to act by conjugation, such that ``to_kraus(A) == to_kraus(sprepost(A, A.dag())) == [A]``. tol : Float, default: 1e-9 Optional threshold parameter for eigenvalues/Kraus ops to be discarded. Returns ------- kraus_ops : list of Qobj A list of quantum objects, each representing a Kraus operator in the decomposition of ``q_oper``. Raises ------ TypeError: if the given quantum object is not a map, or cannot be decomposed into Kraus operators. """ if q_oper.issuper: if q_oper.superrep != 'choi': q_oper = to_choi(q_oper) return _choi_to_kraus(q_oper, tol) elif q_oper.isoper: # Assume unitary return [q_oper] raise TypeError( "Conversion of Qobj with type={0.type} " "and superrep={0.superrep} to Kraus decomposition not " "supported.".format(q_oper) ) def to_stinespring(q_oper: Qobj, threshold: float=1e-10) -> tuple[Qobj, Qobj]: r""" Converts a Qobj representing a quantum map :math:`\Lambda` to a pair of partial isometries ``A`` and ``B`` such that :math:`\Lambda(X) = \Tr_2(A X B^\dagger)` for all inputs ``X``, where the partial trace is taken over a a new index on the output dimensions of ``A`` and ``B``. For completely positive inputs, ``A`` will always equal ``B`` up to precision errors. Parameters ---------- q_oper : Qobj Superoperator to be converted to a Stinespring pair. threshold : float, default: 1e-10 Threshold parameter for eigenvalues/Kraus ops to be discarded. Returns ------- A, B : Qobj Quantum objects representing each of the Stinespring matrices for the input Qobj. """ return _choi_to_stinespring(to_choi(q_oper), threshold) qutip-5.1.1/qutip/core/superoperator.py000066400000000000000000000421701474175217300202550ustar00rootroot00000000000000__all__ = [ 'liouvillian', 'lindblad_dissipator', 'operator_to_vector', 'vector_to_operator', 'stack_columns', 'unstack_columns', 'stacked_index', 'unstacked_index', 'spost', 'spre', 'sprepost', 'reshuffle', ] import functools from typing import TypeVar, overload import numpy as np from .qobj import Qobj from .cy.qobjevo import QobjEvo from . import data as _data from .dimensions import Compound, SuperSpace, Space def _map_over_compound_operators(f): """ Convert a function which takes Qobj into one that can also take compound operators like QobjEvo, and applies itself over all the components. """ @functools.wraps(f) def out(qobj): # To avoid circular dependencies from .cy.qobjevo import QobjEvo if isinstance(qobj, QobjEvo): return qobj.linear_map(f, _skip_check=True) if not isinstance(qobj, Qobj): raise TypeError("expected a quantum object") return f(qobj) return out @overload def liouvillian( H: Qobj, c_ops: list[Qobj], data_only: bool, chi: list[float] ) -> Qobj: ... @overload def liouvillian( H: Qobj | QobjEvo, c_ops: list[Qobj | QobjEvo], data_only: bool, chi: list[float] ) -> QobjEvo: ... def liouvillian( H: Qobj | QobjEvo = None, c_ops: list[Qobj | QobjEvo] = None, data_only: bool = False, chi: list[float] = None, ) -> Qobj | QobjEvo: """Assembles the Liouvillian superoperator from a Hamiltonian and a ``list`` of collapse operators. Parameters ---------- H : Qobj or QobjEvo, optional System Hamiltonian or Hamiltonian component of a Liouvillian. Considered `0` if not given. c_ops : array_like of Qobj or QobjEvo, optional A ``list`` or ``array`` of collapse operators. data_only : bool, default: False Return the data object instead of a Qobj chi : array_like of float, optional In some systems it is possible to determine the statistical moments (mean, variance, etc) of the probability distributions of occupation of various states by numerically evaluating the derivatives of the steady state occupation probability as a function of artificial phase parameters ``chi`` which are included in the :func:`lindblad_dissipator` for each collapse operator. See the documentation of :func:`lindblad_dissipator` for references and further details. This parameter is deprecated and may be removed in QuTiP 5. Returns ------- L : Qobj or QobjEvo Liouvillian superoperator. """ # To avoid circular dependencies from .cy.qobjevo import QobjEvo if ( data_only and (isinstance(H, QobjEvo) or any(isinstance(op, QobjEvo) for op in c_ops)) ): raise ValueError("Cannot return the data object when computing the" " liouvillian with QobjEvo") c_ops = c_ops or [] if isinstance(c_ops, (Qobj, QobjEvo)): c_ops = [c_ops] if chi and len(chi) != len(c_ops): raise ValueError('chi must be a list with same length as c_ops') chi = chi or [0] * len(c_ops) if H is None: # No Hamiltonian, add the lindblad_dissipator of c_ops: if not c_ops: raise ValueError("The liouvillian need an Hamiltonian" " and/or c_ops") out = sum(lindblad_dissipator(c_op, chi=chi_) for c_op, chi_ in zip(c_ops, chi)) return out.data if data_only else out elif not H.isoper: raise TypeError("Invalid type for Hamiltonian.") if isinstance(H, QobjEvo) or any(isinstance(op, QobjEvo) for op in c_ops): # With QobjEvo, faster computation using Data is not used L = -1.0j * (spre(H) - spost(H)) L += sum(lindblad_dissipator(c_op, chi=chi_) for c_op, chi_ in zip(c_ops, chi)) return L spI = _data.identity_like(H.data) data = _data.mul(_data.kron(spI, H.data), -1j) data = _data.add(data, _data.kron_transpose(H.data, spI), scale=1j) for c_op, chi_ in zip(c_ops, chi): c = c_op.data cd = c.adjoint() cdc = _data.matmul(cd, c) data = _data.add(data, _data.kron(c.conj(), c), np.exp(1j*chi_)) data = _data.add(data, _data.kron(spI, cdc), -0.5) data = _data.add(data, _data.kron_transpose(cdc, spI), -0.5) if data_only: return data else: return Qobj(data, dims=[H._dims, H._dims], superrep='super', copy=False) @overload def lindblad_dissipator( a: Qobj, b: Qobj, data_only: bool, chi: list[float] ) -> Qobj: ... @overload def lindblad_dissipator( a: Qobj | QobjEvo, b: Qobj | QobjEvo, data_only: bool, chi: list[float] ) -> QobjEvo: ... def lindblad_dissipator( a: Qobj | QobjEvo, b: Qobj | QobjEvo = None, data_only: bool = False, chi: list[float] = None, ) -> Qobj | QobjEvo: """ Lindblad dissipator (generalized) for a single pair of collapse operators (a, b), or for a single collapse operator (a) when b is not specified: .. math:: \\mathcal{D}[a,b]\\rho = a \\rho b^\\dagger - \\frac{1}{2}a^\\dagger b\\rho - \\frac{1}{2}\\rho a^\\dagger b Parameters ---------- a : Qobj or QobjEvo Left part of collapse operator. b : Qobj or QobjEvo, optional Right part of collapse operator. If not specified, b defaults to a. chi : float, optional In some systems it is possible to determine the statistical moments (mean, variance, etc) of the probability distribution of the occupation numbers of states by numerically evaluating the derivatives of the steady state occupation probability as a function of an artificial phase parameter ``chi`` which multiplies the ``a \\rho a^dagger`` term of the dissipator by ``e ^ (i * chi)``. The factor ``e ^ (i * chi)`` is introduced via the generating function of the statistical moments. For examples of the technique, see `Full counting statistics of nano-electromechanical systems `_ and `Photon-mediated electron transport in hybrid circuit-QED `_. This parameter is deprecated and may be removed in QuTiP 5. data_only : bool, default: False Return the data object instead of a Qobj Returns ------- D : qobj, QobjEvo Lindblad dissipator superoperator. """ # To avoid circular dependencies from .cy.qobjevo import QobjEvo if data_only and (isinstance(a, QobjEvo) or isinstance(b, QobjEvo)): raise ValueError("Cannot return the data object when computing the" " collapse of a QobjEvo") if b is None: b = a ad_b = a.dag() * b if chi: D = ( spre(a) * spost(b.dag()) * np.exp(1j * chi) - 0.5 * spre(ad_b) - 0.5 * spost(ad_b) ) else: D = spre(a) * spost(b.dag()) - 0.5 * spre(ad_b) - 0.5 * spost(ad_b) return D.data if data_only else D @_map_over_compound_operators def operator_to_vector(op: Qobj) -> Qobj: """ Create a vector representation given a quantum operator in matrix form. The passed object should have a ``Qobj.type`` of 'oper' or 'super'; this function is not designed for general-purpose matrix reshaping. Parameters ---------- op : Qobj or QobjEvo Quantum operator in matrix form. This must have a type of 'oper' or 'super'. Returns ------- Qobj or QobjEvo The same object, but re-cast into a column-stacked-vector form of type 'operator-ket'. The output is the same type as the passed object. """ if op.type in ['super', 'operator-ket', 'operator-bra']: raise TypeError("Cannot convert object already " "in super representation") return Qobj(stack_columns(op.data), dims=[op.dims, [1]], superrep="super", copy=False) @_map_over_compound_operators def vector_to_operator(op: Qobj) -> Qobj: """ Create a matrix representation given a quantum operator in vector form. The passed object should have a ``Qobj.type`` of 'operator-ket'; this function is not designed for general-purpose matrix reshaping. Parameters ---------- op : Qobj or QobjEvo Quantum operator in column-stacked-vector form. This must have a type of 'operator-ket'. Returns ------- Qobj or QobjEvo The same object, but re-cast into "standard" operator form. The output is the same type as the passed object. """ if not op.isoperket: raise TypeError("only defined for operator-kets") if op.superrep != "super": raise TypeError("only defined for operator-kets in super format") dims = op.dims[0] return Qobj(unstack_columns(op.data, (np.prod(dims[0]), np.prod(dims[1]))), dims=dims, copy=False) QobjOrArray = TypeVar("QobjOrArray", Qobj, np.ndarray) def stack_columns(matrix: QobjOrArray) -> QobjOrArray: """ Stack the columns in a data-layer type, useful for converting an operator into a superoperator representation. """ if not isinstance(matrix, (_data.Data, np.ndarray)): raise TypeError( "input " + repr(type(matrix)) + " is not data-layer type" ) if isinstance(matrix, np.ndarray): return matrix.ravel('F')[:, None] return _data.column_stack(matrix) def unstack_columns( vector: QobjOrArray, shape: tuple[int, int] = None, ) -> QobjOrArray: """ Unstack the columns in a data-layer type back into a 2D shape, useful for converting an operator in vector form back into a regular operator. If `shape` is not passed, the output operator will be assumed to be square. """ if not isinstance(vector, (_data.Data, np.ndarray)): raise TypeError( "input " + repr(type(vector)) + " is not data-layer type" ) if ( (isinstance(vector, _data.Data) and vector.shape[1] != 1) or (isinstance(vector, np.ndarray) and ((vector.ndim == 2 and vector.shape[1] != 1) or vector.ndim > 2)) ): raise TypeError("input is not a single column") if shape is None: n = int(np.sqrt(vector.shape[0])) if n * n != vector.shape[0]: raise ValueError( "input cannot be made square, but no specific shape given" ) shape = (n, n) if isinstance(vector, np.ndarray): return vector.reshape(shape, order='F') return _data.column_unstack(vector, shape[0]) def unstacked_index(size, index): """ Convert an index into a column-stacked square operator with `size` rows and columns, into a pair of indices into the unstacked operator. """ return index % size, index // size def stacked_index(size, row, col): """ Convert a pair of indices into a square operator of `size` into a single index into the column-stacked version of the operator. """ return row + size*col AnyQobj = TypeVar("AnyQobj", Qobj, QobjEvo) @_map_over_compound_operators def spost(A: AnyQobj) -> AnyQobj: """ Superoperator formed from post-multiplication by operator A Parameters ---------- A : Qobj or QobjEvo Quantum operator for post multiplication. Returns ------- super : Qobj or QobjEvo Superoperator formed from input qauntum object. """ if not A.isoper: raise TypeError('Input is not a quantum operator') data = _data.kron_transpose(A.data, _data.identity_like(A.data)) return Qobj(data, dims=[A._dims, A._dims], superrep='super', isherm=A._isherm, copy=False) @_map_over_compound_operators def spre(A: AnyQobj) -> AnyQobj: """Superoperator formed from pre-multiplication by operator A. Parameters ---------- A : Qobj or QobjEvo Quantum operator for pre-multiplication. Returns ------- super :Qobj or QobjEvo Superoperator formed from input quantum object. """ if not A.isoper: raise TypeError('Input is not a quantum operator') data = _data.kron(_data.identity_like(A.data), A.data) return Qobj(data, dims=[A._dims, A._dims], superrep='super', isherm=A._isherm, copy=False) def _drop_projected_dims(dims): """ Eliminate subsystems that has been collapsed to only one state due to a projection. """ return [d for d in dims if d != 1] @overload def sprepost(A: Qobj, B: Qobj) -> Qobj: ... @overload def sprepost(A: Qobj | QobjEvo, B: Qobj | QobjEvo) -> QobjEvo: ... def sprepost(A, B): """ Superoperator formed from pre-multiplication by A and post-multiplication by B. Parameters ---------- A : Qobj or QobjEvo Quantum operator for pre-multiplication. B : Qobj or QobjEvo Quantum operator for post-multiplication. Returns ------- super : Qobj or QobjEvo Superoperator formed from input quantum objects. """ # To avoid circular dependencies from .cy.qobjevo import QobjEvo if (isinstance(A, QobjEvo) or isinstance(B, QobjEvo)): return spre(A) * spost(B) dims = [[_drop_projected_dims(A.dims[0]), _drop_projected_dims(B.dims[1])], [_drop_projected_dims(A.dims[1]), _drop_projected_dims(B.dims[0])]] return Qobj(_data.kron_transpose(B.data, A.data), dims=dims, superrep='super', isherm=A._isherm and B._isherm, copy=False) def _to_super_of_tensor(q_oper): """ Transform a superoperator composed of multiple space into a superoperator over a composite spaces. """ msg = "Reshuffling is only supported for square operators." if not q_oper._dims.issuper: raise TypeError("Reshuffling is only supported on type='super' " "or type='operator-ket'.") if q_oper.isoper and not q_oper._dims.issquare: raise NotImplementedError(msg) dims = q_oper._dims[0] if isinstance(dims, SuperSpace): return q_oper.copy() perm_idxs = [[], []] if isinstance(dims, Compound): shift = 0 for space in dims.spaces: if not isinstance(space, SuperSpace) or not space.oper.issquare: raise NotImplementedError(msg) space_dims = space.oper.to_ if type(space_dims) is Space: perm_idxs[0] += [shift] perm_idxs[1] += [shift + 1] shift += 2 elif isinstance(space_dims, Compound): N = len(space_dims.spaces) perm_idxs[0] += [shift + i for i in range(N)] perm_idxs[1] += [shift + N + i for i in range(N)] shift += 2 * N else: # ENR space or other complex spaces raise NotImplementedError("Reshuffling with non standard space" "is not supported.") return q_oper.permute(perm_idxs) def _to_tensor_of_super(q_oper): """ Transform a superoperator composed of multiple space into a tensor of superoperator on each spaces. """ msg = "Reshuffling is only supported for square operators." if not q_oper._dims[0].issuper: raise TypeError("Reshuffling is only supported on type='super' " "or type='operator-ket'.") dims = q_oper._dims[0] perm_idxs = [] if isinstance(dims, Compound): shift = 0 for space in dims.spaces: if not isinstance(space, SuperSpace) or not space.oper.issquare: raise TypeError(msg) space_dims = space.oper.to_ if type(space_dims) is Space: perm_idxs += [[shift], [shift + 1]] shift += 2 elif isinstance(space_dims, Compound): N = len(space_dims.spaces) idxs = range(0, N * 2, 2) perm_idxs += [[i + shift] for i in idxs] perm_idxs += [[i + shift + 1] for i in idxs] shift += N * 2 else: # ENR space or other complex spaces raise NotImplementedError("Reshuffling with non standard space" "is not supported.") elif isinstance(dims, SuperSpace): if isinstance(dims.oper.to_, Compound): step = len(dims.oper.to_.spaces) perm_idxs = sum([[[i], [i+step]] for i in range(step)], []) else: return q_oper return q_oper.permute(perm_idxs) def reshuffle(q_oper: Qobj) -> Qobj: """ Column-reshuffles a super operator or a operator-ket Qobj. """ if q_oper.type not in ["super", "operator-ket"]: raise TypeError("Reshuffling is only supported on type='super' " "or type='operator-ket'.") if isinstance(q_oper._dims[0], Compound): return _to_super_of_tensor(q_oper) else: return _to_tensor_of_super(q_oper) qutip-5.1.1/qutip/core/tensor.py000066400000000000000000000406311474175217300166550ustar00rootroot00000000000000""" Module for the creation of composite quantum objects via the tensor product. """ __all__ = [ 'tensor', 'super_tensor', 'composite', 'tensor_swap', 'tensor_contract', 'expand_operator' ] import numpy as np from functools import partial from typing import TypeVar, overload from .operators import qeye from .qobj import Qobj from .cy.qobjevo import QobjEvo from .superoperator import operator_to_vector, reshuffle from .dimensions import ( flatten, enumerate_flat, unflatten, deep_remove, dims_to_tensor_shape, dims_idxs_to_tensor_idxs ) from . import data as _data from .. import settings from ..typing import LayerType class _reverse_partial_tensor: """ Picklable lambda op: tensor(op, right) """ def __init__(self, right): self.right = right def __call__(self, op): return tensor(op, self.right) @overload def tensor(*args: Qobj) -> Qobj: ... @overload def tensor(*args: Qobj | QobjEvo) -> QobjEvo: ... def tensor(*args: Qobj | QobjEvo) -> Qobj | QobjEvo: """Calculates the tensor product of input operators. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects for tensor product. Returns ------- obj : qobj A composite quantum object. Examples -------- >>> tensor([sigmax(), sigmax()]) # doctest: +SKIP Quantum object: dims = [[2, 2], [2, 2]], \ shape = [4, 4], type = oper, isHerm = True Qobj data = [[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j] [ 0.+0.j 0.+0.j 1.+0.j 0.+0.j] [ 0.+0.j 1.+0.j 0.+0.j 0.+0.j] [ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]] """ from .cy.qobjevo import QobjEvo if not args: raise TypeError("Requires at least one input argument") if len(args) == 1 and isinstance(args[0], (Qobj, QobjEvo)): return args[0].copy() if len(args) == 1: try: args = tuple(args[0]) except TypeError: raise TypeError("requires Qobj or QobjEvo operands") from None if not all(isinstance(q, (Qobj, QobjEvo)) for q in args): raise TypeError("requires Qobj or QobjEvo operands") if any(isinstance(q, QobjEvo) for q in args): # First make tensor from pairs only if len(args) >= 3: return tensor(args[0], tensor(args[1:])) left, right = args if isinstance(left, Qobj): return right.linear_map(partial(tensor, left)) if isinstance(right, Qobj): return left.linear_map(_reverse_partial_tensor(right)) left_t = left.linear_map(_reverse_partial_tensor(qeye(right.dims[0]))) right_t = right.linear_map(partial(tensor, qeye(left.dims[1]))) return left_t @ right_t if not all(q.superrep == args[0].superrep for q in args[1:]): raise TypeError("".join([ "In tensor products of superroperators,", " all must have the same representation" ])) isherm = args[0]._isherm isunitary = args[0]._isunitary out_data = args[0].data dims_l = [args[0]._dims[0]] dims_r = [args[0]._dims[1]] for arg in args[1:]: out_data = _data.kron(out_data, arg.data) # If both _are_ Hermitian and/or unitary, then so is the output, but if # both _aren't_, then output still can be. isherm = (isherm and arg._isherm) or None isunitary = (isunitary and arg._isunitary) or None dims_l.append(arg._dims[0]) dims_r.append(arg._dims[1]) return Qobj(out_data, dims=[dims_l, dims_r], isherm=isherm, isunitary=isunitary, copy=False) @overload def super_tensor(*args: Qobj) -> Qobj: ... @overload def super_tensor(*args: Qobj | QobjEvo) -> QobjEvo: ... def super_tensor(*args: Qobj | QobjEvo) -> Qobj | QobjEvo: """ Calculate the tensor product of input superoperators, by tensoring together the underlying Hilbert spaces on which each vectorized operator acts. Parameters ---------- args : array_like ``list`` or ``array`` of quantum objects with ``type="super"``. Returns ------- obj : qobj A composite quantum object. """ if isinstance(args[0], list): args = args[0] # Check if we're tensoring vectors or superoperators. if all(arg.issuper for arg in args): if not all(arg.superrep == "super" for arg in args): raise TypeError( "super_tensor on type='super' is only implemented for " "superrep='super'." ) # Reshuffle the superoperators. shuffled_ops = list(map(reshuffle, args)) # Tensor the result. shuffled_tensor = tensor(shuffled_ops) # Unshuffle and return. out = reshuffle(shuffled_tensor) out.superrep = args[0].superrep return out if all(arg.isoperket for arg in args): # Reshuffle the superoperators. shuffled_ops = list(map(reshuffle, args)) # Tensor the result. shuffled_tensor = tensor(shuffled_ops) # Unshuffle and return. out = reshuffle(shuffled_tensor) return out if all(arg.isoperbra for arg in args): return super_tensor(*(arg.dag() for arg in args)).dag() raise TypeError( "All arguments must be the same type, " "either super, operator-ket or operator-bra." ) def _isoperlike(q): return q.isoper or q.issuper def _isketlike(q): return q.isket or q.isoperket def _isbralike(q): return q.isbra or q.isoperbra @overload def composite(*args: Qobj) -> Qobj: ... @overload def composite(*args: Qobj | QobjEvo) -> QobjEvo: ... def composite(*args): """ Given two or more operators, kets or bras, returns the Qobj corresponding to a composite system over each argument. For ordinary operators and vectors, this is the tensor product, while for superoperators and vectorized operators, this is the column-reshuffled tensor product. If a mix of Qobjs supported on Hilbert and Liouville spaces are passed in, the former are promoted. Ordinary operators are assumed to be unitaries, and are promoted using ``to_super``, while kets and bras are promoted by taking their projectors and using ``operator_to_vector(ket2dm(arg))``. """ import qutip.core.superop_reps # First step will be to ensure everything is a Qobj at all. if not all(isinstance(arg, Qobj) for arg in args): raise TypeError("All arguments must be Qobjs.") # Next, figure out if we have something oper-like (isoper or issuper), # or something ket-like (isket or isoperket). Bra-like we'll deal with # by turning things into ket-likes and back. if all(map(_isoperlike, args)): if any(arg.issuper for arg in args): # to_super will promote 'oper' and leave 'super' untouched return super_tensor(*map(qutip.core.superop_reps.to_super, args)) return tensor(*args) if all(map(_isketlike, args)): if any(arg.isoperket for arg in args): return super_tensor(*( arg if arg.isoperket else operator_to_vector(arg.proj()) for arg in args )) return tensor(*args) if all(map(_isbralike, args)): # Turn into ket-likes and recurse. return composite(*(arg.dag() for arg in args)).dag() raise TypeError("Unsupported Qobj types [{}].".format( ", ".join(arg.type for arg in args) )) def _tensor_contract_single(arr, i, j): """ Contracts a dense tensor along a single index pair. """ if arr.shape[i] != arr.shape[j]: raise ValueError("Cannot contract over indices of different length.") idxs = np.arange(arr.shape[i]) sl = tuple(slice(None, None, None) if idx not in (i, j) else idxs for idx in range(arr.ndim)) contract_at = i if j == i + 1 else 0 return np.sum(arr[sl], axis=contract_at) def _tensor_contract_dense(arr, *pairs): """ Contracts a dense tensor along one or more index pairs, keeping track of how the indices are relabeled by the removal of other indices. """ axis_idxs = list(range(arr.ndim)) for pair in pairs: # axis_idxs.index effectively evaluates the mapping from original index # labels to the labels after contraction. arr = _tensor_contract_single(arr, *map(axis_idxs.index, pair)) axis_idxs.remove(pair[0]) axis_idxs.remove(pair[1]) return arr def tensor_swap(q_oper: Qobj, *pairs: tuple[int, int]) -> Qobj: """Transposes one or more pairs of indices of a Qobj. .. note:: Note that this uses dense representations and thus should *not* be used for very large Qobjs. Parameters ---------- q_oper : Qobj Operator to swap dims. pairs : tuple One or more tuples ``(i, j)`` indicating that the ``i`` and ``j`` dimensions of the original qobj should be swapped. Returns ------- sqobj : Qobj The original Qobj with all named index pairs swapped with each other """ dims = q_oper.dims tensor_pairs = dims_idxs_to_tensor_idxs(dims, pairs) data = q_oper.full() # Reshape into tensor indices data = data.reshape(dims_to_tensor_shape(dims)) # Now permute the dims list so we know how to get back. flat_dims = flatten(dims) perm = list(range(len(flat_dims))) for i, j in pairs: flat_dims[i], flat_dims[j] = flat_dims[j], flat_dims[i] for i, j in tensor_pairs: perm[i], perm[j] = perm[j], perm[i] dims = unflatten(flat_dims, enumerate_flat(dims)) # Next, permute the actual indices of the dense tensor. data = data.transpose(perm) # Reshape back, using the left and right of dims. data = data.reshape(list(map(np.prod, dims))) return Qobj(data, dims=dims, superrep=q_oper.superrep, copy=False) def tensor_contract(qobj: Qobj, *pairs: tuple[int, int]) -> Qobj: """Contracts a qobj along one or more index pairs. .. note:: Note that this uses dense representations and thus should *not* be used for very large Qobjs. Parameters ---------- qobj: Qobj Operator to contract subspaces on. pairs : tuple One or more tuples ``(i, j)`` indicating that the ``i`` and ``j`` dimensions of the original qobj should be contracted. Returns ------- cqobj : Qobj The original Qobj with all named index pairs contracted away. """ # Record and label the original dims. dims = qobj.dims dims_idxs = enumerate_flat(dims) tensor_dims = dims_to_tensor_shape(dims) # Convert to dense first, since sparse won't support the reshaping we need. qtens = qobj.data.to_array() # Reshape by the flattened dims. qtens = qtens.reshape(tensor_dims) # Contract out the indices from the flattened object. # Note that we need to feed pairs through dims_idxs_to_tensor_idxs # to ensure that we are contracting the right indices. qtens = _tensor_contract_dense(qtens, *dims_idxs_to_tensor_idxs(dims, pairs)) # Remove the contracted indexes from dims so we know how to # reshape back. # This concerns dims, and not the tensor indices, so we need # to make sure to use the original dims indices and not the ones # generated by dims_to_* functions. contracted_idxs = deep_remove(dims_idxs, *flatten(list(map(list, pairs)))) contracted_dims = unflatten(flatten(dims), contracted_idxs) # We don't need to check for tensor idxs versus dims idxs here, # as column- versus row-stacking will never move an index for the # vectorized operator spaces all the way from the left to the right. l_mtx_dims, r_mtx_dims = map(np.prod, map(flatten, contracted_dims)) # Reshape back into a 2D matrix. qmtx = qtens.reshape((l_mtx_dims, r_mtx_dims)) # Return back as a qobj. return Qobj(qmtx, dims=contracted_dims, superrep=qobj.superrep, copy=False) def _check_oper_dims(oper, dims=None, targets=None): """ Check if the given operator is valid. Parameters ---------- oper : :class:`.Qobj` The quantum object to be checked. dims : list, optional A list of integer for the dimension of each composite system. e.g ``[2, 2, 2, 2, 2]`` for 5 qubits system. targets : int or list of int, optional The indices of subspace that are acted on. """ # if operator matches N if not isinstance(oper, Qobj) or oper.dims[0] != oper.dims[1]: raise ValueError( "The operator is not an " "Qobj with the same input and output dimensions.") # if operator dims matches the target dims if dims is not None and targets is not None: targ_dims = [dims[t] for t in targets] if oper.dims[0] != targ_dims: raise ValueError( "The operator dims {} do not match " "the target dims {}.".format( oper.dims[0], targ_dims)) def _targets_to_list(targets, oper=None, N=None): """ transform targets to a list and check validity. Parameters ---------- targets : int or list of int The indices of subspace that are acted on. oper : :class:`.Qobj`, optional An operator, the type of the :class:`.Qobj` has to be an operator and the dimension matches the tensored qubit Hilbert space e.g. dims = ``[[2, 2, 2], [2, 2, 2]]`` N : int, optional The number of subspace in the system. """ # if targets is a list of integer if targets is None: targets = list(range(len(oper.dims[0]))) if not hasattr(targets, '__iter__'): targets = [targets] if not all([isinstance(t, int) for t in targets]): raise TypeError( "targets should be " "an integer or a list of integer") # if targets has correct length if oper is not None: req_num = len(oper.dims[0]) if len(targets) != req_num: raise ValueError( "The given operator needs {} " "target qutbis, " "but {} given.".format( req_num, len(targets))) # if targets is smaller than N if N is not None: if not all([t < N for t in targets]): raise ValueError("Targets must be smaller than N={}.".format(N)) return targets QobjOrQobjEvo = TypeVar("QobjOrQobjEvo", Qobj, QobjEvo) def expand_operator( oper: QobjOrQobjEvo, dims: list[int], targets: int, dtype: LayerType = None ) -> QobjOrQobjEvo: """ Expand an operator to one that acts on a system with desired dimensions. e.g. ``` expand_operator(oper, [2, 3, 4, 5], 2) == tensor(qeye(2), qeye(3), oper, qeye(5)) expand_operator(tensor(oper1, oper2), [2, 3, 4, 5], [2, 0]) == tensor(oper2, qeye(3), oper1, qeye(5)) ``` Parameters ---------- oper : :class:`.Qobj` An operator that act on the subsystem, has to be an operator and the dimension matches the tensored dims Hilbert space e.g. oper.dims = ``[[2, 3], [2, 3]]`` dims : list A list of integer for the dimension of each composite system. E.g ``[2, 3, 2, 3, 4]``. targets : int or list of int The indices of subspace that are acted on. dtype : str, optional Data type of the output :class:`.Qobj`. By default it uses the data type specified in settings. If no data type is specified in settings it uses the ``CSR`` data type. Returns ------- expanded_oper : :class:`.Qobj` The expanded operator acting on a system with the desired dimension. """ from .operators import identity dtype = dtype or settings.core["default_dtype"] or _data.CSR oper = oper.to(dtype) N = len(dims) targets = _targets_to_list(targets, oper=oper, N=N) _check_oper_dims(oper, dims=dims, targets=targets) # Generate the correct order for permutation, # eg. if N = 5, targets = [3,0], the order is [1,2,3,0,4]. # If the operator is cnot, # this order means that the 3rd qubit controls the 0th qubit. new_order = [0] * N for i, t in enumerate(targets): new_order[t] = i # allocate the rest qutbits (not targets) to the empty # position in new_order rest_pos = [q for q in list(range(N)) if q not in targets] rest_qubits = list(range(len(targets), N)) for i, ind in enumerate(rest_pos): new_order[ind] = rest_qubits[i] id_list = [identity(dims[i]) for i in rest_pos] return tensor([oper] + id_list).permute(new_order) qutip-5.1.1/qutip/distributions.py000066400000000000000000000401711474175217300173140ustar00rootroot00000000000000""" This module provides classes and functions for working with spatial distributions, such as Wigner distributions, etc. .. note:: Experimental. """ __all__ = ['Distribution', 'WignerDistribution', 'QDistribution', 'TwoModeQuadratureCorrelation', 'HarmonicOscillatorWaveFunction', 'HarmonicOscillatorProbabilityFunction'] import numpy as np from numpy import pi, exp, sqrt from scipy.special import hermite, factorial from . import isket, ket2dm, state_number_index from .wigner import wigner, qfunc from ._distributions import psi_n_single_fock_multiple_position_complex try: import matplotlib as mpl import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D except: pass class Distribution: """A class for representation spatial distribution functions. The Distribution class can be used to prepresent spatial distribution functions of arbitray dimension (although only 1D and 2D distributions are used so far). It is indented as a base class for specific distribution function, and provide implementation of basic functions that are shared among all Distribution functions, such as visualization, calculating marginal distributions, etc. Parameters ---------- data : array_like Data for the distribution. The dimensions must match the lengths of the coordinate arrays in xvecs. xvecs : list List of arrays that spans the space for each coordinate. xlabels : list List of labels for each coordinate. """ def __init__(self, data=None, xvecs=[], xlabels=[]): self.data = data self.xvecs = xvecs self.xlabels = xlabels def visualize(self, fig=None, ax=None, figsize=(8, 6), colorbar=True, cmap=None, style="colormap", show_xlabel=True, show_ylabel=True): """ Visualize the data of the distribution in 1D or 2D, depending on the dimensionality of the underlaying distribution. Parameters: fig : matplotlib Figure instance If given, use this figure instance for the visualization, ax : matplotlib Axes instance If given, render the visualization using this axis instance. figsize : tuple Size of the new Figure instance, if one needs to be created. colorbar: Bool Whether or not the colorbar (in 2D visualization) should be used. cmap: matplotlib colormap instance If given, use this colormap for 2D visualizations. style : string Type of visualization: 'colormap' (default) or 'surface'. Returns ------- fig, ax : tuple A tuple of matplotlib figure and axes instances. """ n = len(self.xvecs) if n == 2: if style == "colormap": return self.visualize_2d_colormap(fig=fig, ax=ax, figsize=figsize, colorbar=colorbar, cmap=cmap, show_xlabel=show_xlabel, show_ylabel=show_ylabel) else: return self.visualize_2d_surface(fig=fig, ax=ax, figsize=figsize, colorbar=colorbar, cmap=cmap, show_xlabel=show_xlabel, show_ylabel=show_ylabel) elif n == 1: return self.visualize_1d(fig=fig, ax=ax, figsize=figsize, show_xlabel=show_xlabel, show_ylabel=show_ylabel) else: raise NotImplementedError("Distribution visualization in " + "%d dimensions is not implemented." % n) def visualize_2d_colormap(self, fig=None, ax=None, figsize=(8, 6), colorbar=True, cmap=None, show_xlabel=True, show_ylabel=True): if not fig and not ax: fig, ax = plt.subplots(1, 1, figsize=figsize) if cmap is None: cmap = mpl.colormaps['RdBu'] lim = abs(self.data.real).max() cf = ax.contourf(self.xvecs[0], self.xvecs[1], self.data.real, 100, norm=mpl.colors.Normalize(-lim, lim), cmap=cmap) if show_xlabel: ax.set_xlabel(self.xlabels[0], fontsize=12) if show_ylabel: ax.set_ylabel(self.xlabels[1], fontsize=12) if colorbar: cb = fig.colorbar(cf, ax=ax) return fig, ax def visualize_2d_surface(self, fig=None, ax=None, figsize=(8, 6), colorbar=True, cmap=None, show_xlabel=True, show_ylabel=True): if not fig and not ax: fig = plt.figure(figsize=figsize) ax = Axes3D(fig, azim=-62, elev=25) if cmap is None: cmap = mpl.colormaps['RdBu'] lim = abs(self.data.real).max() X, Y = np.meshgrid(self.xvecs[0], self.xvecs[1]) s = ax.plot_surface(X, Y, self.data.real, norm=mpl.colors.Normalize(-lim, lim), rstride=5, cstride=5, cmap=cmap, lw=0.1) if show_xlabel: ax.set_xlabel(self.xlabels[0], fontsize=12) if show_ylabel: ax.set_ylabel(self.xlabels[1], fontsize=12) if colorbar: cb = fig.colorbar(s, ax=ax, shrink=0.5) return fig, ax def visualize_1d(self, fig=None, ax=None, figsize=(8, 6), show_xlabel=True, show_ylabel=True): if not fig and not ax: fig, ax = plt.subplots(1, 1, figsize=figsize) p = ax.plot(self.xvecs[0], self.data.real) if show_xlabel: ax.set_xlabel(self.xlabels[0], fontsize=12) if show_ylabel: ax.set_ylabel("Marginal distribution", fontsize=12) return fig, ax def marginal(self, dim=0): """ Calculate the marginal distribution function along the dimension `dim`. Return a new Distribution instance describing this reduced- dimensionality distribution. Parameters ---------- dim : int The dimension (coordinate index) along which to obtain the marginal distribution. Returns ------- d : Distributions A new instances of Distribution that describes the marginal distribution. """ return Distribution(data=self.data.mean(axis=dim), xvecs=[self.xvecs[dim]], xlabels=[self.xlabels[dim]]) def project(self, dim=0): """ Calculate the projection (max value) distribution function along the dimension `dim`. Return a new Distribution instance describing this reduced-dimensionality distribution. Parameters ---------- dim : int The dimension (coordinate index) along which to obtain the projected distribution. Returns ------- d : Distributions A new instances of Distribution that describes the projection. """ return Distribution(data=self.data.max(axis=dim), xvecs=[self.xvecs[dim]], xlabels=[self.xlabels[dim]]) class WignerDistribution(Distribution): def __init__(self, rho=None, extent=[[-5, 5], [-5, 5]], steps=250): self.xvecs = [np.linspace(extent[0][0], extent[0][1], steps), np.linspace(extent[1][0], extent[1][1], steps)] self.xlabels = [r'$\rm{Re}(\alpha)$', r'$\rm{Im}(\alpha)$'] if rho: self.update(rho) def update(self, rho): self.data = wigner(rho, self.xvecs[0], self.xvecs[1]) class QDistribution(Distribution): def __init__(self, rho=None, extent=[[-5, 5], [-5, 5]], steps=250): self.xvecs = [np.linspace(extent[0][0], extent[0][1], steps), np.linspace(extent[1][0], extent[1][1], steps)] self.xlabels = [r'$\rm{Re}(\alpha)$', r'$\rm{Im}(\alpha)$'] if rho: self.update(rho) def update(self, rho): self.data = qfunc(rho, self.xvecs[0], self.xvecs[1]) class TwoModeQuadratureCorrelation(Distribution): def __init__(self, state=None, theta1=0.0, theta2=0.0, extent=[[-5, 5], [-5, 5]], steps=250): self.xvecs = [np.linspace(extent[0][0], extent[0][1], steps), np.linspace(extent[1][0], extent[1][1], steps)] self.xlabels = [r'$X_1(\theta_1)$', r'$X_2(\theta_2)$'] self.theta1 = theta1 self.theta2 = theta2 if state: self.update(state) def update(self, state): """ calculate probability distribution for quadrature measurement outcomes given a two-mode wavefunction or density matrix """ if isket(state): self.update_psi(state) else: self.update_rho(state) def update_psi(self, psi): """ calculate probability distribution for quadrature measurement outcomes given a two-mode wavefunction """ X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1]) p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex) N = psi.dims[0][0] for n1 in range(N): kn1 = exp(-1j * self.theta1 * n1) / \ sqrt(sqrt(pi) * 2 ** n1 * factorial(n1)) * \ exp(-X1 ** 2 / 2.0) * np.polyval(hermite(n1), X1) for n2 in range(N): kn2 = exp(-1j * self.theta2 * n2) / \ sqrt(sqrt(pi) * 2 ** n2 * factorial(n2)) * \ exp(-X2 ** 2 / 2.0) * np.polyval(hermite(n2), X2) i = state_number_index([N, N], [n1, n2]) p += kn1 * kn2 * psi.full()[i, 0] self.data = abs(p) ** 2 def update_rho(self, rho): """ calculate probability distribution for quadrature measurement outcomes given a two-mode density matrix """ X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1]) p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex) N = rho.dims[0][0] M1 = np.zeros( (N, N, len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex) M2 = np.zeros( (N, N, len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex) for m in range(N): for n in range(N): M1[m, n] = exp(-1j * self.theta1 * (m - n)) / \ sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \ exp(-X1 ** 2) * np.polyval( hermite(m), X1) * np.polyval(hermite(n), X1) M2[m, n] = exp(-1j * self.theta2 * (m - n)) / \ sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \ exp(-X2 ** 2) * np.polyval( hermite(m), X2) * np.polyval(hermite(n), X2) for n1 in range(N): for n2 in range(N): i = state_number_index([N, N], [n1, n2]) for p1 in range(N): for p2 in range(N): j = state_number_index([N, N], [p1, p2]) p += M1[n1, p1] * M2[n2, p2] * rho.full()[i, j] self.data = p class HarmonicOscillatorWaveFunction(Distribution): """Calculates and represents the wave function of a quantum harmonic oscillator. The `HarmonicOscillatorWaveFunction` class computes the spatial distribution of the wave function for a quantum harmonic oscillator given a set of state coefficients (`psi`). By extending the `Distribution` base class, this class provides specialized attributes and methods tailored for modeling the harmonic oscillator's wave function.This implementation leverages the Cython function `psi_n_single_fock_multiple_position_complex`from the `_distributions.pyx` module to efficiently compute the wave function's contribution for each Fock state across spatial coordinates using an optimized recurrence relation. Parameters ---------- psi : array_like, optional Coefficients for each harmonic oscillator state (Fock state) to calculate the wave function. Defaults to None, in which case the wave function is not initialized until `update` is called. omega : float, optional The angular frequency of the harmonic oscillator. Defaults to 1.0. extent : list, optional A list with two elements that defines the range of the spatial dimension for calculating the wave function. Defaults to [-5, 5]. steps : int, optional Number of points used to discretize the spatial range defined by `extent`. Higher values increase resolution but may slow down computations. Defaults to 250. Attributes ---------- xvecs : list of arrays A list containing arrays that represent the spatial coordinates over which the wave function is calculated. xlabels : list of str A list of labels for each spatial coordinate, in this case with one element representing the x-axis. omega : float The angular frequency of the harmonic oscillator, stored as an attribute for use in wave function calculations. data : np.ndarray of complex numbers The calculated wave function values across the spatial range. Populated when `update` is called. Methods ------- update(psi) Calculates and updates the wave function values for the harmonic oscillator based on the provided state coefficients, `psi`. References ---------- - PĂŠrez-JordĂĄ, J. M. (2017). On the recursive solution of the quantum harmonic oscillator. *European Journal of Physics*, 39(1), 015402. doi:10.1088/1361-6404/aa9584 - *Fast-Wave*: High-performance wave function calculations for quantum harmonic oscillators.Available at: https://github.com/fobos123deimos/fast-wave """ def __init__(self, psi=None, omega=1.0, extent=[-5, 5], steps=250): self.xvecs = [np.linspace(extent[0], extent[1], steps)] self.xlabels = [r'$x$'] self.omega = omega if psi: self.update(psi) def update(self, psi): """ Calculate the wavefunction for the given state of an harmonic oscillator """ self.data = np.zeros(len(self.xvecs[0]), dtype=complex) N = psi.shape[0] for n in range(N): self.data += ( psi_n_single_fock_multiple_position_complex( n, self.xvecs[0].astype(complex) ) * psi[n, 0] ) self.data *= pow(self.omega, 0.25) class HarmonicOscillatorProbabilityFunction(Distribution): def __init__(self, rho=None, omega=1.0, extent=[-5, 5], steps=250): self.xvecs = [np.linspace(extent[0], extent[1], steps)] self.xlabels = [r'$x$'] self.omega = omega if rho: self.update(rho) def update(self, rho): """ Calculate the probability function for the given state of an harmonic oscillator (as density matrix) """ if isket(rho): rho = ket2dm(rho) self.data = np.zeros(len(self.xvecs[0]), dtype=complex) M, N = rho.shape for m in range(M): k_m = pow(self.omega / pi, 0.25) / \ sqrt(2 ** m * factorial(m)) * \ exp(-self.xvecs[0] ** 2 / 2.0) * \ np.polyval(hermite(m), self.xvecs[0]) for n in range(N): k_n = pow(self.omega / pi, 0.25) / \ sqrt(2 ** n * factorial(n)) * \ exp(-self.xvecs[0] ** 2 / 2.0) * \ np.polyval(hermite(n), self.xvecs[0]) self.data += np.conjugate(k_n) * k_m * rho.full()[m, n] qutip-5.1.1/qutip/entropy.py000066400000000000000000000251421474175217300161130ustar00rootroot00000000000000__all__ = ['entropy_vn', 'entropy_linear', 'entropy_mutual', 'negativity', 'concurrence', 'entropy_conditional', 'entangling_power', 'entropy_relative'] from .core.numpy_backend import np from .partial_transpose import partial_transpose from . import (ptrace, tensor, sigmay, ket2dm, expand_operator) from .core import data as _data def entropy_vn(rho, base=np.e, sparse=False): """ Von-Neumann entropy of density matrix Parameters ---------- rho : qobj Density matrix. base : {e, 2}, default: e Base of logarithm. sparse : bool, default: False Use sparse eigensolver. Returns ------- entropy : float Von-Neumann entropy of `rho`. Examples -------- >>> rho=0.5*fock_dm(2,0)+0.5*fock_dm(2,1) >>> entropy_vn(rho,2) 1.0 """ if rho.type == 'ket' or rho.type == 'bra': rho = ket2dm(rho) vals = rho.eigenenergies(sparse=sparse) threshold = 1e-17 nzvals = np.where(vals < threshold, threshold, vals) if base == 2: logvals = np.log2(nzvals) elif base == np.e: logvals = np.log(nzvals) else: raise ValueError("Base must be 2 or e.") return np.real(-sum(nzvals * logvals)) def entropy_linear(rho): """ Linear entropy of a density matrix. Parameters ---------- rho : qobj sensity matrix or ket/bra vector. Returns ------- entropy : float Linear entropy of rho. Examples -------- >>> rho=0.5*fock_dm(2,0)+0.5*fock_dm(2,1) >>> entropy_linear(rho) 0.5 """ if rho.type == 'ket' or rho.type == 'bra': rho = ket2dm(rho) return np.real(1.0 - (rho ** 2).tr()) def concurrence(rho): """ Calculate the concurrence entanglement measure for a two-qubit state. Parameters ---------- state : qobj Ket, bra, or density matrix for a two-qubit state. Returns ------- concur : float Concurrence References ---------- .. [1] `https://en.wikipedia.org/wiki/Concurrence_(quantum_computing)` """ if rho.isket and rho.dims != [[2, 2], [1, 1]]: raise Exception("Ket must be tensor product of two qubits.") elif rho.isbra and rho.dims != [[1, 1], [2, 2]]: raise Exception("Bra must be tensor product of two qubits.") elif rho.isoper and rho.dims != [[2, 2], [2, 2]]: raise Exception("Density matrix must be tensor product of two qubits.") if rho.isket or rho.isbra: rho = ket2dm(rho) sysy = tensor(sigmay(), sigmay()) rho_tilde = (rho * sysy) * (rho.conj() * sysy) evals = rho_tilde.eigenenergies() # abs to avoid problems with sqrt for very small negative numbers evals = abs(np.sort(np.real(evals))) sqrt_evals = np.sqrt(evals) lsum = sqrt_evals[3] - sqrt_evals[2] - sqrt_evals[1] - sqrt_evals[0] return np.maximum(0, lsum) def negativity(rho, subsys, method='tracenorm', logarithmic=False): """ Compute the negativity for a multipartite quantum system described by the density matrix rho. The subsys argument is an index that indicates which system to compute the negativity for. .. note:: Experimental. """ if rho.isket or rho.isbra: rho = ket2dm(rho) mask = [idx == subsys for idx, n in enumerate(rho.dims[0])] rho_pt = partial_transpose(rho, mask) if method == 'tracenorm': N = ((rho_pt.dag() * rho_pt).sqrtm().tr().real - 1)/2.0 elif method == 'eigenvalues': l = rho_pt.eigenenergies() N = ((abs(l)-l)/2).sum() else: raise ValueError("Unknown method %s" % method) # Return the negativity value (or its logarithm if specified) if logarithmic: return np.log2(2 * N + 1) else: return N def entropy_mutual(rho, selA, selB, base=np.e, sparse=False): """ Calculates the mutual information S(A:B) between selection components of a system density matrix. Parameters ---------- rho : qobj Density matrix for composite quantum systems selA : int/list `int` or `list` of first selected density matrix components. selB : int/list `int` or `list` of second selected density matrix components. base : {e, 2}, default: e Base of logarithm. sparse : bool, default: False Use sparse eigensolver. Returns ------- ent_mut : float Mutual information between selected components. """ if isinstance(selA, int): selA = [selA] if isinstance(selB, int): selB = [selB] if rho.type != 'oper': raise TypeError("Input must be a density matrix.") if (len(selA) + len(selB)) != len(rho.dims[0]): raise TypeError("Number of selected components must match " + "total number.") rhoA = ptrace(rho, selA) rhoB = ptrace(rho, selB) out = (entropy_vn(rhoA, base, sparse=sparse) + entropy_vn(rhoB, base, sparse=sparse) - entropy_vn(rho, base, sparse=sparse)) return out def entropy_relative(rho, sigma, base=np.e, sparse=False, tol=1e-12): """ Calculates the relative entropy S(rho||sigma) between two density matrices. Parameters ---------- rho : :class:`.Qobj` First density matrix (or ket which will be converted to a density matrix). sigma : :class:`.Qobj` Second density matrix (or ket which will be converted to a density matrix). base : {e, 2}, default: e Base of logarithm. Defaults to e. sparse : bool, default: False Flag to use sparse solver when determining the eigenvectors of the density matrices. Defaults to False. tol : float, default: 1e-12 Tolerance to use to detect 0 eigenvalues or dot producted between eigenvectors. Defaults to 1e-12. Returns ------- rel_ent : float Value of relative entropy. Guaranteed to be greater than zero and should equal zero only when rho and sigma are identical. Examples -------- First we define two density matrices: >>> rho = qutip.ket2dm(qutip.ket("00")) >>> sigma = rho + qutip.ket2dm(qutip.ket("01")) >>> sigma = sigma.unit() Then we calculate their relative entropy using base 2 (i.e. ``log2``) and base e (i.e. ``log``). >>> qutip.entropy_relative(rho, sigma, base=2) 1.0 >>> qutip.entropy_relative(rho, sigma) 0.6931471805599453 References ---------- See Nielsen & Chuang, "Quantum Computation and Quantum Information", Section 11.3.1, pg. 511 for a detailed explanation of quantum relative entropy. """ if rho.isket: rho = ket2dm(rho) if sigma.isket: sigma = ket2dm(sigma) if not rho.isoper or not sigma.isoper: raise TypeError("Inputs must be density matrices.") if rho.dims != sigma.dims: raise ValueError("Inputs must have the same shape and dims.") if base == 2: log_base = np.log2 elif base == np.e: log_base = np.log else: raise ValueError("Base must be 2 or e.") # S(rho || sigma) = sum_i(p_i log p_i) - sum_ij(p_i P_ij log q_i) # # S is +inf if the kernel of sigma (i.e. svecs[svals == 0]) has non-trivial # intersection with the support of rho (i.e. rvecs[rvals != 0]). rvals, rvecs = _data.eigs(rho.data, rho.isherm, True) rvecs = rvecs.to_array().T if any(abs(np.imag(rvals)) >= tol): raise ValueError("Input rho has non-real eigenvalues.") rvals = np.real(rvals) svals, svecs = _data.eigs(sigma.data, sigma.isherm, True) svecs = svecs.to_array().T if any(abs(np.imag(svals)) >= tol): raise ValueError("Input sigma has non-real eigenvalues.") svals = np.real(svals) # Calculate inner products of eigenvectors and return +inf if kernel # of sigma overlaps with support of rho. P = abs(np.inner(rvecs, np.conj(svecs))) ** 2 if (rvals >= tol) @ (P >= tol) @ (svals < tol): return np.inf # Avoid -inf from log(0) -- these terms will be multiplied by zero later # anyway svals[abs(svals) < tol] = 1 nzrvals = rvals[abs(rvals) >= tol] # Calculate S S = nzrvals @ log_base(nzrvals) - rvals @ P @ log_base(svals) # the relative entropy is guaranteed to be >= 0, so we clamp the # calculated value to 0 to avoid small violations of the lower bound. return np.maximum(0, S) def entropy_conditional(rho, selB, base=np.e, sparse=False): """ Calculates the conditional entropy :math:`S(A|B)=S(A,B)-S(B)` of a selected density matrix component. Parameters ---------- rho : qobj Density matrix of composite object selB : int/list Selected components for density matrix B base : {e, 2}, default: e Base of logarithm. sparse : bool, default: False Use sparse eigensolver. Returns ------- ent_cond : float Value of conditional entropy """ if rho.type != 'oper': raise TypeError("Input must be density matrix.") if isinstance(selB, int): selB = [selB] B = ptrace(rho, selB) out = (entropy_vn(rho, base, sparse=sparse) - entropy_vn(B, base, sparse=sparse)) return out def participation_ratio(rho): """ Returns the effective number of states for a density matrix. The participation is unity for pure states, and maximally N, where N is the Hilbert space dimensionality, for completely mixed states. Parameters ---------- rho : qobj Density matrix Returns ------- pr : float Effective number of states in the density matrix """ if rho.type == 'ket' or rho.type == 'bra': return 1.0 else: return 1.0 / (rho ** 2).tr() def entangling_power(U): """ Calculate the entangling power of a two-qubit gate U, which is zero of nonentangling gates and 2/9 for maximally entangling gates. Parameters ---------- U : qobj Qobj instance representing a two-qubit gate. Returns ------- ep : float The entanglement power of U (real number between 0 and 2/9) References: Explorations in Quantum Computing, Colin P. Williams (Springer, 2011) """ if not U.isoper: raise Exception("U must be an operator.") if U.dims != [[2, 2], [2, 2]]: raise Exception("U must be a two-qubit gate.") from qutip.core.gates import swap swap13 = expand_operator(swap(dtype=U.dtype), [2, 2, 2, 2], [1, 3]) a = tensor(U, U).dag() * swap13 * tensor(U, U) * swap13 Uswap = swap(dtype=U.dtype) * U b = tensor(Uswap, Uswap).dag() * swap13 * tensor(Uswap, Uswap) * swap13 return 5.0/9 - 1.0/36 * (a.tr() + b.tr()).real qutip-5.1.1/qutip/fileio.py000066400000000000000000000163521474175217300156650ustar00rootroot00000000000000__all__ = ['file_data_store', 'file_data_read', 'qsave', 'qload'] import pickle import numpy as np import sys from .core import Qobj from pathlib import Path # ----------------------------------------------------------------------------- # Write matrix data to a file # def file_data_store(filename, data, numtype="complex", numformat="decimal", sep=","): """Stores a matrix of data to a file to be read by an external program. Parameters ---------- filename : str or pathlib.Path Name of data file to be stored, including extension. data: array_like Data to be written to file. numtype : str {'complex, 'real'}, default: 'complex' Type of numerical data. numformat : str {'decimal','exp'}, default: 'decimal' Format for written data. sep : str, default: ',' Single-character field seperator. Usually a tab, space, comma, or semicolon. """ if filename is None or data is None: raise ValueError("filename or data is unspecified") M, N = np.shape(data) f = open(filename, "w") f.write("# Generated by QuTiP: %dx%d %s matrix " % (M, N, numtype) + "in %s format ['%s' separated values].\n" % (numformat, sep)) if numtype == "complex": if numformat == "exp": for m in range(M): for n in range(N): if np.imag(data[m, n]) >= 0.0: f.write("%.10e+%.10ej" % (np.real(data[m, n]), np.imag(data[m, n]))) else: f.write("%.10e%.10ej" % (np.real(data[m, n]), np.imag(data[m, n]))) if n != N - 1: f.write(sep) f.write("\n") elif numformat == "decimal": for m in range(M): for n in range(N): if np.imag(data[m, n]) >= 0.0: f.write("%.10f+%.10fj" % (np.real(data[m, n]), np.imag(data[m, n]))) else: f.write("%.10f%.10fj" % (np.real(data[m, n]), np.imag(data[m, n]))) if n != N - 1: f.write(sep) f.write("\n") else: raise ValueError("Illegal numformat value (should be " + "'exp' or 'decimal')") elif numtype == "real": if numformat == "exp": for m in range(M): for n in range(N): f.write("%.10e" % (np.real(data[m, n]))) if n != N - 1: f.write(sep) f.write("\n") elif numformat == "decimal": for m in range(M): for n in range(N): f.write("%.10f" % (np.real(data[m, n]))) if n != N - 1: f.write(sep) f.write("\n") else: raise ValueError("Illegal numformat value (should be " + "'exp' or 'decimal')") else: raise ValueError("Illegal numtype value (should be " + "'complex' or 'real')") f.close() # ----------------------------------------------------------------------------- # Read matrix data from a file # def file_data_read(filename, sep=None): """Retrieves an array of data from the requested file. Parameters ---------- filename : str or pathlib.Path Name of file containing reqested data. sep : str, optional Seperator used to store data. Returns ------- data : array_like Data from selected file. """ if filename is None: raise ValueError("filename is unspecified") f = open(filename, "r") # # first count lines and numbers of # M = N = 0 for line in f: # skip comment lines if line[0] == '#' or line[0] == '%': continue # find delim if N == 0 and sep is None: if len(line.rstrip().split(",")) > 1: sep = "," elif len(line.rstrip().split(";")) > 1: sep = ";" elif len(line.rstrip().split(":")) > 1: sep = ":" elif len(line.rstrip().split("|")) > 1: sep = "|" elif len(line.rstrip().split()) > 1: # sepical case for a mix of white space deliminators sep = None else: raise ValueError("Unrecognized column deliminator") # split the line line_vec = line.split(sep) n = len(line_vec) if N == 0 and n > 0: N = n # check type if ("j" in line_vec[0]) or ("i" in line_vec[0]): numtype = "complex" else: numtype = "np.real" # check format if ("e" in line_vec[0]) or ("E" in line_vec[0]): numformat = "exp" else: numformat = "decimal" elif N != n: raise ValueError("Badly formatted data file: " + "unequal number of columns") M += 1 # # read data and store in a matrix # f.seek(0) if numtype == "complex": data = np.zeros((M, N), dtype="complex") m = n = 0 for line in f: # skip comment lines if line[0] == '#' or line[0] == '%': continue n = 0 for item in line.rstrip().split(sep): data[m, n] = complex(item) n += 1 m += 1 else: data = np.zeros((M, N), dtype="float") m = n = 0 for line in f: # skip comment lines if line[0] == '#' or line[0] == '%': continue n = 0 for item in line.rstrip().split(sep): data[m, n] = float(item) n += 1 m += 1 f.close() return data def qsave(data, name='qutip_data'): """ Saves given data to file named 'filename.qu' in current directory. Parameters ---------- data : instance/array_like Input Python object to be stored. filename : str or pathlib.Path, default: "qutip_data" Name of output data file. """ # open the file for writing path = Path(name) path = path.with_suffix(path.suffix + ".qu") with open(path, "wb") as fileObject: # this writes the object a to the file named 'filename.qu' pickle.dump(data, fileObject) def qload(filename): """ Loads data file from file ``filename`` in current directory. Parameters ---------- filename : str or pathlib.Path Name of data file to be loaded. Returns ------- qobject : instance / array_like Object retrieved from requested file. """ path = Path(filename) path = path.with_suffix(path.suffix + ".qu") with open(path, "rb") as fileObject: if sys.version_info >= (3, 0): out = pickle.load(fileObject, encoding='latin1') else: out = pickle.load(fileObject) return out qutip-5.1.1/qutip/ipynbtools.py000066400000000000000000000243471474175217300166230ustar00rootroot00000000000000""" This module contains utility functions for using QuTiP with IPython notebooks. """ from qutip.ui.progressbar import BaseProgressBar, HTMLProgressBar from .settings import _blas_info, available_cpu_count import IPython #IPython parallel routines moved to ipyparallel in V4 #IPython parallel routines not in Anaconda by default if IPython.version_info[0] >= 4: try: from ipyparallel import Client __all__ = ['version_table', 'plot_animation', 'parallel_map'] except: __all__ = ['version_table', 'plot_animation'] else: try: from IPython.parallel import Client __all__ = ['version_table', 'plot_animation', 'parallel_map'] except: __all__ = ['version_table', 'plot_animation'] from IPython.display import HTML, Javascript, display import matplotlib.pyplot as plt from matplotlib import animation from base64 import b64encode import datetime import uuid import sys import os import time import inspect import qutip import numpy import scipy import matplotlib import IPython try: import Cython _cython_available = True except ImportError: _cython_available = False def version_table(verbose=False): """ Print an HTML-formatted table with version numbers for QuTiP and its dependencies. Use it in a IPython notebook to show which versions of different packages that were used to run the notebook. This should make it possible to reproduce the environment and the calculation later on. Parameters ---------- verbose : bool, default: False Add extra information about install location. Returns ------- version_table: str Return an HTML-formatted string containing version information for QuTiP dependencies. """ html = "" html += "" packages = [("QuTiP", qutip.__version__), ("Numpy", numpy.__version__), ("SciPy", scipy.__version__), ("matplotlib", matplotlib.__version__), ("Number of CPUs", available_cpu_count()), ("BLAS Info", _blas_info()), ("IPython", IPython.__version__), ("Python", sys.version), ("OS", "%s [%s]" % (os.name, sys.platform)) ] if _cython_available: packages.append(("Cython", Cython.__version__)) for name, version in packages: html += "" % (name, version) if verbose: html += "" qutip_install_path = os.path.dirname(inspect.getsourcefile(qutip)) html += ("" % qutip_install_path) try: import getpass html += ("" % getpass.getuser()) except: pass html += "" % time.strftime( '%a %b %d %H:%M:%S %Y %Z') html += "
SoftwareVersion
%s%s
Additional information
Installation path%s
User%s
%s
" return HTML(html) def _visualize_parfor_data(metadata): """ Visualizing the task scheduling meta data collected from AsyncResults. """ res = numpy.array(metadata) fig, ax = plt.subplots(figsize=(10, res.shape[1])) yticks = [] yticklabels = [] tmin = min(res[:, 1]) for n, pid in enumerate(numpy.unique(res[:, 0])): yticks.append(n) yticklabels.append("%d" % pid) for m in numpy.where(res[:, 0] == pid)[0]: ax.add_patch(plt.Rectangle((res[m, 1] - tmin, n - 0.25), res[m, 2] - res[m, 1], 0.5, color="green", alpha=0.5)) ax.set_ylim(-.5, n + .5) ax.set_xlim(0, max(res[:, 2]) - tmin + 0.) ax.set_yticks(yticks) ax.set_yticklabels(yticklabels) ax.set_ylabel("Engine") ax.set_xlabel("seconds") ax.set_title("Task schedule") def parfor(task, task_vec, args=None, client=None, view=None, show_scheduling=False, show_progressbar=False): """ Call the function ``tast`` for each value in ``task_vec`` using a cluster of IPython engines. The function ``task`` should have the signature ``task(value, args)`` or ``task(value)`` if ``args=None``. The ``client`` and ``view`` are the IPython.parallel client and load-balanced view that will be used in the parfor execution. If these are ``None``, new instances will be created. Parameters ---------- task: a Python function The function that is to be called for each value in ``task_vec``. task_vec: array / list The list or array of values for which the ``task`` function is to be evaluated. args: list / dictionary The optional additional argument to the ``task`` function. For example a dictionary with parameter values. client: IPython.parallel.Client The IPython.parallel Client instance that will be used in the parfor execution. view: a IPython.parallel.Client view The view that is to be used in scheduling the tasks on the IPython cluster. Preferably a load-balanced view, which is obtained from the IPython.parallel.Client instance client by calling, view = client.load_balanced_view(). show_scheduling: bool {False, True}, default False Display a graph showing how the tasks (the evaluation of ``task`` for for the value in ``task_vec1``) was scheduled on the IPython engine cluster. show_progressbar: bool {False, True}, default False Display a HTML-based progress bar duing the execution of the parfor loop. Returns ------- result : list The result list contains the value of ``task(value, args)`` for each value in ``task_vec``, that is, it should be equivalent to ``[task(v, args) for v in task_vec]``. """ if show_progressbar: progress_bar = HTMLProgressBar() else: progress_bar = None return parallel_map(task, task_vec, task_args=args, client=client, view=view, progress_bar=progress_bar, show_scheduling=show_scheduling) def parallel_map(task, values, task_args=None, task_kwargs=None, client=None, view=None, progress_bar=None, show_scheduling=False, **kwargs): """ Call the function ``task`` for each value in ``values`` using a cluster of IPython engines. The function ``task`` should have the signature ``task(value, *args, **kwargs)``. The ``client`` and ``view`` are the IPython.parallel client and load-balanced view that will be used in the parfor execution. If these are ``None``, new instances will be created. Parameters ---------- task: a Python function The function that is to be called for each value in ``task_vec``. values: array / list The list or array of values for which the ``task`` function is to be evaluated. task_args: list / dictionary The optional additional argument to the ``task`` function. task_kwargs: list / dictionary The optional additional keyword argument to the ``task`` function. client: IPython.parallel.Client The IPython.parallel Client instance that will be used in the parfor execution. view: a IPython.parallel.Client view The view that is to be used in scheduling the tasks on the IPython cluster. Preferably a load-balanced view, which is obtained from the IPython.parallel.Client instance client by calling, view = client.load_balanced_view(). show_scheduling: bool {False, True}, default False Display a graph showing how the tasks (the evaluation of ``task`` for for the value in ``task_vec1``) was scheduled on the IPython engine cluster. show_progressbar: bool {False, True}, default False Display a HTML-based progress bar during the execution of the parfor loop. Returns ------- result : list The result list contains the value of ``task(value, task_args, task_kwargs)`` for each value in ``values``. """ submitted = datetime.datetime.now() if task_args is None: task_args = tuple() if task_kwargs is None: task_kwargs = {} if client is None: client = Client() # make sure qutip is available at engines dview = client[:] dview.block = True dview.execute("from qutip import *") if view is None: view = client.load_balanced_view() ar_list = [view.apply_async(task, value, *task_args, **task_kwargs) for value in values] if progress_bar is None: view.wait(ar_list) else: if progress_bar is True: progress_bar = HTMLProgressBar(len(ar_list)) prev_finished = 0 while True: n_finished = sum([ar.progress for ar in ar_list]) for _ in range(prev_finished, n_finished): progress_bar.update() prev_finished = n_finished if view.wait(ar_list, timeout=0.5): break progress_bar.finished() if show_scheduling: metadata = [[ar.engine_id, (ar.started - submitted).total_seconds(), (ar.completed - submitted).total_seconds()] for ar in ar_list] _visualize_parfor_data(metadata) return [ar.get() for ar in ar_list] def plot_animation(plot_setup_func, plot_func, result, name="movie", writer="avconv", codec="libx264", verbose=False): """ Create an animated plot of a Result object, as returned by one of the qutip evolution solvers. .. note :: experimental """ fig, axes = plot_setup_func(result) def update(n): return plot_func(result, n, fig=fig, axes=axes) anim = animation.FuncAnimation( fig, update, frames=len(result.times), blit=True) anim.save(name + '.mp4', fps=10, writer=writer, codec=codec) plt.close(fig) if verbose: print("Created %s.m4v" % name) video = open(name + '.mp4', "rb").read() video_encoded = b64encode(video).decode("ascii") video_tag = '

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************* Frontmatter ************* .. _about-docs: About This Documentation ========================== This document contains a user guide and automatically generated API documentation for QuTiP. A PDF version of this text is available at the `documentation page `_. **For more information see the** `QuTiP project web page`_. .. _QuTiP project web page: https://qutip.org/ :Author: J.R. Johansson :Author: P.D. Nation :Author: Alexander Pitchford :Author: Arne Grimsmo :Author: Chris Grenade :Author: Nathan Shammah :Author: Shahnawaz Ahmed :Author: Neill Lambert :Author: Eric Giguere :Author: Boxi Li :Author: Jake Lishman :Author: Simon Cross :Author: Asier Galicia :Author: Paul Menczel :Author: Patrick Hopf :release: |release| :copyright: The text of this documentation is licensed under the Creative Commons Attribution 3.0 Unported License. All contained code samples, and the source code of QuTiP, are licensed under the 3-clause BSD licence. Full details of the copyright notices can be found on the `Copyright and Licensing `_ page of this documentation. .. _citing-qutip: Citing This Project ========================== If you find this project useful, then please cite: .. centered:: J. R. Johansson, P.D. Nation, and F. Nori, "QuTiP 2: A Python framework for the dynamics of open quantum systems", Comp. Phys. Comm. **184**, 1234 (2013). or .. centered:: J. R. Johansson, P.D. Nation, and F. Nori, "QuTiP: An open-source Python framework for the dynamics of open quantum systems", Comp. Phys. Comm. **183**, 1760 (2012). which may also be downloaded from https://arxiv.org/abs/1211.6518 or https://arxiv.org/abs/1110.0573, respectively. .. _funding-qutip: Funding ======= QuTiP is developed under the auspice of the non-profit organizations: .. _image-numfocus: .. figure:: figures/NumFocus_logo.png :width: 3in :figclass: align-center .. _image-unitaryfund: .. figure:: figures/unitaryfund_logo.png :width: 3in :figclass: align-center QuTiP was partially supported by .. _image-jsps: .. figure:: figures/jsps.jpg :width: 2in :figclass: align-center .. _image-riken: .. figure:: figures/riken-logo.png :width: 1.5in :figclass: align-center .. _image-korea: .. figure:: figures/korea-logo.png :width: 2in :figclass: align-center .. figure:: figures/inst_quant_sher.png :width: 2in :figclass: align-center .. _about: About QuTiP =========== Every quantum system encountered in the real world is an open quantum system. For although much care is taken experimentally to eliminate the unwanted influence of external interactions, there remains, if ever so slight, a coupling between the system of interest and the external world. In addition, any measurement performed on the system necessarily involves coupling to the measuring device, therefore introducing an additional source of external influence. Consequently, developing the necessary tools, both theoretical and numerical, to account for the interactions between a system and its environment is an essential step in understanding the dynamics of practical quantum systems. In general, for all but the most basic of Hamiltonians, an analytical description of the system dynamics is not possible, and one must resort to numerical simulations of the equations of motion. In absence of a quantum computer, these simulations must be carried out using classical computing techniques, where the exponentially increasing dimensionality of the underlying Hilbert space severely limits the size of system that can be efficiently simulated. However, in many fields such as quantum optics, trapped ions, superconducting circuit devices, and most recently nanomechanical systems, it is possible to design systems using a small number of effective oscillator and spin components, excited by a limited number of quanta, that are amenable to classical simulation in a truncated Hilbert space. The Quantum Toolbox in Python, or QuTiP, is an open-source framework written in the Python programming language, designed for simulating the open quantum dynamics of systems such as those listed above. This framework distinguishes itself from other available software solutions in providing the following advantages: * QuTiP relies entirely on open-source software. You are free to modify and use it as you wish with no licensing fees or limitations. * QuTiP is based on the Python scripting language, providing easy to read, fast code generation without the need to compile after modification. * The numerics underlying QuTiP are time-tested algorithms that run at C-code speeds, thanks to the `Numpy `_, `Scipy `_, and `Cython `_ libraries, and are based on many of the same algorithms used in propriety software. * QuTiP allows for solving the dynamics of Hamiltonians with (almost) arbitrary time-dependence, including collapse operators. * Time-dependent problems can be automatically compiled into C++-code at run-time for increased performance. * Takes advantage of the multiple processing cores found in essentially all modern computers. * QuTiP was designed from the start to require a minimal learning curve for those users who have experience using the popular quantum optics toolbox by Sze M. Tan. * Includes the ability to create high-quality plots, and animations, using the excellent `Matplotlib `_ package. For detailed information about new features of each release of QuTiP, see the :ref:`changelog`. .. _plugin-qutip: QuTiP Plugins ============= Several libraries depend on QuTiP heavily making QuTiP a super-library :Matsubara: `Matsubara `_ is a plugin to study the ultrastrong coupling regime with structured baths :QNET: `QNET `_ is a computer algebra package for quantum mechanics and photonic quantum networks .. _libraries: Libraries Using QuTiP ===================== Several libraries rely on QuTiP for quantum physics or quantum information processing. Some of them are: :Krotov: `Krotov `_ focuses on the python implementation of Krotov's method for quantum optimal control :pyEPR: `pyEPR `_ interfaces classical distributed microwave analysis with that of quantum structures and hamiltonians by providing easy to use analysis function and automation for the design of quantum chips :scQubits: `scQubits `_ is a Python library which provides a convenient way to simulate superconducting qubits by providing an interface to QuTiP :SimulaQron: `SimulaQron `_ is a distributed simulation of the end nodes in a quantum internet with the specific goal to explore application development :QInfer: `QInfer `_ is a library for working with sequential Monte Carlo methods for parameter estimation in quantum information :QPtomographer: `QPtomographer `_ derive quantum error bars for quantum processes in terms of the diamond norm to a reference quantum channel :QuNetSim: `QuNetSim `_ is a quantum networking simulation framework to develop and test protocols for quantum networks :qupulse: `qupulse `_ is a toolkit to facilitate experiments involving pulse driven state manipulation of physical qubits :Pulser: `Pulser `_ is a framework for composing, simulating and executing pulse sequences for neutral-atom quantum devices. Contributing to QuTiP ===================== We welcome anyone who is interested in helping us make QuTiP the best package for simulating quantum systems. There are :ref:`detailed instructions on how to contribute code and documentation ` in the developers' section of this guide. You can also help out our users by answering questions in the `QuTiP discussion mailing list `_, or by raising issues in `the main GitHub repository `_ if you find any bugs. Anyone who contributes code will be duly recognized. Even small contributions are noted. See :ref:`developers-contributors` for a list of people who have helped in one way or another. qutip-5.1.1/doc/guide/000077500000000000000000000000001474175217300145355ustar00rootroot00000000000000qutip-5.1.1/doc/guide/dynamics/000077500000000000000000000000001474175217300163445ustar00rootroot00000000000000qutip-5.1.1/doc/guide/dynamics/dynamics-bloch-redfield.rst000066400000000000000000000445021474175217300235530ustar00rootroot00000000000000.. _bloch_redfield: ****************************** Bloch-Redfield master equation ****************************** .. plot:: :context: reset :include-source: False import pylab as plt from scipy import * from qutip import * import numpy as np .. _bloch-redfield-intro: Introduction ============ The Lindblad master equation introduced earlier is constructed so that it describes a physical evolution of the density matrix (i.e., trace and positivity preserving), but it does not provide a connection to any underlying microscopic physical model. The Lindblad operators (collapse operators) describe phenomenological processes, such as for example dephasing and spin flips, and the rates of these processes are arbitrary parameters in the model. In many situations the collapse operators and their corresponding rates have clear physical interpretation, such as dephasing and relaxation rates, and in those cases the Lindblad master equation is usually the method of choice. However, in some cases, for example systems with varying energy biases and eigenstates and that couple to an environment in some well-defined manner (through a physically motivated system-environment interaction operator), it is often desirable to derive the master equation from more fundamental physical principles, and relate it to for example the noise-power spectrum of the environment. The Bloch-Redfield formalism is one such approach to derive a master equation from a microscopic system. It starts from a combined system-environment perspective, and derives a perturbative master equation for the system alone, under the assumption of weak system-environment coupling. One advantage of this approach is that the dissipation processes and rates are obtained directly from the properties of the environment. On the downside, it does not intrinsically guarantee that the resulting master equation unconditionally preserves the physical properties of the density matrix (because it is a perturbative method). The Bloch-Redfield master equation must therefore be used with care, and the assumptions made in the derivation must be honored. (The Lindblad master equation is in a sense more robust -- it always results in a physical density matrix -- although some collapse operators might not be physically justified). For a full derivation of the Bloch Redfield master equation, see e.g. [Coh92]_ or [Bre02]_. Here we present only a brief version of the derivation, with the intention of introducing the notation and how it relates to the implementation in QuTiP. .. _bloch-redfield-derivation: Brief Derivation and Definitions ================================ The starting point of the Bloch-Redfield formalism is the total Hamiltonian for the system and the environment (bath): :math:`H = H_{\rm S} + H_{\rm B} + H_{\rm I}`, where :math:`H` is the total system+bath Hamiltonian, :math:`H_{\rm S}` and :math:`H_{\rm B}` are the system and bath Hamiltonians, respectively, and :math:`H_{\rm I}` is the interaction Hamiltonian. The most general form of a master equation for the system dynamics is obtained by tracing out the bath from the von-Neumann equation of motion for the combined system (:math:`\dot\rho = -i\hbar^{-1}[H, \rho]`). In the interaction picture the result is .. math:: :label: br-nonmarkovian-form-one \frac{d}{dt}\rho_S(t) = - \hbar^{-2}\int_0^t d\tau\; {\rm Tr}_B [H_I(t), [H_I(\tau), \rho_S(\tau)\otimes\rho_B]], where the additional assumption that the total system-bath density matrix can be factorized as :math:`\rho(t) \approx \rho_S(t) \otimes \rho_B`. This assumption is known as the Born approximation, and it implies that there never is any entanglement between the system and the bath, neither in the initial state nor at any time during the evolution. *It is justified for weak system-bath interaction.* The master equation :eq:`br-nonmarkovian-form-one` is non-Markovian, i.e., the change in the density matrix at a time :math:`t` depends on states at all times :math:`\tau < t`, making it intractable to solve both theoretically and numerically. To make progress towards a manageable master equation, we now introduce the Markovian approximation, in which :math:`\rho_S(\tau)` is replaced by :math:`\rho_S(t)` in Eq. :eq:`br-nonmarkovian-form-one`. The result is the Redfield equation .. math:: :label: br-nonmarkovian-form-two \frac{d}{dt}\rho_S(t) = - \hbar^{-2}\int_0^t d\tau\; {\rm Tr}_B [H_I(t), [H_I(\tau), \rho_S(t)\otimes\rho_B]], which is local in time with respect the density matrix, but still not Markovian since it contains an implicit dependence on the initial state. By extending the integration to infinity and substituting :math:`\tau \rightarrow t-\tau`, a fully Markovian master equation is obtained: .. math:: :label: br-markovian-form \frac{d}{dt}\rho_S(t) = - \hbar^{-2}\int_0^\infty d\tau\; {\rm Tr}_B [H_I(t), [H_I(t-\tau), \rho_S(t)\otimes\rho_B]]. The two Markovian approximations introduced above are valid if the time-scale with which the system dynamics changes is large compared to the time-scale with which correlations in the bath decays (corresponding to a "short-memory" bath, which results in Markovian system dynamics). The master equation :eq:`br-markovian-form` is still on a too general form to be suitable for numerical implementation. We therefore assume that the system-bath interaction takes the form :math:`H_I = \sum_\alpha A_\alpha \otimes B_\alpha` and where :math:`A_\alpha` are system operators and :math:`B_\alpha` are bath operators. This allows us to write master equation in terms of system operators and bath correlation functions: .. math:: \frac{d}{dt}\rho_S(t) = -\hbar^{-2} \sum_{\alpha\beta} \int_0^\infty d\tau\; \left\{ g_{\alpha\beta}(\tau) \left[A_\alpha(t)A_\beta(t-\tau)\rho_S(t) - A_\alpha(t-\tau)\rho_S(t)A_\beta(t)\right] \right. \nonumber\\ \left. g_{\alpha\beta}(-\tau) \left[\rho_S(t)A_\alpha(t-\tau)A_\beta(t) - A_\alpha(t)\rho_S(t)A_\beta(t-\tau)\right] \right\}, where :math:`g_{\alpha\beta}(\tau) = {\rm Tr}_B\left[B_\alpha(t)B_\beta(t-\tau)\rho_B\right] = \left`, since the bath state :math:`\rho_B` is a steady state. In the eigenbasis of the system Hamiltonian, where :math:`A_{mn}(t) = A_{mn} e^{i\omega_{mn}t}`, :math:`\omega_{mn} = \omega_m - \omega_n` and :math:`\omega_m` are the eigenfrequencies corresponding the eigenstate :math:`\left|m\right>`, we obtain in matrix form in the SchrĂśdinger picture .. math:: \frac{d}{dt}\rho_{ab}(t) =& -i\omega_{ab}\rho_{ab}(t) \nonumber\\ &-\hbar^{-2} \sum_{\alpha,\beta} \sum_{c,d}^{\rm sec} \int_0^\infty d\tau\; \left\{ g_{\alpha\beta}(\tau) \left[\delta_{bd}\sum_nA^\alpha_{an}A^\beta_{nc}e^{i\omega_{cn}\tau} - A^\alpha_{ac} A^\beta_{db} e^{i\omega_{ca}\tau} \right] \right. \nonumber\\ &+ \left. g_{\alpha\beta}(-\tau) \left[\delta_{ac}\sum_n A^\alpha_{dn}A^\beta_{nb} e^{i\omega_{nd}\tau} - A^\alpha_{ac}A^\beta_{db}e^{i\omega_{bd}\tau} \right] \right\} \rho_{cd}(t), \nonumber\\ where the "sec" above the summation symbol indicate summation of the secular terms which satisfy :math:`|\omega_{ab}-\omega_{cd}| \ll \tau_ {\rm decay}`. This is an almost-useful form of the master equation. The final step before arriving at the form of the Bloch-Redfield master equation that is implemented in QuTiP, involves rewriting the bath correlation function :math:`g(\tau)` in terms of the noise-power spectrum of the environment :math:`S(\omega) = \int_{-\infty}^\infty d\tau e^{i\omega\tau} g(\tau)`: .. math:: :label: br-nonmarkovian-form-four \int_0^\infty d\tau\; g_{\alpha\beta}(\tau) e^{i\omega\tau} = \frac{1}{2}S_{\alpha\beta}(\omega) + i\lambda_{\alpha\beta}(\omega), where :math:`\lambda_{ab}(\omega)` is an energy shift that is neglected here. The final form of the Bloch-Redfield master equation is .. math:: :label: br-final \frac{d}{dt}\rho_{ab}(t) = -i\omega_{ab}\rho_{ab}(t) + \sum_{c,d}^{\rm sec}R_{abcd}\rho_{cd}(t), where .. math:: :label: br-nonmarkovian-form-five R_{abcd} = -\frac{\hbar^{-2}}{2} \sum_{\alpha,\beta} \left\{ \delta_{bd}\sum_nA^\alpha_{an}A^\beta_{nc}S_{\alpha\beta}(\omega_{cn}) - A^\alpha_{ac} A^\beta_{db} S_{\alpha\beta}(\omega_{ca}) \right. \nonumber\\ + \left. \delta_{ac}\sum_n A^\alpha_{dn}A^\beta_{nb} S_{\alpha\beta}(\omega_{dn}) - A^\alpha_{ac}A^\beta_{db} S_{\alpha\beta}(\omega_{db}) \right\}, is the Bloch-Redfield tensor. The Bloch-Redfield master equation in the form Eq. :eq:`br-final` is suitable for numerical implementation. The input parameters are the system Hamiltonian :math:`H`, the system operators through which the environment couples to the system :math:`A_\alpha`, and the noise-power spectrum :math:`S_{\alpha\beta}(\omega)` associated with each system-environment interaction term. To simplify the numerical implementation we assume that :math:`A_\alpha` are Hermitian and that cross-correlations between different environment operators vanish, so that the final expression for the Bloch-Redfield tensor that is implemented in QuTiP is .. math:: :label: br-tensor R_{abcd} = -\frac{\hbar^{-2}}{2} \sum_{\alpha} \left\{ \delta_{bd}\sum_nA^\alpha_{an}A^\alpha_{nc}S_{\alpha}(\omega_{cn}) - A^\alpha_{ac} A^\alpha_{db} S_{\alpha}(\omega_{ca}) \right. \nonumber\\ + \left. \delta_{ac}\sum_n A^\alpha_{dn}A^\alpha_{nb} S_{\alpha}(\omega_{dn}) - A^\alpha_{ac}A^\alpha_{db} S_{\alpha}(\omega_{db}) \right\}. .. _bloch-redfield-qutip: Bloch-Redfield master equation in QuTiP ======================================= In QuTiP, the Bloch-Redfield tensor Eq. :eq:`br-tensor` can be calculated using the function :func:`.bloch_redfield_tensor`. It takes two mandatory arguments: The system Hamiltonian :math:`H`, a nested list of operator :math:`A_\alpha`, spectral density functions :math:`S_\alpha(\omega)` pairs that characterize the coupling between system and bath. The spectral density functions are Python callback functions that takes the (angular) frequency as a single argument. To illustrate how to calculate the Bloch-Redfield tensor, let's consider a two-level atom .. math:: :label: qubit H = -\frac{1}{2}\Delta\sigma_x - \frac{1}{2}\epsilon_0\sigma_z .. testcode:: [dynamics-br] delta = 0.2 * 2*np.pi eps0 = 1.0 * 2*np.pi gamma1 = 0.5 H = - delta/2.0 * sigmax() - eps0/2.0 * sigmaz() def ohmic_spectrum(w): if w == 0.0: # dephasing inducing noise return gamma1 else: # relaxation inducing noise return gamma1 / 2 * (w / (2 * np.pi)) * (w > 0.0) R, ekets = bloch_redfield_tensor(H, a_ops=[[sigmax(), ohmic_spectrum]]) print(R) **Output**: .. testoutput:: [dynamics-br] Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = False Qobj data = [[ 0. +0.j 0. +0.j 0. +0.j 0.24514517+0.j ] [ 0. +0.j -0.16103412-6.4076169j 0. +0.j 0. +0.j ] [ 0. +0.j 0. +0.j -0.16103412+6.4076169j 0. +0.j ] [ 0. +0.j 0. +0.j 0. +0.j -0.24514517+0.j ]] Note that it is also possible to add Lindblad dissipation superoperators in the Bloch-Refield tensor by passing the operators via the ``c_ops`` keyword argument like you would in the :func:`.mesolve` or :func:`.mcsolve` functions. For convenience, the function :func:`.bloch_redfield_tensor` also returns the basis transformation operator, the eigen vector matrix, since they are calculated in the process of calculating the Bloch-Redfield tensor `R`, and the `ekets` are usually needed again later when transforming operators between the laboratory basis and the eigen basis. The tensor can be obtained in the laboratory basis by setting ``fock_basis=True``, in that case, the transformation operator is not returned. The evolution of a wavefunction or density matrix, according to the Bloch-Redfield master equation :eq:`br-final`, can be calculated using the QuTiP function :func:`.mesolve` using Bloch-Refield tensor in the laboratory basis instead of a liouvillian. For example, to evaluate the expectation values of the :math:`\sigma_x`, :math:`\sigma_y`, and :math:`\sigma_z` operators for the example above, we can use the following code: .. plot:: :context: delta = 0.2 * 2*np.pi eps0 = 1.0 * 2*np.pi gamma1 = 0.5 H = - delta/2.0 * sigmax() - eps0/2.0 * sigmaz() def ohmic_spectrum(w): if w == 0.0: # dephasing inducing noise return gamma1 else: # relaxation inducing noise return gamma1 / 2 * (w / (2 * np.pi)) * (w > 0.0) R = bloch_redfield_tensor(H, [[sigmax(), ohmic_spectrum]], fock_basis=True) tlist = np.linspace(0, 15.0, 1000) psi0 = rand_ket(2, seed=1) e_ops = [sigmax(), sigmay(), sigmaz()] expt_list = mesolve(R, psi0, tlist, e_ops=e_ops).expect sphere = Bloch() sphere.add_points([expt_list[0], expt_list[1], expt_list[2]]) sphere.vector_color = ['r'] sphere.add_vectors(np.array([delta, 0, eps0]) / np.sqrt(delta ** 2 + eps0 ** 2)) sphere.make_sphere() The two steps of calculating the Bloch-Redfield tensor and evolving according to the corresponding master equation can be combined into one by using the function :func:`.brmesolve`, which takes same arguments as :func:`.mesolve` and :func:`.mcsolve`, save for the additional nested list of operator-spectrum pairs that is called ``a_ops``. .. plot:: :context: close-figs output = brmesolve(H, psi0, tlist, a_ops=[[sigmax(),ohmic_spectrum]], e_ops=e_ops) where the resulting `output` is an instance of the class :class:`.Result`. .. note:: While the code example simulates the Bloch-Redfield equation in the secular approximation, QuTiP's implementation allows the user to simulate the non-secular version of the Bloch-Redfield equation by setting ``sec_cutoff=-1``, as well as do a partial secular approximation by setting it to a ``float`` , this float will become the cutoff for the sum in :eq:`br-final` meaning terms with :math:`|\omega_{ab}-\omega_{cd}|` greater than the cutoff will be neglected. Its default value is 0.1 which corresponds to the secular approximation. For example the command :: output = brmesolve(H, psi0, tlist, a_ops=[[sigmax(), ohmic_spectrum]], e_ops=e_ops, sec_cutoff=-1) will simulate the same example as above without the secular approximation. Note that using the non-secular version may lead to negativity issues. .. _td-bloch-redfield: Time-dependent Bloch-Redfield Dynamics ======================================= If you have not done so already, please read the section: :ref:`time`. As we have already discussed, the Bloch-Redfield master equation requires transforming into the eigenbasis of the system Hamiltonian. For time-independent systems, this transformation need only be done once. However, for time-dependent systems, one must move to the instantaneous eigenbasis at each time-step in the evolution, thus greatly increasing the computational complexity of the dynamics. In addition, the requirement for computing all the eigenvalues severely limits the scalability of the method. Fortunately, this eigen decomposition occurs at the Hamiltonian level, as opposed to the super-operator level, and thus, with efficient programming, one can tackle many systems that are commonly encountered. For time-dependent Hamiltonians, the Hamiltonian itself can be passed into the solver like any other time dependent Hamiltonian, as thus we will not discuss this topic further. Instead, here the focus is on time-dependent bath coupling terms. To this end, suppose that we have a dissipative harmonic oscillator, where the white-noise dissipation rate decreases exponentially with time :math:`\kappa(t) = \kappa(0)\exp(-t)`. In the Lindblad or Monte Carlo solvers, this could be implemented as a time-dependent collapse operator list ``c_ops = [[a, 'sqrt(kappa*exp(-t))']]``. In the Bloch-Redfield solver, the bath coupling terms must be Hermitian. As such, in this example, our coupling operator is the position operator ``a+a.dag()``. The complete example, and comparison to the analytic expression is: .. plot:: :context: close-figs N = 10 # number of basis states to consider a = destroy(N) H = a.dag() * a psi0 = basis(N, 9) # initial state kappa = 0.2 # coupling to oscillator a_ops = [ ([a+a.dag(), f'sqrt({kappa}*exp(-t))'], '(w>=0)') ] tlist = np.linspace(0, 10, 100) out = brmesolve(H, psi0, tlist, a_ops, e_ops=[a.dag() * a]) actual_answer = 9.0 * np.exp(-kappa * (1.0 - np.exp(-tlist))) plt.figure() plt.plot(tlist, out.expect[0]) plt.plot(tlist, actual_answer) plt.show() In many cases, the bath-coupling operators can take the form :math:`A = f(t)a + f(t)^* a^{+}`. The operator parts of the `a_ops` can be made of as many time-dependent terms as needed to construct such operator. For example consider a white-noise bath that is coupled to an operator of the form ``exp(1j*t)*a + exp(-1j*t)* a.dag()``. In this example, the ``a_ops`` list would be: .. plot:: :context: close-figs a_ops = [ ([[a, 'exp(1j*t)'], [a.dag(), 'exp(-1j*t)']], f'{kappa} * (w >= 0)') ] where the first tuple element ``[[a, 'exp(1j*t)'], [a.dag(), 'exp(-1j*t)']]`` tells the solver what is the time-dependent Hermitian coupling operator. The second tuple ``f'{kappa} * (w >= 0)'``, gives the noise power spectrum. A full example is: .. plot:: :context: close-figs N = 10 w0 = 1.0 * 2 * np.pi g = 0.05 * w0 kappa = 0.15 times = np.linspace(0, 25, 1000) a = destroy(N) H = w0 * a.dag() * a + g * (a + a.dag()) psi0 = ket2dm((basis(N, 4) + basis(N, 2) + basis(N, 0)).unit()) a_ops = [[ QobjEvo([[a, 'exp(1j*t)'], [a.dag(), 'exp(-1j*t)']]), (f'{kappa} * (w >= 0)') ]] e_ops = [a.dag() * a, a + a.dag()] res_brme = brmesolve(H, psi0, times, a_ops, e_ops=e_ops) plt.figure() plt.plot(times, res_brme.expect[0], label=r'$a^{+}a$') plt.plot(times, res_brme.expect[1], label=r'$a+a^{+}$') plt.legend() plt.show() Further examples on time-dependent Bloch-Redfield simulations can be found in the online tutorials. .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-class.rst000066400000000000000000000133261474175217300220150ustar00rootroot00000000000000.. _solver_class: ******************************************* Solver Class Interface ******************************************* In QuTiP version 5 and later, solvers such as :func:`.mesolve`, :func:`.mcsolve` also have a class interface. The class interface allows reusing the Hamiltonian and fine tuning many details of how the solver is run. Examples of some of the solver class features are given below. Reusing Hamiltonian Data ------------------------ There are many cases where one would like to study multiple evolutions of the same quantum system, whether by changing the initial state or other parameters. In order to evolve a given system as fast as possible, the solvers in QuTiP take the given input operators (Hamiltonian, collapse operators, etc) and prepare them for use with the selected ODE solver. These operations are usually reasonably fast, but for some solvers, such as :func:`.brmesolve` or :func:`.fmmesolve`, the overhead can be significant. Even for simpler solvers, the time spent organizing data can become appreciable when repeatedly solving a system. The class interface allows us to setup the system once and reuse it with various parameters. Most ``...solve`` function have a paired ``...Solver`` class, with a ``..Solver.run`` method to run the evolution. At class instance creation, the physics (``H``, ``c_ops``, ``a_ops``, etc.) and options are passed. The initial state, times and expectation operators are only passed when calling ``run``: .. plot:: :context: close-figs times = np.linspace(0.0, 6.0, 601) a = tensor(qeye(2), destroy(10)) sm = tensor(destroy(2), qeye(10)) e_ops = [a.dag() * a, sm.dag() * sm] H = QobjEvo( [a.dag()*a + sm.dag()*sm, [(sm*a.dag() + sm.dag()*a), lambda t, A: A]], args={"A": 0.5*np.pi} ) solver = MESolver(H, c_ops=[np.sqrt(0.1) * a], options={"atol": 1e-8}) solver.options["normalize_output"] = True psi0 = tensor(fock(2, 0), fock(10, 5)) data1 = solver.run(psi0, times, e_ops=e_ops) psi1 = tensor(fock(2, 0), coherent(10, 2 - 1j)) data2 = solver.run(psi1, times, e_ops=e_ops) plt.figure() plt.plot(times, data1.expect[0], "b", times, data1.expect[1], "r", lw=2) plt.plot(times, data2.expect[0], 'b--', times, data2.expect[1], 'r--', lw=2) plt.title('Master Equation time evolution') plt.xlabel('Time', fontsize=14) plt.ylabel('Expectation values', fontsize=14) plt.legend(("cavity photon number", "atom excitation probability")) plt.show() Note that as shown, options can be set at initialization or with the ``options`` property. The simulation parameters, the ``args`` of the :class:`.QobjEvo` passed as system operators, can be updated at the start of a run: .. plot:: :context: close-figs data1 = solver.run(psi0, times, e_ops=e_ops) data2 = solver.run(psi0, times, e_ops=e_ops, args={"A": 0.25*np.pi}) data3 = solver.run(psi0, times, e_ops=e_ops, args={"A": 0.125*np.pi}) plt.figure() plt.plot(times, data1.expect[0], label="A=pi/2") plt.plot(times, data2.expect[0], label="A=pi/4") plt.plot(times, data3.expect[0], label="A=pi/8") plt.title('Master Equation time evolution') plt.xlabel('Time', fontsize=14) plt.ylabel('Expectation values', fontsize=14) plt.legend() plt.show() Stepping through the run ------------------------ The solver class also allows to run through a simulation one step at a time, updating args at each step: .. plot:: :context: close-figs data = [5.] solver.start(state0=psi0, t0=times[0]) for t in times[1:]: psi_t = solver.step(t, args={"A": np.pi*np.exp(-(t-3)**2)}) data.append(expect(e_ops[0], psi_t)) plt.figure() plt.plot(times, data) plt.title('Master Equation time evolution') plt.xlabel('Time', fontsize=14) plt.ylabel('Expectation values', fontsize=14) plt.legend(("cavity photon number")) plt.show() .. note:: This is an example only, updating a constant ``args`` parameter between step should not replace using a function as QobjEvo's coefficient. .. note:: It is possible to create multiple solvers and to advance them using ``step`` in parallel. However, many ODE solver, including the default ``adams`` method, only allow one instance at a time per process. QuTiP supports using multiple solver instances of these ODE solvers but with a performance cost. In these situations, using ``dop853`` or ``vern9`` integration method is recommended instead. Feedback: Accessing the solver state from evolution operators ============================================================= The state of the system during the evolution is accessible via properties of the solver classes. Each solver has a ``StateFeedback`` and ``ExpectFeedback`` class method that can be passed as arguments to time dependent systems. For example, ``ExpectFeedback`` can be used to create a system which uncouples when there are 5 or fewer photons in the cavity. .. plot:: :context: close-figs def f(t, e1): ex = (e1.real - 5) return (ex > 0) * ex * 10 times = np.linspace(0.0, 1.0, 301) a = tensor(qeye(2), destroy(10)) sm = tensor(destroy(2), qeye(10)) e_ops = [a.dag() * a, sm.dag() * sm] psi0 = tensor(fock(2, 0), fock(10, 8)) e_ops = [a.dag() * a, sm.dag() * sm] H = [a*a.dag(), [sm*a.dag() + sm.dag()*a, f]] data = mesolve(H, psi0, times, c_ops=[a], e_ops=e_ops, args={"e1": MESolver.ExpectFeedback(a.dag() * a)} ).expect plt.figure() plt.plot(times, data[0]) plt.plot(times, data[1]) plt.title('Master Equation time evolution') plt.xlabel('Time', fontsize=14) plt.ylabel('Expectation values', fontsize=14) plt.legend(("cavity photon number", "atom excitation probability")) plt.show() qutip-5.1.1/doc/guide/dynamics/dynamics-data.rst000066400000000000000000000205241474175217300216170ustar00rootroot00000000000000.. _solver_result: ******************************************************** Dynamics Simulation Results ******************************************************** .. _solver_result-class: The solver.Result Class ======================= Before embarking on simulating the dynamics of quantum systems, we will first look at the data structure used for returning the simulation results. This object is a :func:`~qutip.solver.result.Result` class that stores all the crucial data needed for analyzing and plotting the results of a simulation. A generic ``Result`` object ``result`` contains the following properties for storing simulation data: .. cssclass:: table-striped +------------------------+-----------------------------------------------------------------------+ | Property | Description | +========================+=======================================================================+ | ``result.solver`` | String indicating which solver was used to generate the data. | +------------------------+-----------------------------------------------------------------------+ | ``result.times`` | List/array of times at which simulation data is calculated. | +------------------------+-----------------------------------------------------------------------+ | ``result.expect`` | List/array of expectation values, if requested. | +------------------------+-----------------------------------------------------------------------+ | ``result.e_data`` | Dictionary of expectation values, if requested. | +------------------------+-----------------------------------------------------------------------+ | ``result.states`` | List/array of state vectors/density matrices calculated at ``times``, | | | if requested. | +------------------------+-----------------------------------------------------------------------+ | ``result.final_state`` | State vector or density matrix at the last time of the evolution. | +------------------------+-----------------------------------------------------------------------+ | ``result.stats`` | Various statistics about the evolution. | +------------------------+-----------------------------------------------------------------------+ .. _odedata-access: Accessing Result Data ====================== To understand how to access the data in a Result object we will use an example as a guide, although we do not worry about the simulation details at this stage. Like all solvers, the Master Equation solver used in this example returns an Result object, here called simply ``result``. To see what is contained inside ``result`` we can use the print function: .. doctest:: :options: +SKIP >>> print(result) The first line tells us that this data object was generated from the Master Equation solver :func:`.mesolve`. Next we have the statistics including the ODE solver used, setup time, number of collpases. Then the integration interval is described, followed with the number of expectation value computed. Finally, it says whether the states are stored. Now we have all the information needed to analyze the simulation results. To access the data for the two expectation values one can do: .. testcode:: :skipif: True expt0 = result.expect[0] expt1 = result.expect[1] Recall that Python uses C-style indexing that begins with zero (i.e., [0] => 1st collapse operator data). Alternatively, expectation values can be obtained as a dictionary: .. testcode:: :skipif: True e_ops = {"sx": sigmax(), "sy": sigmay(), "sz": sigmaz()} ... expt_sx = result.e_data["sx"] When ``e_ops`` is a list, ``e_data`` ca be used with the list index. Together with the array of times at which these expectation values are calculated: .. testcode:: :skipif: True times = result.times we can plot the resulting expectation values: .. testcode:: :skipif: True plot(times, expt0) plot(times, expt1) show() State vectors, or density matrices, are accessed in a similar manner, although typically one does not need an index (i.e [0]) since there is only one list for each of these components. Some other solver can have other output, :func:`.heomsolve`'s results can have ``ado_states`` output if the options ``store_ados`` is set, similarly, :func:`.fmmesolve` can return ``floquet_states``. Multiple Trajectories Solver Results ==================================== Solver which compute multiple trajectories such as the Monte Carlo Equations Solvers or the Stochastics Solvers result will differ depending on whether the trajectories are flags to be saved. For example: .. doctest:: :options: +SKIP >>> mcsolve(H, psi, np.linspace(0, 1, 11), c_ops, e_ops=[num(N)], ntraj=25, options={"keep_runs_results": False}) >>> np.shape(result.expect) (1, 11) >>> mcsolve(H, psi, np.linspace(0, 1, 11), c_ops, e_ops=[num(N)], ntraj=25, options={"keep_runs_results": True}) >>> np.shape(result.expect) (1, 25, 11) When the runs are not saved, the expectation values and states are averaged over all trajectories, while a list over the runs are given when they are stored. For a fix output format, ``average_expect`` return the average, while ``runs_states`` return the list over trajectories. The ``runs_`` output will return ``None`` when the trajectories are not saved. Standard derivation of the expectation values is also available: +-------------------------+----------------------+------------------------------------------------------------------------+ | Reduced result | Trajectories results | Description | +=========================+======================+========================================================================+ | ``average_states`` | ``runs_states`` | State vectors or density matrices calculated at each times of tlist | +-------------------------+----------------------+------------------------------------------------------------------------+ | ``average_final_state`` | ``runs_final_state`` | State vectors or density matrices calculated at the last time of tlist | +-------------------------+----------------------+------------------------------------------------------------------------+ | ``average_expect`` | ``runs_expect`` | List/array of expectation values, if requested. | +-------------------------+----------------------+------------------------------------------------------------------------+ | ``std_expect`` | | List/array of standard derivation of the expectation values. | +-------------------------+----------------------+------------------------------------------------------------------------+ | ``average_e_data`` | ``runs_e_data`` | Dictionary of expectation values, if requested. | +-------------------------+----------------------+------------------------------------------------------------------------+ | ``std_e_data`` | | Dictionary of standard derivation of the expectation values. | +-------------------------+----------------------+------------------------------------------------------------------------+ Multiple trajectories results also keep the trajectories ``seeds`` to allows recomputing the results. .. testcode:: :skipif: True seeds = result.seeds One last feature specific to multi-trajectories results is the addition operation that can be used to merge sets of trajectories. .. code-block:: >>> run1 = smesolve(H, psi, np.linspace(0, 1, 11), c_ops, e_ops=[num(N)], ntraj=25) >>> print(run1.num_trajectories) 25 >>> run2 = smesolve(H, psi, np.linspace(0, 1, 11), c_ops, e_ops=[num(N)], ntraj=25) >>> print(run2.num_trajectories) 25 >>> merged = run1 + run2 >>> print(merged.num_trajectories) 50 This allows one to improve statistics while keeping previous computations. qutip-5.1.1/doc/guide/dynamics/dynamics-floquet.rst000066400000000000000000000374571474175217300224020ustar00rootroot00000000000000.. _floquet: ***************** Floquet Formalism ***************** .. _floquet-intro: Introduction ============ Many time-dependent problems of interest are periodic. The dynamics of such systems can be solved for directly by numerical integration of the SchrĂśdinger or Master equation, using the time-dependent Hamiltonian. But they can also be transformed into time-independent problems using the Floquet formalism. Time-independent problems can be solve much more efficiently, so such a transformation is often very desirable. In the standard derivations of the Lindblad and Bloch-Redfield master equations the Hamiltonian describing the system under consideration is assumed to be time independent. Thus, strictly speaking, the standard forms of these master equation formalisms should not blindly be applied to system with time-dependent Hamiltonians. However, in many relevant cases, in particular for weak driving, the standard master equations still turns out to be useful for many time-dependent problems. But a more rigorous approach would be to rederive the master equation taking the time-dependent nature of the Hamiltonian into account from the start. The Floquet-Markov Master equation is one such a formalism, with important applications for strongly driven systems (see e.g., [Gri98]_). Here we give an overview of how the Floquet and Floquet-Markov formalisms can be used for solving time-dependent problems in QuTiP. To introduce the terminology and naming conventions used in QuTiP we first give a brief summary of quantum Floquet theory. .. _floquet-unitary: Floquet theory for unitary evolution ==================================== The SchrĂśdinger equation with a time-dependent Hamiltonian :math:`H(t)` is .. math:: :label: eq_td_schrodinger H(t)\Psi(t) = i\hbar\frac{\partial}{\partial t}\Psi(t), where :math:`\Psi(t)` is the wave function solution. Here we are interested in problems with periodic time-dependence, i.e., the Hamiltonian satisfies :math:`H(t) = H(t+T)` where :math:`T` is the period. According to the Floquet theorem, there exist solutions to :eq:`eq_td_schrodinger` of the form .. math:: :label: eq_floquet_states \Psi_\alpha(t) = \exp(-i\epsilon_\alpha t/\hbar)\Phi_\alpha(t), where :math:`\Psi_\alpha(t)` are the *Floquet states* (i.e., the set of wave function solutions to the SchrĂśdinger equation), :math:`\Phi_\alpha(t)=\Phi_\alpha(t+T)` are the periodic *Floquet modes*, and :math:`\epsilon_\alpha` are the *quasienergy levels*. The quasienergy levels are constants in time, but only uniquely defined up to multiples of :math:`2\pi/T` (i.e., unique value in the interval :math:`[0, 2\pi/T]`). If we know the Floquet modes (for :math:`t \in [0,T]`) and the quasienergies for a particular :math:`H(t)`, we can easily decompose any initial wavefunction :math:`\Psi(t=0)` in the Floquet states and immediately obtain the solution for arbitrary :math:`t` .. math:: :label: eq_floquet_wavefunction_expansion \Psi(t) = \sum_\alpha c_\alpha \Psi_\alpha(t) = \sum_\alpha c_\alpha \exp(-i\epsilon_\alpha t/\hbar)\Phi_\alpha(t), where the coefficients :math:`c_\alpha` are determined by the initial wavefunction :math:`\Psi(0) = \sum_\alpha c_\alpha \Psi_\alpha(0)`. This formalism is useful for finding :math:`\Psi(t)` for a given :math:`H(t)` only if we can obtain the Floquet modes :math:`\Phi_a(t)` and quasienergies :math:`\epsilon_\alpha` more easily than directly solving :eq:`eq_td_schrodinger`. By substituting :eq:`eq_floquet_states` into the SchrĂśdinger equation :eq:`eq_td_schrodinger` we obtain an eigenvalue equation for the Floquet modes and quasienergies .. math:: :label: eq_floquet_eigen_problem \mathcal{H}(t)\Phi_\alpha(t) = \epsilon_\alpha\Phi_\alpha(t), where :math:`\mathcal{H}(t) = H(t) - i\hbar\partial_t`. This eigenvalue problem could be solved analytically or numerically, but in QuTiP we use an alternative approach for numerically finding the Floquet states and quasienergies [see e.g. Creffield et al., Phys. Rev. B 67, 165301 (2003)]. Consider the propagator for the time-dependent SchrĂśdinger equation :eq:`eq_td_schrodinger`, which by definition satisfies .. math:: U(T+t,t)\Psi(t) = \Psi(T+t). Inserting the Floquet states from :eq:`eq_floquet_states` into this expression results in .. math:: U(T+t,t)\exp(-i\epsilon_\alpha t/\hbar)\Phi_\alpha(t) = \exp(-i\epsilon_\alpha(T+t)/\hbar)\Phi_\alpha(T+t), or, since :math:`\Phi_\alpha(T+t)=\Phi_\alpha(t)`, .. math:: U(T+t,t)\Phi_\alpha(t) = \exp(-i\epsilon_\alpha T/\hbar)\Phi_\alpha(t) = \eta_\alpha \Phi_\alpha(t), which shows that the Floquet modes are eigenstates of the one-period propagator. We can therefore find the Floquet modes and quasienergies :math:`\epsilon_\alpha = -\hbar\arg(\eta_\alpha)/T` by numerically calculating :math:`U(T+t,t)` and diagonalizing it. In particular this method is useful to find :math:`\Phi_\alpha(0)` by calculating and diagonalize :math:`U(T,0)`. The Floquet modes at arbitrary time :math:`t` can then be found by propagating :math:`\Phi_\alpha(0)` to :math:`\Phi_\alpha(t)` using the wave function propagator :math:`U(t,0)\Psi_\alpha(0) = \Psi_\alpha(t)`, which for the Floquet modes yields .. math:: U(t,0)\Phi_\alpha(0) = \exp(-i\epsilon_\alpha t/\hbar)\Phi_\alpha(t), so that :math:`\Phi_\alpha(t) = \exp(i\epsilon_\alpha t/\hbar) U(t,0)\Phi_\alpha(0)`. Since :math:`\Phi_\alpha(t)` is periodic we only need to evaluate it for :math:`t \in [0, T]`, and from :math:`\Phi_\alpha(t \in [0,T])` we can directly evaluate :math:`\Phi_\alpha(t)`, :math:`\Psi_\alpha(t)` and :math:`\Psi(t)` for arbitrary large :math:`t`. Floquet formalism in QuTiP -------------------------- QuTiP provides a family of functions to calculate the Floquet modes and quasi energies, Floquet state decomposition, etc., given a time-dependent Hamiltonian. Consider for example the case of a strongly driven two-level atom, described by the Hamiltonian .. math:: :label: eq_driven_qubit H(t) = -\frac{1}{2}\Delta\sigma_x - \frac{1}{2}\epsilon_0\sigma_z + \frac{1}{2}A\sin(\omega t)\sigma_z. In QuTiP we can define this Hamiltonian as follows: .. code-block:: python >>> delta = 0.2 * 2*np.pi >>> eps0 = 1.0 * 2*np.pi >>> A = 2.5 * 2*np.pi >>> omega = 1.0 * 2*np.pi >>> H0 = - delta/2.0 * sigmax() - eps0/2.0 * sigmaz() >>> H1 = A/2.0 * sigmaz() >>> args = {'w': omega} >>> H = [H0, [H1, 'sin(w * t)']] The :math:`t=0` Floquet modes corresponding to the Hamiltonian :eq:`eq_driven_qubit` can then be calculated using the :class:`.FloquetBasis` class, which encapsulates the Floquet modes and the quasienergies: .. code-block:: python >>> T = 2*np.pi / omega >>> floquet_basis = FloquetBasis(H, T, args) >>> f_energies = floquet_basis.e_quasi >>> f_energies # doctest: +NORMALIZE_WHITESPACE array([-2.83131212, 2.83131212]) >>> f_modes_0 = floquet_basis.mode(0) >>> f_modes_0 # doctest: +NORMALIZE_WHITESPACE [Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[ 0.72964231+0.j ] [-0.39993746+0.554682j]], Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.39993746+0.554682j] [0.72964231+0.j ]]] For some problems interesting observations can be draw from the quasienergy levels alone. Consider for example the quasienergies for the driven two-level system introduced above as a function of the driving amplitude, calculated and plotted in the following example. For certain driving amplitudes the quasienergy levels cross. Since the quasienergies can be associated with the time-scale of the long-term dynamics due that the driving, degenerate quasienergies indicates a "freezing" of the dynamics (sometimes known as coherent destruction of tunneling). .. plot:: :context: close-figs >>> delta = 0.2 * 2 * np.pi >>> eps0 = 0.0 * 2 * np.pi >>> omega = 1.0 * 2 * np.pi >>> A_vec = np.linspace(0, 10, 100) * omega >>> T = (2 * np.pi) / omega >>> tlist = np.linspace(0.0, 10 * T, 101) >>> spsi0 = basis(2, 0) >>> q_energies = np.zeros((len(A_vec), 2)) >>> H0 = delta / 2.0 * sigmaz() - eps0 / 2.0 * sigmax() >>> args = {'w': omega} >>> for idx, A in enumerate(A_vec): # doctest: +SKIP >>> H1 = A / 2.0 * sigmax() # doctest: +SKIP >>> H = [H0, [H1, lambda t, args: np.sin(args['w'] * t)]] # doctest: +SKIP >>> floquet_basis = FloquetBasis(H, T, args) >>> q_energies[idx,:] = floquet_basis.e_quasi # doctest: +SKIP >>> plt.figure() # doctest: +SKIP >>> plt.plot(A_vec/omega, q_energies[:,0] / delta, 'b', A_vec/omega, q_energies[:,1] / delta, 'r') # doctest: +SKIP >>> plt.xlabel(r'$A/\omega$') # doctest: +SKIP >>> plt.ylabel(r'Quasienergy / $\Delta$') # doctest: +SKIP >>> plt.title(r'Floquet quasienergies') # doctest: +SKIP >>> plt.show() # doctest: +SKIP Given the Floquet modes at :math:`t=0`, we obtain the Floquet mode at some later time :math:`t` using :meth:`.FloquetBasis.mode`: .. plot:: :context: close-figs >>> f_modes_t = floquet_basis.mode(2.5) >>> f_modes_t # doctest: +SKIP [Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[-0.89630512-0.23191946j] [ 0.37793106-0.00431336j]], Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[-0.37793106-0.00431336j] [-0.89630512+0.23191946j]]] The purpose of calculating the Floquet modes is to find the wavefunction solution to the original problem :eq:`eq_driven_qubit` given some initial state :math:`\left|\psi_0\right>`. To do that, we first need to decompose the initial state in the Floquet states, using the function :meth:`.FloquetBasis.to_floquet_basis` .. plot:: :context: close-figs >>> psi0 = rand_ket(2) >>> f_coeff = floquet_basis.to_floquet_basis(psi0) >>> f_coeff # doctest: +SKIP [(-0.645265993068382+0.7304552549315746j), (0.15517002114250228-0.1612116102238258j)] and given this decomposition of the initial state in the Floquet states we can easily evaluate the wavefunction that is the solution to :eq:`eq_driven_qubit` at an arbitrary time :math:`t` using the function :meth:`.FloquetBasis.from_floquet_basis`: .. plot:: :context: close-figs >>> t = 10 * np.random.rand() >>> psi_t = floquet_basis.from_floquet_basis(f_coeff, t) The following example illustrates how to use the functions introduced above to calculate and plot the time-evolution of :eq:`eq_driven_qubit`. .. plot:: guide/scripts/floquet_ex1.py :width: 4.0in :include-source: Pre-computing the Floquet modes for one period ---------------------------------------------- When evaluating the Floquet states or the wavefunction at many points in time it is useful to pre-compute the Floquet modes for the first period of the driving with the required times. The list of times to pre-compute modes for may be passed to :class:`.FloquetBasis` using ``precompute=tlist``, and then :meth:`.FloquetBasis.from_floquet_basis` and :meth:`.FloquetBasis.to_floquet_basis` can be used to efficiently retrieve the wave function at the pre-computed times. The following example illustrates how the example from the previous section can be solved more efficiently using these functions for pre-computing the Floquet modes: .. plot:: guide/scripts/floquet_ex2.py :width: 4.0in :include-source: Note that the parameters and the Hamiltonian used in this example is not the same as in the previous section, and hence the different appearance of the resulting figure. For convenience, all the steps described above for calculating the evolution of a quantum system using the Floquet formalisms are encapsulated in the function :func:`.fsesolve`. Using this function, we could have achieved the same results as in the examples above using .. code-block:: python output = fsesolve(H, psi0=psi0, tlist=tlist, e_ops=[qutip.num(2)], args=args) p_ex = output.expect[0] .. _floquet-dissipative: Floquet theory for dissipative evolution ======================================== A driven system that is interacting with its environment is not necessarily well described by the standard Lindblad master equation, since its dissipation process could be time-dependent due to the driving. In such cases a rigorious approach would be to take the driving into account when deriving the master equation. This can be done in many different ways, but one way common approach is to derive the master equation in the Floquet basis. That approach results in the so-called Floquet-Markov master equation, see Grifoni et al., Physics Reports 304, 299 (1998) for details. For a brief summary of the derivation, the important contents for the implementation in QuTiP are listed below. The floquet mode :math:`\ket{\phi_\alpha(t)}` refers to a full class of quasienergies defined by :math:`\epsilon_\alpha + k \Omega` for arbitrary :math:`k`. Hence, the quasienenergy difference between two floquet modes is given by .. math:: \Delta_{\alpha \beta k} = \frac{\epsilon_\alpha - \epsilon_\beta}{\hbar} + k \Omega For any coupling operator :math:`q` (given by the user) the matrix elements in the floquet basis are calculated as: .. math:: X_{\alpha \beta k} = \frac{1}{T} \int_0^T dt \; e^{-ik \Omega t} \bra{\phi_\alpha(t)}q\ket{\phi_\beta(t)} From the matrix elements and the spectral density :math:`J(\omega)`, the decay rate :math:`\gamma_{\alpha \beta k}` is defined: .. math:: \gamma_{\alpha \beta k} = 2 \pi J(\Delta_{\alpha \beta k}) | X_{\alpha \beta k}|^2 The master equation is further simplified by the RWA, which makes the following matrix useful: .. math:: A_{\alpha \beta} = \sum_{k = -\infty}^\infty [\gamma_{\alpha \beta k} + n_{th}(|\Delta_{\alpha \beta k}|)(\gamma_{\alpha \beta k} + \gamma_{\alpha \beta -k}) The density matrix of the system then evolves according to: .. math:: \dot{\rho}_{\alpha \alpha}(t) = \sum_\nu (A_{\alpha \nu} \rho_{\nu \nu}(t) - A_{\nu \alpha} \rho_{\alpha \alpha} (t)) .. math:: \dot{\rho}_{\alpha \beta}(t) = -\frac{1}{2} \sum_\nu (A_{\nu \alpha} + A_{\nu \beta}) \rho_{\alpha \beta}(t) \qquad \alpha \neq \beta The Floquet-Markov master equation in QuTiP ------------------------------------------- The QuTiP function :func:`.fmmesolve` implements the Floquet-Markov master equation. It calculates the dynamics of a system given its initial state, a time-dependent Hamiltonian, a list of operators through which the system couples to its environment and a list of corresponding spectral-density functions that describes the environment. In contrast to the :func:`.mesolve` and :func:`.mcsolve`, and the :func:`.fmmesolve` does characterize the environment with dissipation rates, but extract the strength of the coupling to the environment from the noise spectral-density functions and the instantaneous Hamiltonian parameters (similar to the Bloch-Redfield master equation solver :func:`.brmesolve`). .. note:: Currently the :func:`.fmmesolve` can only accept a single environment coupling operator and spectral-density function. The noise spectral-density function of the environment is implemented as a Python callback function that is passed to the solver. For example: .. code-block:: python gamma1 = 0.1 def noise_spectrum(omega): return (omega>0) * 0.5 * gamma1 * omega/(2*pi) The other parameters are similar to the :func:`.mesolve` and :func:`.mcsolve`, and the same format for the return value is used :class:`.Result`. The following example extends the example studied above, and uses :func:`.fmmesolve` to introduce dissipation into the calculation .. plot:: guide/scripts/floquet_ex3.py :width: 4.0in :include-source: Finally, :func:`.fmmesolve` always expects the ``e_ops`` to be specified in the laboratory basis (as for other solvers) and we can calculate expectation values using: .. code-block:: python output = fmmesolve(H, psi0, tlist, [sigmax()], e_ops=[num(2)], spectra_cb=[noise_spectrum], T=T, args=args) p_ex = output.expect[0] .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-intro.rst000066400000000000000000000057231474175217300220450ustar00rootroot00000000000000.. _intro: ************ Introduction ************ Although in some cases, we want to find the stationary states of a quantum system, often we are interested in the dynamics: how the state of a system or an ensemble of systems evolves with time. QuTiP provides many ways to model dynamics. There are two kinds of quantum systems: open systems that interact with a larger environment and closed systems that do not. In a closed system, the state can be described by a state vector. When we are modeling an open system, or an ensemble of systems, the use of the density matrix is mandatory. The following table lists of the solvers QuTiP provides for dynamic quantum systems and indicates the type of object returned by the solver: .. list-table:: QuTiP Solvers :widths: 50 25 25 25 :header-rows: 1 * - Equation - Function - Class - Returns * - Unitary evolution, SchrĂśdinger equation. - :func:`~qutip.solver.sesolve.sesolve` - :obj:`~qutip.solver.sesolve.SESolver` - :obj:`~qutip.solver.result.Result` * - Periodic SchrĂśdinger equation. - :func:`~qutip.solver.floquet.fsesolve` - None - :obj:`~qutip.solver.result.Result` * - SchrĂśdinger equation using Krylov method - :func:`~qutip.solver.krylovsolve.krylovsolve` - None - :obj:`~qutip.solver.result.Result` * - Lindblad master eqn. or Von Neuman eqn. - :func:`~qutip.solver.mesolve.mesolve` - :obj:`~qutip.solver.mesolve.MESolver` - :obj:`~qutip.solver.result.Result` * - Monte Carlo evolution - :func:`~qutip.solver.mcsolve.mcsolve` - :obj:`~qutip.solver.mcsolve.MCSolver` - :obj:`~qutip.solver.multitrajresult.McResult` * - Non-Markovian Monte Carlo - :func:`~qutip.solver.nm_mcsolve.nm_mcsolve` - :obj:`~qutip.solver.nm_mcsolve.NonMarkovianMCSolver` - :obj:`~qutip.solver.multitrajresult.NmmcResult` * - Bloch-Redfield master equation - :func:`~qutip.solver.brmesolve.brmesolve` - :obj:`~qutip.solver.brmesolve.BRSolver` - :obj:`~qutip.solver.result.Result` * - Floquet-Markov master equation - :func:`~qutip.solver.floquet.fmmesolve` - :obj:`~qutip.solver.floquet.FMESolver` - :obj:`~qutip.solver.floquet.FloquetResult` * - Stochastic SchrĂśdinger equation - :func:`~qutip.solver.stochastic.ssesolve` - :obj:`~qutip.solver.stochastic.SSESolver` - :obj:`~qutip.solver.multitrajresult.MultiTrajResult` * - Stochastic master equation - :func:`~qutip.solver.stochastic.smesolve` - :obj:`~qutip.solver.stochastic.SMESolver` - :obj:`~qutip.solver.multitrajresult.MultiTrajResult` * - Transfer Tensor Method time-evolution - :func:`~qutip.solver.nonmarkov.transfertensor.ttmsolve` - None - :obj:`~qutip.solver.result.Result` * - Hierarchical Equations of Motion evolution - :func:`~qutip.solver.heom.bofin_solvers.heomsolve` - :obj:`~qutip.solver.heom.bofin_solvers.HEOMSolver` - :obj:`~qutip.solver.heom.bofin_solvers.HEOMResult` qutip-5.1.1/doc/guide/dynamics/dynamics-krylov.rst000066400000000000000000000101171474175217300222310ustar00rootroot00000000000000.. _krylov: ******************************************* Krylov Solver ******************************************* .. _krylov-intro: Introduction ============= The Krylov-subspace method is a standard method to approximate quantum dynamics. Let :math:`\left|\psi\right\rangle` be a state in a :math:`D`-dimensional complex Hilbert space that evolves under a time-independent Hamiltonian :math:`H`. Then, the :math:`N`-dimensional Krylov subspace associated with that state and Hamiltonian is given by .. math:: :label: krylovsubspace \mathcal{K}_{N}=\operatorname{span}\left\{|\psi\rangle, H|\psi\rangle, \ldots, H^{N-1}|\psi\rangle\right\}, where the dimension :math:`N>> dim = 100 >>> jx = jmat((dim - 1) / 2.0, "x") >>> jy = jmat((dim - 1) / 2.0, "y") >>> jz = jmat((dim - 1) / 2.0, "z") >>> e_ops = [jx, jy, jz] >>> H = (jz + jx) / 2 >>> psi0 = rand_ket(dim, seed=1) >>> tlist = np.linspace(0.0, 10.0, 200) >>> results = krylovsolve(H, psi0, tlist, krylov_dim=20, e_ops=e_ops) >>> plt.figure() >>> for expect in results.expect: >>> plt.plot(tlist, expect) >>> plt.legend(('jmat x', 'jmat y', 'jmat z')) >>> plt.xlabel('Time') >>> plt.ylabel('Expectation values') >>> plt.show() .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-master.rst000066400000000000000000000340341474175217300222020ustar00rootroot00000000000000.. _master: ********************************* Lindblad Master Equation Solver ********************************* .. _master-unitary: Unitary evolution ==================== The dynamics of a closed (pure) quantum system is governed by the SchrĂśdinger equation .. math:: :label: schrodinger i\hbar\frac{\partial}{\partial t}\Psi = \hat H \Psi, where :math:`\Psi` is the wave function, :math:`\hat H` the Hamiltonian, and :math:`\hbar` is Planck's constant. In general, the SchrĂśdinger equation is a partial differential equation (PDE) where both :math:`\Psi` and :math:`\hat H` are functions of space and time. For computational purposes it is useful to expand the PDE in a set of basis functions that span the Hilbert space of the Hamiltonian, and to write the equation in matrix and vector form .. math:: i\hbar\frac{d}{dt}\left|\psi\right> = H \left|\psi\right> where :math:`\left|\psi\right>` is the state vector and :math:`H` is the matrix representation of the Hamiltonian. This matrix equation can, in principle, be solved by diagonalizing the Hamiltonian matrix :math:`H`. In practice, however, it is difficult to perform this diagonalization unless the size of the Hilbert space (dimension of the matrix :math:`H`) is small. Analytically, it is a formidable task to calculate the dynamics for systems with more than two states. If, in addition, we consider dissipation due to the inevitable interaction with a surrounding environment, the computational complexity grows even larger, and we have to resort to numerical calculations in all realistic situations. This illustrates the importance of numerical calculations in describing the dynamics of open quantum systems, and the need for efficient and accessible tools for this task. The SchrĂśdinger equation, which governs the time-evolution of closed quantum systems, is defined by its Hamiltonian and state vector. In the previous section, :ref:`tensor`, we showed how Hamiltonians and state vectors are constructed in QuTiP. Given a Hamiltonian, we can calculate the unitary (non-dissipative) time-evolution of an arbitrary state vector :math:`\left|\psi_0\right>` (``psi0``) using the QuTiP solver :obj:`.SESolver` or the function :func:`.sesolve`. It evolves the state vector and evaluates the expectation values for a set of operators ``e_ops`` at the points in time in the list ``times``, using an ordinary differential equation solver. For example, the time evolution of a quantum spin-1/2 system with tunneling rate 0.1 that initially is in the up state is calculated, and the expectation values of the :math:`\sigma_z` operator evaluated, with the following code .. plot:: :context: reset >>> H = 2*np.pi * 0.1 * sigmax() >>> psi0 = basis(2, 0) >>> times = np.linspace(0.0, 10.0, 20) >>> solver = SESolver(H) >>> result = solver.run(psi0, times, e_ops=[sigmaz()]) >>> result.expect [array([ 1. , 0.78914057, 0.24548543, -0.40169579, -0.87947417, -0.98636112, -0.67728018, -0.08257665, 0.54695111, 0.94581862, 0.94581574, 0.54694361, -0.08258559, -0.67728679, -0.9863626 , -0.87946979, -0.40168705, 0.24549517, 0.78914703, 1. ])] See the next section for examples on evolution with dissipation using :func:`.mesolve`. The function returns an instance of :class:`.Result`, as described in the previous section :ref:`solver_result`. The attribute ``expect`` in ``result`` is a list of expectation values for the operator(s) that are passed to the ``e_ops`` parameter. Passing multiple operators to ``e_ops`` as a list or dict results in a vector of expectation value for each operators. ``result.e_data`` present the expectation values as a dict of list of expect outputs, while ``result.expect`` coerce the values to numpy arrays. .. plot:: :context: close-figs >>> solver.run(psi0, times, e_ops={"s_z": sigmaz(), "s_y": sigmay()}).e_data {'s_z': [1.0, 0.7891405656865187, 0.24548542861367784, -0.40169578982499127, ..., 0.24549516882108563, 0.7891470300925004, 0.9999999999361128], 's_y': [0.0, -0.6142126403681064, -0.9694002807604085, -0.9157731664756708, ..., 0.9693978141534602, 0.6142043348073879, -1.1303742482923297e-05]} The resulting expectation values can easily be visualized using matplotlib's plotting functions: .. plot:: :context: close-figs >>> H = 2*np.pi * 0.1 * sigmax() >>> psi0 = basis(2, 0) >>> times = np.linspace(0.0, 10.0, 100) >>> result = sesolve(H, psi0, times, e_ops=[sigmaz(), sigmay()]) >>> fig, ax = plt.subplots() >>> ax.plot(result.times, result.expect[0]) >>> ax.plot(result.times, result.expect[1]) >>> ax.set_xlabel('Time') >>> ax.set_ylabel('Expectation values') >>> ax.legend(("Sigma-Z", "Sigma-Y")) >>> plt.show() If an empty list of operators is passed to the ``e_ops`` parameter, the :func:`.sesolve` and :func:`.mesolve` functions return a :class:`.Result` instance that contains a list of state vectors for the times specified in ``times`` .. plot:: :context: close-figs >>> times = [0.0, 1.0] >>> result = sesolve(H, psi0, times) >>> result.states [Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[1.] [0.]], Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.80901699+0.j ] [0. -0.58778526j]]] .. _master-nonunitary: Non-unitary evolution ======================= While the evolution of the state vector in a closed quantum system is deterministic, open quantum systems are stochastic in nature. The effect of an environment on the system of interest is to induce stochastic transitions between energy levels, and to introduce uncertainty in the phase difference between states of the system. The state of an open quantum system is therefore described in terms of ensemble averaged states using the density matrix formalism. A density matrix :math:`\rho` describes a probability distribution of quantum states :math:`\left|\psi_n\right>`, in a matrix representation :math:`\rho = \sum_n p_n \left|\psi_n\right>\left<\psi_n\right|`, where :math:`p_n` is the classical probability that the system is in the quantum state :math:`\left|\psi_n\right>`. The time evolution of a density matrix :math:`\rho` is the topic of the remaining portions of this section. .. _master-master: The Lindblad Master equation ============================= The standard approach for deriving the equations of motion for a system interacting with its environment is to expand the scope of the system to include the environment. The combined quantum system is then closed, and its evolution is governed by the von Neumann equation .. math:: :label: neumann_total \dot \rho_{\rm tot}(t) = -\frac{i}{\hbar}[H_{\rm tot}, \rho_{\rm tot}(t)], the equivalent of the SchrĂśdinger equation :eq:`schrodinger` in the density matrix formalism. Here, the total Hamiltonian .. math:: H_{\rm tot} = H_{\rm sys} + H_{\rm env} + H_{\rm int}, includes the original system Hamiltonian :math:`H_{\rm sys}`, the Hamiltonian for the environment :math:`H_{\rm env}`, and a term representing the interaction between the system and its environment :math:`H_{\rm int}`. Since we are only interested in the dynamics of the system, we can at this point perform a partial trace over the environmental degrees of freedom in Eq. :eq:`neumann_total`, and thereby obtain a master equation for the motion of the original system density matrix. The most general trace-preserving and completely positive form of this evolution is the Lindblad master equation for the reduced density matrix :math:`\rho = {\rm Tr}_{\rm env}[\rho_{\rm tot}]` .. math:: :label: lindblad_master_equation \dot\rho(t)=-\frac{i}{\hbar}[H(t),\rho(t)]+\sum_n \frac{1}{2} \left[2 C_n \rho(t) C_n^\dagger - \rho(t) C_n^\dagger C_n - C_n^\dagger C_n \rho(t)\right] where the :math:`C_n = \sqrt{\gamma_n} A_n` are collapse operators, and :math:`A_n` are the operators through which the environment couples to the system in :math:`H_{\rm int}`, and :math:`\gamma_n` are the corresponding rates. The derivation of Eq. :eq:`lindblad_master_equation` may be found in several sources, and will not be reproduced here. Instead, we emphasize the approximations that are required to arrive at the master equation in the form of Eq. :eq:`lindblad_master_equation` from physical arguments, and hence perform a calculation in QuTiP: - **Separability:** At :math:`t=0` there are no correlations between the system and its environment such that the total density matrix can be written as a tensor product :math:`\rho^I_{\rm tot}(0) = \rho^I(0) \otimes \rho^I_{\rm env}(0)`. - **Born approximation:** Requires: (1) that the state of the environment does not significantly change as a result of the interaction with the system; (2) The system and the environment remain separable throughout the evolution. These assumptions are justified if the interaction is weak, and if the environment is much larger than the system. In summary, :math:`\rho_{\rm tot}(t) \approx \rho(t)\otimes\rho_{\rm env}`. - **Markov approximation** The time-scale of decay for the environment :math:`\tau_{\rm env}` is much shorter than the smallest time-scale of the system dynamics :math:`\tau_{\rm sys} \gg \tau_{\rm env}`. This approximation is often deemed a "short-memory environment" as it requires that environmental correlation functions decay on a time-scale fast compared to those of the system. - **Secular approximation** Stipulates that elements in the master equation corresponding to transition frequencies satisfy :math:`|\omega_{ab}-\omega_{cd}| \ll 1/\tau_{\rm sys}`, i.e., all fast rotating terms in the interaction picture can be neglected. It also ignores terms that lead to a small renormalization of the system energy levels. This approximation is not strictly necessary for all master-equation formalisms (e.g., the Block-Redfield master equation), but it is required for arriving at the Lindblad form :eq:`lindblad_master_equation` which is used in :func:`.mesolve`. For systems with environments satisfying the conditions outlined above, the Lindblad master equation :eq:`lindblad_master_equation` governs the time-evolution of the system density matrix, giving an ensemble average of the system dynamics. In order to ensure that these approximations are not violated, it is important that the decay rates :math:`\gamma_n` be smaller than the minimum energy splitting in the system Hamiltonian. Situations that demand special attention therefore include, for example, systems strongly coupled to their environment, and systems with degenerate or nearly degenerate energy levels. For non-unitary evolution of a quantum systems, i.e., evolution that includes incoherent processes such as relaxation and dephasing, it is common to use master equations. In QuTiP, the function :func:`.mesolve` is used for both: the evolution according to the SchrĂśdinger equation and to the master equation, even though these two equations of motion are very different. The :func:`.mesolve` function automatically determines if it is sufficient to use the SchrĂśdinger equation (if no collapse operators were given) or if it has to use the master equation (if collapse operators were given). Note that to calculate the time evolution according to the SchrĂśdinger equation is easier and much faster (for large systems) than using the master equation, so if possible the solver will fall back on using the SchrĂśdinger equation. What is new in the master equation compared to the SchrĂśdinger equation are processes that describe dissipation in the quantum system due to its interaction with an environment. These environmental interactions are defined by the operators through which the system couples to the environment, and rates that describe the strength of the processes. In QuTiP, the product of the square root of the rate and the operator that describe the dissipation process is called a collapse operator. A list of collapse operators (``c_ops``) is passed as the fourth argument to the :func:`.mesolve` function in order to define the dissipation processes in the master equation. When the ``c_ops`` isn't empty, the :func:`.mesolve` function will use the master equation instead of the unitary SchrĂśdinger equation. Using the example with the spin dynamics from the previous section, we can easily add a relaxation process (describing the dissipation of energy from the spin to its environment), by adding ``np.sqrt(0.05) * sigmax()`` in the fourth parameter to the :func:`.mesolve` function. .. plot:: :context: close-figs >>> times = np.linspace(0.0, 10.0, 100) >>> result = mesolve(H, psi0, times, [np.sqrt(0.05) * sigmax()], e_ops=[sigmaz(), sigmay()]) >>> fig, ax = plt.subplots() >>> ax.plot(times, result.expect[0]) >>> ax.plot(times, result.expect[1]) >>> ax.set_xlabel('Time') >>> ax.set_ylabel('Expectation values') >>> ax.legend(("Sigma-Z", "Sigma-Y")) >>> plt.show() Here, 0.05 is the rate and the operator :math:`\sigma_x` (:func:`.sigmax`) describes the dissipation process. Now a slightly more complex example: Consider a two-level atom coupled to a leaky single-mode cavity through a dipole-type interaction, which supports a coherent exchange of quanta between the two systems. If the atom initially is in its groundstate and the cavity in a 5-photon Fock state, the dynamics is calculated with the lines following code .. plot:: :context: close-figs >>> times = np.linspace(0.0, 10.0, 200) >>> psi0 = tensor(fock(2,0), fock(10, 5)) >>> a = tensor(qeye(2), destroy(10)) >>> sm = tensor(destroy(2), qeye(10)) >>> H = 2 * np.pi * a.dag() * a + 2 * np.pi * sm.dag() * sm + 2 * np.pi * 0.25 * (sm * a.dag() + sm.dag() * a) >>> result = mesolve(H, psi0, times, [np.sqrt(0.1)*a], e_ops=[a.dag()*a, sm.dag()*sm]) >>> plt.figure() >>> plt.plot(times, result.expect[0]) >>> plt.plot(times, result.expect[1]) >>> plt.xlabel('Time') >>> plt.ylabel('Expectation values') >>> plt.legend(("cavity photon number", "atom excitation probability")) >>> plt.show() .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-monte.rst000066400000000000000000000610501474175217300220270ustar00rootroot00000000000000.. _monte: ******************************************* Monte Carlo Solver ******************************************* .. _monte-intro: Introduction ============ Where as the density matrix formalism describes the ensemble average over many identical realizations of a quantum system, the Monte Carlo (MC), or quantum-jump approach to wave function evolution, allows for simulating an individual realization of the system dynamics. Here, the environment is continuously monitored, resulting in a series of quantum jumps in the system wave function, conditioned on the increase in information gained about the state of the system via the environmental measurements. In general, this evolution is governed by the SchrĂśdinger equation with a **non-Hermitian** effective Hamiltonian .. math:: :label: heff H_{\rm eff}=H_{\rm sys}-\frac{i\hbar}{2}\sum_{i}C^{+}_{n}C_{n}, where again, the :math:`C_{n}` are collapse operators, each corresponding to a separate irreversible process with rate :math:`\gamma_{n}`. Here, the strictly negative non-Hermitian portion of Eq. :eq:`heff` gives rise to a reduction in the norm of the wave function, that to first-order in a small time :math:`\delta t`, is given by :math:`\left<\psi(t+\delta t)|\psi(t+\delta t)\right>=1-\delta p` where .. math:: :label: jump \delta p =\delta t \sum_{n}\left<\psi(t)|C^{+}_{n}C_{n}|\psi(t)\right>, and :math:`\delta t` is such that :math:`\delta p \ll 1`. With a probability of remaining in the state :math:`\left|\psi(t+\delta t)\right>` given by :math:`1-\delta p`, the corresponding quantum jump probability is thus Eq. :eq:`jump`. If the environmental measurements register a quantum jump, say via the emission of a photon into the environment, or a change in the spin of a quantum dot, the wave function undergoes a jump into a state defined by projecting :math:`\left|\psi(t)\right>` using the collapse operator :math:`C_{n}` corresponding to the measurement .. math:: :label: project \left|\psi(t+\delta t)\right>=C_{n}\left|\psi(t)\right>/\left<\psi(t)|C_{n}^{+}C_{n}|\psi(t)\right>^{1/2}. If more than a single collapse operator is present in Eq. :eq:`heff`, the probability of collapse due to the :math:`i\mathrm{th}`-operator :math:`C_{i}` is given by .. math:: :label: pcn P_{i}(t)=\left<\psi(t)|C_{i}^{+}C_{i}|\psi(t)\right>/\delta p. Evaluating the MC evolution to first-order in time is quite tedious. Instead, QuTiP uses the following algorithm to simulate a single realization of a quantum system. Starting from a pure state :math:`\left|\psi(0)\right>`: - **Ia:** Choose a random number :math:`r_1` between zero and one, representing the probability that a quantum jump occurs. - **Ib:** Choose a random number :math:`r_2` between zero and one, used to select which collapse operator was responsible for the jump. - **II:** Integrate the SchrĂśdinger equation, using the effective Hamiltonian :eq:`heff` until a time :math:`\tau` such that the norm of the wave function satisfies :math:`\left<\psi(\tau)\right.\left|\psi(\tau)\right> = r_1`, at which point a jump occurs. - **III:** The resultant jump projects the system at time :math:`\tau` into one of the renormalized states given by Eq. :eq:`project`. The corresponding collapse operator :math:`C_{n}` is chosen such that :math:`n` is the smallest integer satisfying: .. math:: :label: mc3 \sum_{i=1}^{n} P_{n}(\tau) \ge r_2 where the individual :math:`P_{n}` are given by Eq. :eq:`pcn`. Note that the left hand side of Eq. :eq:`mc3` is, by definition, normalized to unity. - **IV:** Using the renormalized state from step III as the new initial condition at time :math:`\tau`, draw a new random number, and repeat the above procedure until the final simulation time is reached. .. _monte-qutip: Monte Carlo in QuTiP ==================== In QuTiP, Monte Carlo evolution is implemented with the :func:`.mcsolve` function. It takes nearly the same arguments as the :func:`.mesolve` function for master-equation evolution, except that the initial state must be a ket vector, as oppose to a density matrix, and there is an optional keyword parameter ``ntraj`` that defines the number of stochastic trajectories to be simulated. By default, ``ntraj=500`` indicating that 500 Monte Carlo trajectories will be performed. To illustrate the use of the Monte Carlo evolution of quantum systems in QuTiP, let's again consider the case of a two-level atom coupled to a leaky cavity. The only differences to the master-equation treatment is that in this case we invoke the :func:`.mcsolve` function instead of :func:`.mesolve` .. plot:: :context: reset times = np.linspace(0.0, 10.0, 200) psi0 = tensor(fock(2, 0), fock(10, 8)) a = tensor(qeye(2), destroy(10)) sm = tensor(destroy(2), qeye(10)) H = 2*np.pi*a.dag()*a + 2*np.pi*sm.dag()*sm + 2*np.pi*0.25*(sm*a.dag() + sm.dag()*a) data = mcsolve(H, psi0, times, [np.sqrt(0.1) * a], e_ops=[a.dag() * a, sm.dag() * sm]) plt.figure() plt.plot(times, data.expect[0], times, data.expect[1]) plt.title('Monte Carlo time evolution') plt.xlabel('Time') plt.ylabel('Expectation values') plt.legend(("cavity photon number", "atom excitation probability")) plt.show() .. guide-dynamics-mc1: The advantage of the Monte Carlo method over the master equation approach is that only the state vector is required to be kept in the computers memory, as opposed to the entire density matrix. For large quantum system this becomes a significant advantage, and the Monte Carlo solver is therefore generally recommended for such systems. For example, simulating a Heisenberg spin-chain consisting of 10 spins with random parameters and initial states takes almost 7 times longer using the master equation rather than Monte Carlo approach with the default number of trajectories running on a quad-CPU machine. Furthermore, it takes about 7 times the memory as well. However, for small systems, the added overhead of averaging a large number of stochastic trajectories to obtain the open system dynamics, as well as starting the multiprocessing functionality, outweighs the benefit of the minor (in this case) memory saving. Master equation methods are therefore generally more efficient when Hilbert space sizes are on the order of a couple of hundred states or smaller. Monte Carlo Solver Result ------------------------- The Monte Carlo solver returns a :class:`.McResult` object consisting of expectation values and/or states. The main difference with :func:`.mesolve`'s :class:`.Result` is that it optionally stores the result of each trajectory together with their averages. When trajectories are stored, ``result.runs_expect`` is a list over the expectation operators, trajectories and times in that order. The averages are stored in ``result.average_expect`` and the standard derivation of the expectation values in ``result.std_expect``. When the states are returned, ``result.runs_states`` will be an array of length ``ntraj``. Each element contains an array of "Qobj" type ket with the same number of elements as ``times``. ``result.average_states`` is a list of density matrices computed as the average of the states at each time step. Furthermore, the output will also contain a list of times at which the collapse occurred, and which collapse operators did the collapse. These can be obtained in ``result.col_times`` and ``result.col_which`` respectively. .. _monte-ntraj: Changing the Number of Trajectories ----------------------------------- By default, the ``mcsolve`` function runs 500 trajectories. This value was chosen because it gives good accuracy, Monte Carlo errors scale as :math:`1/n` where :math:`n` is the number of trajectories, and simultaneously does not take an excessive amount of time to run. However, you can change the number of trajectories to fit your needs. In order to run 1000 trajectories in the above example, we can simply modify the call to ``mcsolve`` like: .. code-block:: data = mcsolve(H, psi0, times, c_ops e_ops=e_ops, ntraj=1000) where we have added the keyword argument ``ntraj=1000`` at the end of the inputs. Now, the Monte Carlo solver will calculate expectation values for both operators, ``a.dag() * a, sm.dag() * sm`` averaging over 1000 trajectories. Other than a target number of trajectories, it is possible to use a computation time or errors bars as condition to stop computing trajectories. ``timeout`` is quite simple as ``mcsolve`` will stop starting the computation of new trajectories when it is reached. Thus: .. code-block:: data = mcsolve(H, psi0, times, [np.sqrt(0.1) * a], e_ops=e_ops, ntraj=1000, timeout=60) Will compute 60 seconds of trajectories or 1000, which ever is reached first. The solver will finish any trajectory started when the timeout is reached. Therefore if the computation time of a single trajectory is quite long, the overall computation time can be much longer that the provided timeout. Lastly, ``mcsolve`` can be instructed to stop when the statistical error of the expectation values get under a certain value. When computing the average over trajectories, the error on these are computed using `jackknife resampling `_ for each expect and each time and the computation will be stopped when all these values are under the tolerance passed to ``target_tol``. Therefore: .. code-block:: data = mcsolve(H, psi0, times, [np.sqrt(0.1) * a], e_ops=e_ops, ntraj=1000, target_tol=0.01, timeout=600) will stop either after all errors bars on expectation values are under ``0.01``, 1000 trajectories are computed or 10 minutes have passed, whichever comes first. When a single values is passed, it is used as the absolute value of the tolerance. When a pair of values is passed, it is understood as an absolute and relative tolerance pair. For even finer control, one such pair can be passed for each ``e_ops``. For example: .. code-block:: data = mcsolve(H, psi0, times, c_ops, e_ops=e_ops, target_tol=[ (1e-5, 0.1), (0, 0), ]) will stop when the error bars on the expectation values of the first ``e_ops`` are under 10% of their average values. If after computation of some trajectories, it is determined that more are needed, it is possible to add trajectories to existing result by adding result together: .. code-block:: >>> run1 = mcsolve(H, psi, times, c_ops, e_ops=e_ops, ntraj=25) >>> print(run1.num_trajectories) 25 >>> run2 = mcsolve(H, psi, times, c_ops, e_ops=e_ops, ntraj=25) >>> print(run2.num_trajectories) 25 >>> merged = run1 + run2 >>> print(merged.num_trajectories) 50 Note that this merging operation only checks that the result are compatible -- i.e. that the ``e_ops`` and ``tlist`` are the same. It does not check that the same initial state or Hamiltonian where used. This can be used to explore the convergence of the Monte Carlo solver. For example, the following code block plots expectation values for 1, 10 and 100 trajectories: .. plot:: :context: close-figs solver = MCSolver(H, c_ops=[np.sqrt(0.1) * a]) c_ops=[np.sqrt(0.1) * a] e_ops = [a.dag() * a, sm.dag() * sm] data1 = mcsolve(H, psi0, times, c_ops, e_ops=e_ops, ntraj=1) data10 = data1 + mcsolve(H, psi0, times, c_ops, e_ops=e_ops, ntraj=9) data100 = data10 + mcsolve(H, psi0, times, c_ops, e_ops=e_ops, ntraj=90) expt1 = data1.expect expt10 = data10.expect expt100 = data100.expect plt.figure() plt.plot(times, expt1[0], label="ntraj=1") plt.plot(times, expt10[0], label="ntraj=10") plt.plot(times, expt100[0], label="ntraj=100") plt.title('Monte Carlo time evolution') plt.xlabel('Time') plt.ylabel('Expectation values') plt.legend() plt.show() Mixed Initial states -------------------- The Monte-Carlo solver can be used for mixed initial states. For example, if a qubit can initially be in the excited state :math:`|+\rangle` with probability :math:`p` or in the ground state :math:`|-\rangle` with probability :math:`(1-p)`, the initial state is described by the density matrix :math:`\rho_0 = p | + \rangle\langle + | + (1-p) | - \rangle\langle - |`. In QuTiP, this initial density matrix can be created as follows: .. code-block:: ground = qutip.basis(2, 0) excited = qutip.basis(2, 1) density_matrix = p * excited.proj() + (1 - p) * ground.proj() One can then pass this density matrix directly to ``mcsolve``, as in .. code-block:: mcsolve(H, density_matrix, ...) Alternatively, using the class interface, if ``solver`` is an :class:`.MCSolver` object, one can either call ``solver.run(density_matrix, ...)`` or pass the list of initial states like .. code-block:: solver.run([(excited, p), (ground, 1-p)], ...) The number of trajectories can still be specified as a single number ``ntraj``. In that case, QuTiP will automatically decide how many trajectories to use for each of the initial states, guaranteeing that the total number of trajectories is exactly the specified number. When using the class interface and providing the initial state as a list, the `ntraj` parameter may also be a list specifying the number of trajectories to use for each state manually. In either case, the resulting :class:`McResult` will have attributes ``initial_states`` and ``ntraj_per_initial_state`` listing the initial states and the corresponding numbers of trajectories that were actually used. Note that in general, the fraction of trajectories starting in a given initial state will (and can) not exactly match the probability :math:`p` of that state in the initial ensemble. In this case, QuTiP will automatically apply a correction to the averages, weighting for example the initial states with "too few" trajectories more strongly. Therefore, the initial state returned in the result object will always match the provided one up to numerical inaccuracies. Furthermore, the result returned by the `mcsolve` call above is equivalent to the following: .. code-block:: result1 = qutip.mcsolve(H, excited, ...) result2 = qutip.mcsolve(H, ground, ...) result1.merge(result2, p) However, the single ``mcsolve`` call allows for more parallelization (see below). The Monte-Carlo solver with a mixed initial state currently does not support specifying a target tolerance. Also, in case the simulation ends early due to timeout, it is not guaranteed that all initial states have been sampled. If not all initial states have been sampled, the resulting states will not be normalized, and the result should be discarded. Finally note that what we just discussed concerns the case of mixed initial states where the provided Hamiltonian is an operator. If it is a superoperator (i.e., a Liouvillian), ``mcsolve`` will generate trajectories of mixed states (see below) and the present discussion does not apply. Using the Improved Sampling Algorithm ------------------------------------- Oftentimes, quantum jumps are rare. This is especially true in the context of simulating gates for quantum information purposes, where typical gate times are orders of magnitude smaller than typical timescales for decoherence. In this case, using the standard monte-carlo sampling algorithm, we often repeatedly sample the no-jump trajectory. We can thus reduce the number of required runs by only sampling the no-jump trajectory once. We then extract the no-jump probability :math:`p`, and for all future runs we only sample random numbers :math:`r_1` where :math:`r_1>p`, thus ensuring that a jump will occur. When it comes time to compute expectation values, we weight the no-jump trajectory by :math:`p` and the jump trajectories by :math:`1-p`. This algorithm is described in [Abd19]_ and can be utilized by setting the option ``"improved_sampling"`` in the call to ``mcsolve``: .. plot:: :context: close-figs data = mcsolve(H, psi0, times, [np.sqrt(0.1) * a], options={"improved_sampling": True}) where in this case the first run samples the no-jump trajectory, and the remaining 499 trajectories are all guaranteed to include (at least) one jump. The power of this algorithm is most obvious when considering systems that rarely undergo jumps. For instance, consider the following T1 simulation of a qubit with a lifetime of 10 microseconds (assuming time is in units of nanoseconds) .. plot:: :context: close-figs times = np.linspace(0.0, 300.0, 100) psi0 = fock(2, 1) sm = fock(2, 0) * fock(2, 1).dag() omega = 2.0 * np.pi * 1.0 H0 = -0.5 * omega * sigmaz() gamma = 1/10000 data = mcsolve( [H0], psi0, times, [np.sqrt(gamma) * sm], e_ops=[sm.dag() * sm], ntraj=100 ) data_imp = mcsolve( [H0], psi0, times, [np.sqrt(gamma) * sm], e_ops=[sm.dag() * sm], ntraj=100, options={"improved_sampling": True} ) plt.figure() plt.plot(times, data.expect[0], label="original") plt.plot(times, data_imp.expect[0], label="improved sampling") plt.plot(times, np.exp(-gamma * times), label=r"$\exp(-\gamma t)$") plt.title('Monte Carlo: improved sampling algorithm') plt.xlabel("time [ns]") plt.ylabel(r"$p_{1}$") plt.legend() plt.show() The original sampling algorithm samples the no-jump trajectory on average 96.7% of the time, while the improved sampling algorithm only does so once. .. _monte-seeds: Reproducibility --------------- For reproducibility of Monte-Carlo computations it is possible to set the seed of the random number generator: .. code-block:: >>> res1 = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, seeds=1, ntraj=1) >>> res2 = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, seeds=1, ntraj=1) >>> res3 = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, seeds=2, ntraj=1) >>> np.allclose(res1, res2) True >>> np.allclose(res1, res3) False The ``seeds`` parameter can either be an integer or a numpy ``SeedSequence``, which will then be used to create seeds for each trajectory. Alternatively it may be a list of intergers or ``SeedSequence`` s with one seed for each trajectories. Seeds available in the result object can be used to redo the same evolution: .. code-block:: >>> res1 = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, ntraj=10) >>> res2 = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, seeds=res1.seeds, ntraj=10) >>> np.allclose(res1, res2) True .. _monte-parallel: Running trajectories in parallel -------------------------------- Monte-Carlo evolutions often need hundreds of trajectories to obtain sufficient statistics. Since all trajectories are independent of each other, they can be computed in parallel. The option ``map`` can take ``"serial"``, ``"parallel"``, ``"loky"`` or ``"mpi"``. Both ``"parallel"`` and ``"loky"`` compute trajectories on multiple CPUs using respectively the `multiprocessing `_ and `loky `_ python modules. The ``"mpi"`` option is for computing trajectories in a computing cluster, see the :ref:`MPI section` below. .. code-block:: >>> res_par = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, options={"map": "parallel"}, seeds=1) >>> res_ser = mcsolve(H, psi0, tlist, c_ops, e_ops=e_ops, options={"map": "serial"}, seeds=1) >>> np.allclose(res_par.average_expect, res_ser.average_expect) True Note that when running in parallel, the order in which the trajectories are added to the result can differ. Therefore .. code-block:: >>> print(res_par.seeds[:3]) [SeedSequence(entropy=1,spawn_key=(1,),), SeedSequence(entropy=1,spawn_key=(0,),), SeedSequence(entropy=1,spawn_key=(2,),)] >>> print(res_ser.seeds[:3]) [SeedSequence(entropy=1,spawn_key=(0,),), SeedSequence(entropy=1,spawn_key=(1,),), SeedSequence(entropy=1,spawn_key=(2,),)] Photocurrent ------------ The photocurrent, previously computed using the ``photocurrent_sesolve`` and ``photocurrent_sesolve`` functions, are now included in the output of :func:`.mcsolve` as ``result.photocurrent``. .. plot:: :context: close-figs times = np.linspace(0.0, 10.0, 200) psi0 = tensor(fock(2, 0), fock(10, 8)) a = tensor(qeye(2), destroy(10)) sm = tensor(destroy(2), qeye(10)) e_ops = [a.dag() * a, sm.dag() * sm] H = 2*np.pi*a.dag()*a + 2*np.pi*sm.dag()*sm + 2*np.pi*0.25*(sm*a.dag() + sm.dag()*a) data = mcsolve(H, psi0, times, [np.sqrt(0.1) * a], e_ops=e_ops) plt.figure() plt.plot((times[:-1] + times[1:])/2, data.photocurrent[0]) plt.title('Monte Carlo Photocurrent') plt.xlabel('Time') plt.ylabel('Photon detections') plt.show() .. openmcsolve: Open Systems ------------ ``mcsolve`` can be used to study systems which have measurement and dissipative interactions with their environment. This is done by passing a Liouvillian including the dissipative interaction to the solver instead of a Hamiltonian. In this case the effective Liouvillian becomes: .. math:: :label: Leff L_{\rm eff}\rho = L_{\rm sys}\rho -\frac{1}{2}\sum_{i}\left( C^{+}_{n}C_{n}\rho + \rho C^{+}_{n}C_{n}\right), With the collapse probability becoming: .. math:: :label: L_jump \delta p =\delta t \sum_{n}\mathrm{tr}\left(\rho(t)C^{+}_{n}C_{n}\right), And a jump with the collapse operator ``n`` changing the state as: .. math:: :label: L_project \rho(t+\delta t) = C_{n} \rho(t) C^{+}_{n} / \mathrm{tr}\left( C_{n} \rho(t) C^{+}_{n} \right), We can redo the previous example for a situation where only half the emitted photons are detected. .. plot:: :context: close-figs times = np.linspace(0.0, 10.0, 200) psi0 = tensor(fock(2, 0), fock(10, 8)) a = tensor(qeye(2), destroy(10)) sm = tensor(destroy(2), qeye(10)) H = 2*np.pi*a.dag()*a + 2*np.pi*sm.dag()*sm + 2*np.pi*0.25*(sm*a.dag() + sm.dag()*a) L = liouvillian(H, [np.sqrt(0.05) * a]) data = mcsolve(L, psi0, times, [np.sqrt(0.05) * a], e_ops=[a.dag() * a, sm.dag() * sm]) plt.figure() plt.plot((times[:-1] + times[1:])/2, data.photocurrent[0]) plt.title('Monte Carlo Photocurrent') plt.xlabel('Time') plt.ylabel('Photon detections') plt.show() .. _monte-mpi: Distributed Simulations Using MPI ================================= .. adapted from the `nm_mcsolve` tutorial notebook Sometimes, many trajectories are needed to see the convergence of the trajectory average. Using QuTiP's MPI capabilities, large numbers of trajectories can be computed in parallel on multiple nodes of a computing cluster. On the QuTiP side, running Monte Carlo simulations through MPI is as easy as replacing ``"map": "parallel"`` by ``"map": "mpi"`` in the provided options. In addition, one should always provide the ``"num_cpus"`` option, which in this case specifies the number of available worker processes. The number of available worker processes is typically one less than the total number of processes assigned to the task. The call to the Monte Carlo solver might look like this (for a more detailed example, see e.g. `this tutorial notebook `_): .. code-block:: python qutip.mcsolve(H, psi0, times, c_ops, ntraj=NTRAJ, options={'store_states': True, 'progress_bar': False, 'map': 'mpi', 'num_cpus': NUM_WORKER_PROCESSES}) To invoke the MPI API, QuTiP relies on the ``MPIPoolExecutor`` class from the `mpi4py `_ module. For instructions on how to set up an environment in which an ``MPIPoolExecutor`` can successfully be created and communicate across nodes, we generally refer to the `documentation of mpi4py `_ and to your system administrator. Below, we provide an example batch script that can be submitted to a SLURM workload manager. The authors of this guide used this script to perform a parallel calculation on 500 CPUs distributed over 5 nodes of the supercomputer `HOKUSAI `_, using the `MPICH `_ implementation of the MPI standard. However, one should expect that adjustments to the script are required depending on the available MPI implementations and their versions, as well as the workload manager and its version and configuration. .. code-block:: bash #!/bin/bash #SBATCH --partition=XXXXX #SBATCH --account=XXXXX #SBATCH --nodes=5 #SBATCH --ntasks=501 #SBATCH --mem-per-cpu=1G #SBATCH --time=0-10:00 source ~/.bashrc module purge module load mpi/mpich-x86_64 conda activate qutip-environment mpirun -np $SLURM_NTASKS -bind-to core python -m mpi4py.futures XXXXX.py .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-nmmonte.rst000066400000000000000000000122251474175217300223620ustar00rootroot00000000000000.. _monte-nonmarkov: ******************************************* Monte Carlo for Non-Markovian Dynamics ******************************************* The Monte Carlo solver of QuTiP can also be used to solve the dynamics of time-local non-Markovian master equations, i.e., master equations of the Lindblad form .. math:: :label: lindblad_master_equation_with_rates \dot\rho(t) = -\frac{i}{\hbar} [H, \rho(t)] + \sum_n \frac{\gamma_n(t)}{2} \left[2 A_n \rho(t) A_n^\dagger - \rho(t) A_n^\dagger A_n - A_n^\dagger A_n \rho(t)\right] with "rates" :math:`\gamma_n(t)` that can take negative values. This can be done with the :func:`.nm_mcsolve` function. The function is based on the influence martingale formalism [Donvil22]_ and formally requires that the collapse operators :math:`A_n` satisfy a completeness relation of the form .. math:: :label: nmmcsolve_completeness \sum_n A_n^\dagger A_n = \alpha \mathbb{I} , where :math:`\mathbb{I}` is the identity operator on the system Hilbert space and :math:`\alpha>0`. Note that when the collapse operators of a model don't satisfy such a relation, ``nm_mcsolve`` automatically adds an extra collapse operator such that :eq:`nmmcsolve_completeness` is satisfied. The rate corresponding to this extra collapse operator is set to zero. Technically, the influence martingale formalism works as follows. We introduce an influence martingale :math:`\mu(t)`, which follows the evolution of the system state. When no jump happens, it evolves as .. math:: :label: influence_cont \mu(t) = \exp\left( \alpha\int_0^t K(\tau) d\tau \right) where :math:`K(t)` is for now an arbitrary function. When a jump corresponding to the collapse operator :math:`A_n` happens, the influence martingale becomes .. math:: :label: influence_disc \mu(t+\delta t) = \mu(t)\left(\frac{K(t)-\gamma_n(t)}{\gamma_n(t)}\right) Assuming that the state :math:`\bar\rho(t)` computed by the Monte Carlo average .. math:: :label: mc_paired_state \bar\rho(t) = \frac{1}{N}\sum_{l=1}^N |\psi_l(t)\rangle\langle \psi_l(t)| solves a Lindblad master equation with collapse operators :math:`A_n` and rates :math:`\Gamma_n(t)`, the state :math:`\rho(t)` defined by .. math:: :label: mc_martingale_state \rho(t) = \frac{1}{N}\sum_{l=1}^N \mu_l(t) |\psi_l(t)\rangle\langle \psi_l(t)| solves a Lindblad master equation with collapse operators :math:`A_n` and shifted rates :math:`\gamma_n(t)-K(t)`. Thus, while :math:`\Gamma_n(t) \geq 0`, the new "rates" :math:`\gamma_n(t) = \Gamma_n(t) - K(t)` satisfy no positivity requirement. The input of :func:`.nm_mcsolve` is almost the same as for :func:`.mcsolve`. The only difference is how the collapse operators and rate functions should be defined. ``nm_mcsolve`` requires collapse operators :math:`A_n` and target "rates" :math:`\gamma_n` (which are allowed to take negative values) to be given in list form ``[[C_1, gamma_1], [C_2, gamma_2], ...]``. Note that we give the actual rate and not its square root, and that ``nm_mcsolve`` automatically computes associated jump rates :math:`\Gamma_n(t)\geq0` appropriate for simulation. We conclude with a simple example demonstrating the usage of the ``nm_mcsolve`` function. For more elaborate, physically motivated examples, we refer to the `accompanying tutorial notebook `_. Note that the example also demonstrates the usage of the ``improved_sampling`` option (which is explained in the guide for the :ref:`Monte Carlo Solver`) in ``nm_mcsolve``. .. plot:: :context: reset times = np.linspace(0, 1, 201) psi0 = basis(2, 1) a0 = destroy(2) H = a0.dag() * a0 # Rate functions gamma1 = "kappa * nth" gamma2 = "kappa * (nth+1) + 12 * np.exp(-2*t**3) * (-np.sin(15*t)**2)" # gamma2 becomes negative during some time intervals # nm_mcsolve integration ops_and_rates = [] ops_and_rates.append([a0.dag(), gamma1]) ops_and_rates.append([a0, gamma2]) nm_options = {'map': 'parallel', 'improved_sampling': True} MCSol = nm_mcsolve(H, psi0, times, ops_and_rates, args={'kappa': 1.0 / 0.129, 'nth': 0.063}, e_ops=[a0.dag() * a0, a0 * a0.dag()], options=nm_options, ntraj=2500) # mesolve integration for comparison d_ops = [[lindblad_dissipator(a0.dag(), a0.dag()), gamma1], [lindblad_dissipator(a0, a0), gamma2]] MESol = mesolve(H, psi0, times, d_ops, e_ops=[a0.dag() * a0, a0 * a0.dag()], args={'kappa': 1.0 / 0.129, 'nth': 0.063}) plt.figure() plt.plot(times, MCSol.expect[0], 'g', times, MCSol.expect[1], 'b', times, MCSol.trace, 'r') plt.plot(times, MESol.expect[0], 'g--', times, MESol.expect[1], 'b--') plt.title('Monte Carlo time evolution') plt.xlabel('Time') plt.ylabel('Expectation values') plt.legend((r'$\langle 1 | \rho | 1 \rangle$', r'$\langle 0 | \rho | 0 \rangle$', r'$\operatorname{tr} \rho$')) plt.show() .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-options.rst000066400000000000000000000030511474175217300223750ustar00rootroot00000000000000.. _options: ********************************************* Setting Options for the Dynamics Solvers ********************************************* .. testsetup:: [dynamics_options] from qutip.solver.mesolve import MESolver, mesolve import numpy as np Occasionally it is necessary to change the built in parameters of the dynamics solvers used by for example the :func:`.mesolve` and :func:`.mcsolve` functions. The options for all dynamics solvers may be changed by using the dictionaries. .. testcode:: [dynamics_options] options = {"store_states": True, "atol": 1e-12} Supported items come from 2 sources, the solver and the ODE integration method. Supported solver options and their default can be seen using the class interface: .. testcode:: [dynamics_options] help(MESolver.options) Options supported by the ODE integration depend on the "method" options of the solver, they can be listed through the integrator method of the solvers: .. testcode:: [dynamics_options] help(MESolver.integrator("adams").options) See :ref:`api-ode` for a list of supported methods. As an example, let us consider changing the integrator, turn the GUI off, and strengthen the absolute tolerance. .. testcode:: [dynamics_options] options = {method="bdf", "atol": 1e-10, "progress_bar": False} To use these new settings we can use the keyword argument ``options`` in either the :func:`.mesolve` and :func:`.mcsolve` function:: >>> mesolve(H0, psi0, tlist, c_op_list, [sigmaz()], options=options) or:: >>> MCSolver(H0, c_op_list, options=options) qutip-5.1.1/doc/guide/dynamics/dynamics-propagator.rst000066400000000000000000000044571474175217300230730ustar00rootroot00000000000000.. _propagator: ********************* Computing propagators ********************* Sometime the evolution of a single state is not sufficient and the full propagator is desired. QuTiP has the :func:`.propagator` function to compute them: .. code-block:: >>> H = sigmaz() + np.pi *sigmax() >>> psi_t = sesolve(H, basis(2, 1), [0, 0.5, 1]).states >>> prop = propagator(H, [0, 0.5, 1]) >>> print((psi_t[1] - prop[1] @ basis(2, 1)).norm()) 2.455965272327082e-06 >>> print((psi_t[2] - prop[2] @ basis(2, 1)).norm()) 2.0071900004562142e-06 The first argument is the Hamiltonian, any time dependent system format is accepted. The function also accepts an optional `c_ops` argument for collapse operators. When used, a propagator for density matrices is computed: :math:`\rho(t) = U(t)(\rho(0))`: .. code-block:: >>> rho_t = mesolve(H, fock_dm(2, 1), [0, 0.5, 1], c_ops=[sigmam()]).states >>> prop = propagator(H, [0, 0.5, 1], c_ops=[sigmam()]) >>> print((rho_t[1] - prop[1](fock_dm(2, 1))).norm()) 7.23009476734681e-07 >>> print((rho_t[2] - prop[2](fock_dm(2, 1))).norm()) 1.2666967766644768e-06 The propagator function is also available as a class: .. code-block:: >>> U = Propagator(H, c_ops=[sigmam()]) >>> state_0_5 = U(0.5)(fock_dm(2, 1)) >>> state_1 = U(1., t_start=0.5)(state_0_5) >>> print((rho_t[1] - state_0_5).norm()) 7.23009476734681e-07 >>> print((rho_t[2] - state_1).norm()) 8.355518501351504e-07 The :obj:`.Propagator` can take ``options`` and ``args`` as a solver instance. .. _propagator_solver: Using a solver to compute a propagator ====================================== Many solvers accept an operator as the initial state. When an identity matrix is passed as the initial state, the propagator is computed. This can be used to compute a propagator for Bloch-Redfield or Floquet equations: .. code-block:: >>> delta = 0.2 * 2*np.pi >>> eps0 = 1.0 * 2*np.pi >>> gamma1 = 0.5 >>> H = - delta/2.0 * sigmax() - eps0/2.0 * sigmaz() >>> def ohmic_spectrum(w): >>> if w == 0.0: # dephasing inducing noise >>> return gamma1 >>> else: # relaxation inducing noise >>> return gamma1 / 2 * (w / (2 * np.pi)) * (w > 0.0) >>> prop = brmesolve(H, qeye(2), [0, 1], a_ops=[[sigmax(), ohmic_spectrum]]).final_state qutip-5.1.1/doc/guide/dynamics/dynamics-stochastic.rst000066400000000000000000000203351474175217300230520ustar00rootroot00000000000000.. _stochastic: ******************************************* Stochastic Solver ******************************************* .. _stochastic-intro: When a quantum system is subjected to continuous measurement, through homodyne detection for example, it is possible to simulate the conditional quantum state using stochastic Schrodinger and master equations. The solution of these stochastic equations are quantum trajectories, which represent the conditioned evolution of the system given a specific measurement record. In general, the stochastic evolution of a quantum state is calculated in QuTiP by solving the general equation .. math:: :label: general_form d \rho (t) = d_1 \rho \, dt + \sum_n d_{2,n} \rho \, dW_n, where :math:`dW_n` is a Wiener increment, which has the expectation values :math:`E[dW] = 0` and :math:`E[dW^2] = dt`. Stochastic Schrodinger Equation =============================== .. _sse-solver: The stochastic Schrodinger equation is given by (see section 4.4, [Wis09]_) .. math:: :label: jump_ssesolve d \psi(t) = - i H \psi(t) dt - \sum_n \left( \frac{S_n^\dagger S_n}{2} -\frac{e_n}{2} S_n + \frac{e_n^2}{8} \right) \psi(t) dt + \sum_n \left( S_n - \frac{e_n}{2} \right) \psi(t) dW_n, where :math:`H` is the Hamiltonian, :math:`S_n` are the stochastic collapse operators, and :math:`e_n` is .. math:: :label: jump_matrix_element e_n = \left<\psi(t)|S_n + S_n^\dagger|\psi(t)\right> In QuTiP, this equation can be solved using the function :func:`~qutip.solver.stochastic.ssesolve`, which is implemented by defining :math:`d_1` and :math:`d_{2,n}` from Equation :eq:`general_form` as .. math:: :label: d1_def d_1 = -iH - \frac{1}{2} \sum_n \left(S_n^\dagger S_n - e_n S_n + \frac{e_i^2}{4} \right), and .. math:: :label: d2_def d_{2, n} = S_n - \frac{e_n}{2}. The solver :func:`~qutip.solver.stochastic.ssesolve` will construct the operators :math:`d_1` and :math:`d_{2,n}` once the user passes the Hamiltonian (``H``) and the stochastic operator list (``sc_ops``). As with the :func:`~qutip.solver.mcsolve.mcsolve`, the number of trajectories and the seed for the noise realisation can be fixed using the arguments: ``ntraj`` and ``seeds``, respectively. If the user also requires the measurement output, the options entry ``{"store_measurement": True}`` should be included. Per default, homodyne is used. Heterodyne detections can be easily simulated by passing the arguments ``'heterodyne=True'`` to :func:`~qutip.solver.stochastic.ssesolve`. .. Examples of how to solve the stochastic Schrodinger equation using QuTiP can be found in this `development notebook <...TODO-Merge 61...>`_. Stochastic Master Equation ========================== .. Stochastic Master equation When the initial state of the system is a density matrix :math:`\rho`, the stochastic master equation solver :func:`qutip.stochastic.smesolve` must be used. The stochastic master equation is given by (see section 4.4, [Wis09]_) .. math:: :label: stochastic_master d \rho (t) = -i[H, \rho(t)] dt + D[A]\rho(t) dt + \mathcal{H}[A]\rho dW(t) where .. math:: :label: dissipator D[A] \rho = \frac{1}{2} \left[2 A \rho A^\dagger - \rho A^\dagger A - A^\dagger A \rho \right], and .. math:: :label: h_cal \mathcal{H}[A]\rho = A\rho(t) + \rho(t) A^\dagger - \mathrm{tr}[A\rho(t) + \rho(t) A^\dagger]. In QuTiP, solutions for the stochastic master equation are obtained using the solver :func:`~qutip.solver.stochastic.smesolve`. The implementation takes into account 2 types of collapse operators. :math:`C_i` (``c_ops``) represent the dissipation in the environment, while :math:`S_n` (``sc_ops``) are monitored operators. The deterministic part of the evolution, described by the :math:`d_1` in Equation :eq:`general_form`, takes into account all operators :math:`C_i` and :math:`S_n`: .. math:: :label: liouvillian d_1 = - i[H(t),\rho(t)] + \sum_i D[C_i]\rho + \sum_n D[S_n]\rho, The stochastic part, :math:`d_{2,n}`, is given solely by the operators :math:`S_n` .. math:: :label: stochastic_smesolve d_{2,n} = S_n \rho(t) + \rho(t) S_n^\dagger - \mathrm{tr}\left(S_n \rho (t) + \rho(t) S_n^\dagger \right)\,\rho(t). As in the stochastic Schrodinger equation, heterodyne detection can be chosen by passing ``heterodyne=True``. Example ------- Below, we solve the dynamics for an optical cavity at 0K whose output is monitored using homodyne detection. The cavity decay rate is given by :math:`\kappa` and the :math:`\Delta` is the cavity detuning with respect to the driving field. The homodyne current :math:`J_x` is calculated using .. math:: :label: measurement_result J_x = \langle x \rangle + dW / dt, where :math:`x` is the operator build from the ``sc_ops`` as .. math:: x_n = S_n + S_n^\dagger The results are available in ``result.measurement``. .. plot:: :context: reset # parameters DIM = 20 # Hilbert space dimension DELTA = 5 * 2 * np.pi # cavity detuning KAPPA = 2 # cavity decay rate INTENSITY = 4 # intensity of initial state NUMBER_OF_TRAJECTORIES = 500 # operators a = destroy(DIM) x = a + a.dag() H = DELTA * a.dag() * a rho_0 = coherent(DIM, np.sqrt(INTENSITY)) times = np.arange(0, 1, 0.0025) stoc_solution = smesolve( H, rho_0, times, c_ops=[], sc_ops=[np.sqrt(KAPPA) * a], e_ops=[x], ntraj=NUMBER_OF_TRAJECTORIES, options={"dt": 0.00125, "store_measurement": True,} ) fig, ax = plt.subplots() ax.set_title('Stochastic Master Equation - Homodyne Detection') ax.plot(times[1:], np.array(stoc_solution.measurement).mean(axis=0)[0, :].real, 'r', lw=2, label=r'$J_x$') ax.plot(times, stoc_solution.expect[0], 'k', lw=2, label=r'$\langle x \rangle$') ax.set_xlabel('Time') ax.legend() Run from known measurements =========================== In situations where instead of running multiple trajectories, we want to reproduce a single trajectory from known noise or measurements obtained in lab. In these cases, we can use :meth:`~qutip.solver.stochastic.SMESolver.run_from_experiment`. Let use the measurement output ``J_x`` of the first trajectory of the previous simulation as the input to recompute a trajectory: .. code-block:: # Create a stochastic solver instance with the some Hamiltonian as the # previous evolution. solver = SMESolver( H, sc_ops=[np.sqrt(KAPPA) * a], options={"dt": 0.00125, "store_measurement": True,} ) # Run the evolution, noise recreated_solution = solver.run_from_experiment( rho_0, tlist, stoc_solution.measurements[0], e_ops=[H], # The third parameter is the measurement, not the Wiener increment measurement=True, ) This will recompute the states, expectation values and wiener increments for that trajectory. .. note:: The measurement in the result is by default computed from the state at the end of the time step. However, when using ``run_from_experiment`` with measurement input, the state at the start of the time step is used. To obtain the measurement at the start of the time step in the output of ``smesolve``, one may use the option ``{'store_measurement': 'start'}``. For other examples on :func:`qutip.solver.stochastic.smesolve`, see the notebooks available on the `QuTiP Tutorials page `_: * `Heterodyne detection `_ * `Inefficient detection `_ .. TODO: Add back when the notebook is migrated * `Feedback control `_ The stochastic solvers share many features with :func:`.mcsolve`, such as end conditions, seed control and running in parallel. See the sections :ref:`monte-ntraj`, :ref:`monte-seeds` and :ref:`monte-parallel` for details. .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/dynamics/dynamics-time.rst000066400000000000000000000435311474175217300216470ustar00rootroot00000000000000.. _time: ************************************************* Solving Problems with Time-dependent Hamiltonians ************************************************* Time-Dependent Operators ======================== In the previous examples of quantum evolution, we assumed that the systems under consideration were described by time-independent Hamiltonians. However, many systems have explicit time dependence in either the Hamiltonian, or the collapse operators describing coupling to the environment, and sometimes both components might depend on time. The time-evolutions solvers such as :func:`.sesolve`, :func:`.brmesolve`, etc. are all capable of handling time-dependent Hamiltonians and collapse terms. QuTiP use :obj:`.QobjEvo` to represent time-dependent quantum operators. There are three different ways to build a :obj:`.QobjEvo`: 1. **Function based**: Build the time dependent operator from a function returning a :obj:`.Qobj`: .. code-block:: python def oper(t): return num(N) + (destroy(N) + create(N)) * np.sin(t) H_t = QobjEvo(oper) 1. **List based**: The time dependent quantum operator is represented as a list of ``qobj`` and ``[qobj, coefficient]`` pairs: .. code-block:: python H_t = QobjEvo([num(N), [create(N), lambda t: np.sin(t)], [destroy(N), lambda t: np.sin(t)]]) 3. **coefficent based**: The product of a :obj:`.Qobj` with a :obj:`.Coefficient`, created by the :func:`.coefficient` function, result in a :obj:`.QobjEvo`: .. code-block:: python coeff = coefficent(lambda t: np.sin(t)) H_t = num(N) + (destroy(N) + create(N)) * coeff These 3 examples will create the same time dependent operator, however the function based method will usually be slower when used in solver. Most solvers accept a :obj:`.QobjEvo` when an operator is expected: this include the Hamiltonian ``H``, collapse operators, expectation values operators, the operator of :func:`.brmesolve`'s ``a_ops``, etc. Exception are :func:`.krylovsolve`'s Hamiltonian and HEOM's Bath operators. Most solvers will accept any format that could be made into a :obj:`.QobjEvo` for the Hamiltonian. All of the following are equivalent: .. code-block:: python result = mesolve(H_t, ...) result = mesolve([num(N), [destroy(N) + create(N), lambda t: np.sin(t)]], ...) result = mesolve(oper, ...) Collapse operator also accept a list of object that could be made into :obj:`.QobjEvo`. However one needs to be careful about not confusing the list nature of the `c_ops` parameter with list format quantum system. In the following call: .. code-block:: python result = mesolve(H_t, ..., c_ops=[num(N), [destroy(N) + create(N), lambda t: np.sin(t)]]) :func:`.mesolve` will see 2 collapses operators: ``num(N)`` and ``[destroy(N) + create(N), lambda t: np.sin(t)]``. It is therefore preferred to pass each collapse operator as either a :obj:`.Qobj` or a :obj:`.QobjEvo`. As an example, we will look at a case with a time-dependent Hamiltonian of the form :math:`H=H_{0}+f(t)H_{1}` where :math:`f(t)` is the time-dependent driving strength given as :math:`f(t)=A\exp\left[-\left( t/\sigma \right)^{2}\right]`. The following code sets up the problem .. plot:: :context: reset ustate = basis(3, 0) excited = basis(3, 1) ground = basis(3, 2) N = 2 # Set where to truncate Fock state for cavity sigma_ge = tensor(qeye(N), ground * excited.dag()) # |g>u c_ops.append(np.sqrt(4*gamma/9) * sigma_ge) # 4/9 e->g t = np.linspace(-15, 15, 100) # Define time vector psi0 = tensor(basis(N, 0), ustate) # Define initial state state_GG = tensor(basis(N, 1), ground) # Define states onto which to project sigma_GG = state_GG * state_GG.dag() state_UU = tensor(basis(N, 0), ustate) sigma_UU = state_UU * state_UU.dag() g = 5 # coupling strength H0 = -g * (sigma_ge.dag() * a + a.dag() * sigma_ge) # time-independent term H1 = (sigma_ue.dag() + sigma_ue) # time-dependent term Given that we have a single time-dependent Hamiltonian term, and constant collapse terms, we need to specify a single Python function for the coefficient :math:`f(t)`. In this case, one can simply do .. plot:: :context: close-figs :nofigs: def H1_coeff(t): return 9 * np.exp(-(t / 5.) ** 2) In this case, the return value depends only on time. However it is possible to add optional arguments to the call, see `Using arguments`_. Having specified our coefficient function, we can now specify the Hamiltonian in list format and call the solver (in this case :func:`.mesolve`) .. plot:: :context: close-figs H = [H0, [H1, H1_coeff]] output = mesolve(H, psi0, t, c_ops, e_ops=[ada, sigma_UU, sigma_GG]) We can call the Monte Carlo solver in the exact same way (if using the default ``ntraj=500``): .. Hacky fix because plot has complicated conditional code execution .. doctest:: :skipif: True output = mcsolve(H, psi0, t, c_ops, e_ops=[ada, sigma_UU, sigma_GG]) The output from the master equation solver is identical to that shown in the examples, the Monte Carlo however will be noticeably off, suggesting we should increase the number of trajectories for this example. In addition, we can also consider the decay of a simple Harmonic oscillator with time-varying decay rate .. plot:: :context: close-figs kappa = 0.5 def col_coeff(t, args): # coefficient function return np.sqrt(kappa * np.exp(-t)) N = 10 # number of basis states a = destroy(N) H = a.dag() * a # simple HO psi0 = basis(N, 9) # initial state c_ops = [QobjEvo([a, col_coeff])] # time-dependent collapse term times = np.linspace(0, 10, 100) output = mesolve(H, psi0, times, c_ops, e_ops=[a.dag() * a]) Qobjevo ======= :obj:`.QobjEvo` as a time dependent quantum system, as it's main functionality create a :obj:`.Qobj` at a time: .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> print(H_t(np.pi / 2)) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=True Qobj data = [[0. 1.] [1. 1.]] :obj:`.QobjEvo` shares a lot of properties with the :obj:`.Qobj`. +----------------+------------------+----------------------------------------+ | Property | Attribute | Description | +================+==================+========================================+ | Dimensions | ``Q.dims`` | Shapes the tensor structure. | +----------------+------------------+----------------------------------------+ | Shape | ``Q.shape`` | Dimensions of underlying data matrix. | +----------------+------------------+----------------------------------------+ | Type | ``Q.type`` | Is object of type 'ket, 'bra', | | | | 'oper', or 'super'? | +----------------+------------------+----------------------------------------+ | Representation | ``Q.superrep`` | Representation used if `type` is | | | | 'super'? | +----------------+------------------+----------------------------------------+ | Is constant | ``Q.isconstant`` | Does the QobjEvo depend on time. | +----------------+------------------+----------------------------------------+ :obj:`.QobjEvo`'s follow the same mathematical operations rules than :obj:`.Qobj`. They can be added, subtracted and multiplied with scalar, ``Qobj`` and ``QobjEvo``. They also support the ``dag`` and ``trans`` and ``conj`` method and can be used for tensor operations and super operator transformation: .. code-block:: python H = tensor(H_t, qeye(2)) c_op = tensor(QobjEvo([destroy(N), lambda t: np.exp(-t)]), sigmax()) L = -1j * (spre(H) - spost(H.dag())) L += spre(c_op) * spost(c_op.dag()) - 0.5 * spre(c_op.dag() * c_op) - 0.5 * spost(c_op.dag() * c_op) Or equivalently: .. code-block:: python L = liouvillian(H, [c_op]) Using arguments --------------- Until now, the coefficients were only functions of time. In the definition of ``H1_coeff``, the driving amplitude ``A`` and width ``sigma`` were hardcoded with their numerical values. This is fine for problems that are specialized, or that we only want to run once. However, in many cases, we would like study the same problem with a range of parameters and not have to worry about manually changing the values on each run. QuTiP allows you to accomplish this using by adding extra arguments to coefficients function that make the :obj:`.QobjEvo`. For instance, instead of explicitly writing 9 for the amplitude and 5 for the width of the gaussian driving term, we can add an `args` positional variable: .. code-block:: python >>> def H1_coeff(t, args): >>> return args['A'] * np.exp(-(t/args['sigma'])**2) or, new from v5, add the extra parameter directly: .. code-block:: python >>> def H1_coeff(t, A, sigma): >>> return A * np.exp(-(t / sigma)**2) When the second positional input of the coefficient function is named ``args``, the arguments are passed as a Python dictionary of ``key: value`` pairs. Otherwise the coefficient function is called as ``coeff(t, **args)``. In the last example, ``args = {'A': a, 'sigma': b}`` where ``a`` and ``b`` are the two parameters for the amplitude and width, respectively. This ``args`` dictionary need to be given at creation of the :obj:`.QobjEvo` when function using then are included: .. code-block:: python >>> system = [sigmaz(), [sigmax(), H1_coeff]] >>> args={'A': 9, 'sigma': 5} >>> qevo = QobjEvo(system, args=args) But without ``args``, the :obj:`.QobjEvo` creation will fail: .. code-block:: python >>> QobjEvo(system) TypeError: H1_coeff() missing 2 required positional arguments: 'A' and 'sigma' When evaluation the :obj:`.QobjEvo` at a time, new arguments can be passed either with the ``args`` dictionary positional arguments, or with specific keywords arguments: .. code-block:: python >>> print(qevo(1)) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=True Qobj data = [[ 1. 8.64710495] [ 8.64710495 -1. ]] >>> print(qevo(1, {"A": 5, "sigma": 0.2})) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=True Qobj data = [[ 1.00000000e+00 6.94397193e-11] [ 6.94397193e-11 -1.00000000e+00]] >>> print(qevo(1, A=5)) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=True Qobj data = [[ 1. 4.8039472] [ 4.8039472 -1. ]] Whether the original coefficient used the ``args`` or specific input does not matter. It is fine to mix the different signatures. Solver calls take an ``args`` input that is used to build the time dependent system. If the Hamiltonian or collapse operators are already :obj:`.QobjEvo`, their arguments will be overwritten. .. code-block:: python def system(t, A, sigma): return H0 + H1 * (A * np.exp(-(t / sigma)**2)) mesolve(system, ..., args=args) To update arguments of an existing time dependent quantum system, you can pass the previous object as the input of a :obj:`.QobjEvo` with new ``args``: .. code-block:: python >>> new_qevo = QobjEvo(qevo, args={"A": 5, "sigma": 0.2}) >>> new_qevo(1) == qevo(1, {"A": 5, "sigma": 0.2}) True :obj:`.QobjEvo` created from a monolithic function can also use arguments: .. code-block:: python def oper(t, w): return num(N) + (destroy(N) + create(N)) * np.sin(t*w) H_t = QobjEvo(oper, args={"w": np.pi}) When merging two or more :obj:`.QobjEvo`, each will keep it arguments, but calling it with updated are will affect all parts: .. code-block:: python >>> qevo1 = QobjEvo([[sigmap(), lambda t, a: a]], args={"a": 1}) >>> qevo2 = QobjEvo([[sigmam(), lambda t, a: a]], args={"a": 2}) >>> summed_evo = qevo1 + qevo2 >>> print(summed_evo(0)) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=False Qobj data = [[0. 1.] [2. 0.]] >>> print(summed_evo(0, a=3, b=1)) Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', isherm=True Qobj data = [[0. 3.] [3. 0.]] Coefficients ============ To build time dependent quantum system we often use a list of :obj:`.Qobj` and :obj:`.Coefficient`. These :obj:`.Coefficient` represent the strength of the corresponding quantum object a function that of time. Up to now, we used functions for these, but QuTiP support multiple formats: ``callable``, ``strings``, ``array``. **Function coefficients** : Use a callable with the signature ``f(t: double, ...) -> double`` as coefficient. Any function or method that can be called by ``f(t, args)``, ``f(t, **args)`` is accepted. .. code-block:: python def coeff(t, A, sigma): return A * np.exp(-(t / sigma)**2) H = QobjEvo([H0, [H1, coeff]], args=args) **String coefficients** : Use a string containing a simple Python expression. The variable ``t``, common mathematical functions such as ``sin`` or ``exp`` an variable in args will be available. If available, the string will be compiled using cython, fixing variable type when possible, allowing slightly faster execution than function. While the speed up is usually very small, in long evolution, numerous calls to the functions are made and it's can accumulate. From version 5, compilation of the coefficient is done only once and saved between sessions. When either the cython or filelock modules are not available, the code will be executed in python using ``exec`` with the same environment . This, however, as no advantage over using python function. .. code-block:: python coeff = "A * exp(-(t / sigma)**2)" H = QobjEvo([H0, [H1, coeff]], args=args) Here is a list of defined variables: ``sin``, ``cos``, ``tan``, ``asin``, ``acos``, ``atan``, ``pi``, ``sinh``, ``cosh``, ``tanh``, ``asinh``, ``acosh``, ``atanh``, ``exp``, ``log``, ``log10``, ``erf``, ``zerf``, ``sqrt``, ``real``, ``imag``, ``conj``, ``abs``, ``norm``, ``arg``, ``proj``, ``np`` (numpy), ``spe`` (scipy.special) and ``cython_special`` (scipy cython interface). **Array coefficients** : Use the spline interpolation of an array. Useful when the coefficient is hard to define as a function or obtained from experimental data. The times at which the array are defined must be passed as ``tlist``: .. code-block:: python times = np.linspace(-sigma*5, sigma*5, 500) coeff = A * exp(-(times / sigma)**2) H = QobjEvo([H0, [H1, coeff]], tlist=times) Per default, a cubic spline interpolation is used, but the order of the interpolation can be controlled with the order input: Outside the interpolation range, the first or last value are used. .. plot:: :context: close-figs times = np.array([0, 0.1, 0.3, 0.6, 1.0]) coeff = times * (1.1 - times) tlist = np.linspace(-0.1, 1.1, 25) H = QobjEvo([qeye(1), coeff], tlist=times) plt.plot(tlist, [H(t).norm() for t in tlist], label="CubicSpline") H = QobjEvo([qeye(1), coeff], tlist=times, order=0) plt.plot(tlist, [H(t).norm() for t in tlist], label="step") H = QobjEvo([qeye(1), coeff], tlist=times, order=1) plt.plot(tlist, [H(t).norm() for t in tlist], label="linear") plt.legend() When using array coefficients in solver, if the time dependent quantum system is in list format, the solver tlist is used as times of the array. This is often not ideal as the interpolation is usually less precise close the extremities of the range. It is therefore better to create the QobjEvo using an extended range prior to the solver: .. plot:: :context: close-figs N = 5 times = np.linspace(-0.1, 1.1, 13) coeff = np.exp(-times) c_ops = [QobjEvo([destroy(N), coeff], tlist=times)] tlist = np.linspace(0, 1, 11) data = mesolve(qeye(N), basis(N, N-1), tlist, c_ops=c_ops, e_ops=[num(N)]).expect[0] plt.plot(tlist, data) Different coefficient types can be mixed in a :obj:`.QobjEvo`. Given the multiple choices of input style, the first question that arises is which option to choose? In short, the function based method (first option) is the most general, allowing for essentially arbitrary coefficients expressed via user defined functions. However, by automatically compiling your system into C++ code, the second option (string based) tends to be more efficient and run faster. Of course, for small system sizes and evolution times, the difference will be minor. Lastly the spline method is usually as fast the string method, but it cannot be modified once created. .. _time_max_step: Working with pulses =================== Special care is needed when working with pulses. ODE solvers select the step length automatically and can miss thin pulses when not properly warned. Integrations methods with variable step sizes have the ``max_step`` option that control the maximum length of a single internal integration step. This value should be set to under half the pulse width to be certain they are not missed. For example, the following pulse is missed without fixing the maximum step length. .. plot:: :context: close-figs def pulse(t): return 10 * np.pi * (0.7 < t < 0.75) tlist = np.linspace(0, 1, 201) H = [sigmaz(), [sigmax(), pulse]] psi0 = basis(2,1) data1 = sesolve(H, psi0, tlist, e_ops=num(2)).expect[0] data2 = sesolve(H, psi0, tlist, e_ops=num(2), options={"max_step": 0.01}).expect[0] plt.plot(tlist, data1, label="no max_step") plt.plot(tlist, data2, label="fixed max_step") plt.fill_between(tlist, [pulse(t) for t in tlist], color="g", alpha=0.2, label="pulse") plt.ylim([-0.1, 1.1]) plt.legend(loc="center left") .. plot:: :context: reset :include-source: false :nofigs: qutip-5.1.1/doc/guide/figures/000077500000000000000000000000001474175217300162015ustar00rootroot00000000000000qutip-5.1.1/doc/guide/figures/qtrl-code_object_model.png000066400000000000000000000546361474175217300233250ustar00rootroot00000000000000‰PNG  IHDRä9ĺř pHYs  šœtIMEß h}˙ IDATxÚěwxUĆß;3[˛Ůô B !D:Ą÷Ň;Hľ!˝ˆŠ ˘ˆTPŠ"EEPšAŢ{€„PCB€tŇłuĘýţŘŔîďهg™˝SrfćsÎ=÷Ą”‚Á`0Š3ƒÁ`‚Ĺ`0L° ,ƒÁ`‚Ĺ`0L° ,ƒÁ`‚Ĺ`0L° ,ƒÁ(RĚE“K—.>|řŇĽKVŤ•Yă‰888Ô¨QŁqăĆĚL°/”ž}űŽ^˝šŮĄĚ›7oôčŃĚŻ*„ ~.jTŻ^ýěŮło–+7ąaĂ2NNÇÂö']ĀY’.ßšóţ–-ńŮŮożýöňĺ˙Y˜`1 >}úüńÇÖŤ÷]ťvEf§ „:‹ˆ‹[ľjUßž}™=˜`1 ‘ăǏ׭[ˇ[HČúˇŢ‚$1ƒ€lŤŐećL{˝>33“YăՃ…EˆmŰśń7˝ysŚVĆÁÎnzóćYYY`Ö`‚Ĺ(DŽ_żŽáy7Ž™˘ŕ(JďŠœřä“O˜`1ňő˜ó;÷ӆ źý6Ńj#nÝŞ˙óĎ*Ž›Ńşu|zz“•+éŹY0™l-asžŠ .+ŤÉʕtćL˜Í yĎIY~Ý$ĚbąÔŞU+<<Üą„Ş\s˝˝;ĎĘTžĽČN“.Ǝ?~÷îÝ;wî|L/,DĽ¤ˆŠňq˝z„X,•<=ŻăŹŐf•.ŕóő××GÖj4ooŘđëůó!6œŇŹY†ÉTeŃ">ӦŌ“j4ś[˝úlB‚ŁăŇږ+÷Z™ąbŊQQQA­Şötb!őÓɖ‚Ł‹RwíÚŐ¤I“ÇŒR`I÷"ÄKœ˜!ĐĂCŻRőZˇîpl,jľ‡^Żâ8˝Z=ťeK{ÔŞŐ5/ŽËĘş>zôĺ#V…‡/>uĘYŤŃ˘…­U–ýćÍ;věŚŢ˝űnܘmąź>§oéŇĽQQQŢt¨9Ŕ™ŠŐÓB84ëîWĎţŕÁƒŰˇog‚Uԑ$éüůó/m÷˛|űŁĚ’Ônőj2iRƒĹ‹ˇ]žL)ĺ puěí E95dČö~ý\íěÜtşöAA]şžpqą5EŚÔAŁqłł -U*í‹/´Ú×ç .Y˛„W“ í$ Ëĺč´ŇĘÝ ‡Ĺ‹ł°H#ŠbHHHTT”NĽzYÇŕ¨Vď8Đ,I&QÜŐ}íÚzĽKďyçű‚$ěö햿ţša6;iľfQŹ_ŚĚý[pśł;řöŰÍůEŚ´Şˇ÷Ҏ+{y˝>'ń̙3nţj=ŻČL° ˆÎMPŰóGŽa‚U„ŁwJ[ľjĽ×땗CIŠŸ]ĆÉI+ZAč[ĽŠť]ťßĎ2óÚd™ÍĄ?ý´¸}űÁuę€ç'mß~âöí˙ü%uýüŒ_|ż':şĘ˘EWFŽ rw}Rď=ĎŽçgś!—s'‡…„EW­Úľkˇ˙ţ>ř WŻ^/ë0Ś8PqáÂT“ „€(Ęľ´4Z}Ďă#$ÇjĽ”6ňő…$)&ÓĽ¸/[“i6ĎÜż”VööۨQs˙Cąąě3žÖKXdiҤÉÁƒťté˛xńâŢ˝{żŹĂ˜ŇŹŮľ´4Ÿďž+çęęŞÓEĽŚŚ™LáC‡ <ďjg Ň÷ß˙Ţ­[i'§śŤVŐ)UjoLĚGőëňďżËNŞĺă Ň?ŹěŇeŢńăKϜŠ_ŚĚŔ”›™™ťú÷gĹYŒçŹ—É|pđŕÁŽ]ťnذáĽ;zŤ{őş’”t.!Á,IĽœšůůŮ~¨Z˛äţAƒsrĘšşŢ7n݅ ˘,Żęڕ縊eœœŢ(Qbß AI99!‰&ěş|963łÇo´+WŽM™Ŕ`‚őŠđŢ{ď-[śŹZľj/]­`Ťn”¤ňnnĺÝÜţű›˘4.[6ď{ź_rËŹdšI^QlŔN.ِ`9Ź—ĂĐĄCmjuęÔ)f ƒ VŃĺ›ožYźxqŐŞUĂÂÂň3ŕ“QŹ!˙Ŕ‡ă‰hT2o‹Ď1SŠä+ŮJé9“{ßy5‘E*[)Ż*ô`Ž´°đE3c̉'ş¸¸;vŒYăuŕäŠô胆ű—hřĆcÝo5VďëLĽgę”P$ş˙›”śÓźźr/Ód*S{w€)UŢ;;%'E`ďĆ7çńĐUž‰Ě^!Ďżl˜ Ö eůňĺ'N,[śě… ´ŻSřëL՞N•:;ń*윒\oˆŤÎM3ď¤MŠ !”ÂjT5!„đ*ä¤Čöîź­\žă ̙˛˝ť š„!Ē%ëÜɢ<. „Ę0gËzw^´PBHäć,ײęrÍUi7ŹťŚ&7ĺć¨č(qűÄÄÎsKj9N ”œ)ë=xŃDđjBeŞHEŞ˛ăcŞŹsĺe‘4D‘!š^ œ@™r…­\–×E¤TÁţďîôý­´dÍ]Ő*ëœyJĄČ”ăAx˘ˆT4SAC˜`Q6lŘđîťďşťť‡……ŮŰŰ3ƒEm *•§˛ƒ- Óč9­G’.š/mĎnňĄűďýnľĐ'D˜ł“¤š]˘,9 Ż"m§zž\ů7űâÖ,­#o1*ÍÇ{8xŤŽíɉܒĽśçLrýanîęť6Îý™}(ÇΉ7eČM?öE}ČpëŒI‘iŇe‹_}]ÉJZJ•5ífxk8“ˆMY×÷ćh9s–ÜěOW?ő֏Ę6°9d0ŚKŐz9'Fš3ă%s†Üůű’‚†üńö튝cŒŠňC:8ž\žîXBnŁ!ëŢż]w°Űľý96 ďş dú ńŔœľ=gL—ßhďÔĘáňΜk{r¨‚€FöÚ90Á*ŠěÚľŤ{÷î*•*""ÂĹĹĺĄm\]]eE1Š˘­ô‰Q0.¤¤đńń)ډ-"h8¸—ÓTË9jŸáŇöěöł˝ylŻ(4'QŠÜœŐńťœ@2n‰űžI鞨Ôé_Ó;Í)Ąuâe‘&_śäĽ¨˛“ĽŤť˛{ţ\J‘ib„ůŘŇ´ś_yš¨ýęÚ4łżúoNđűŽyJNč=J‘mÚ›ÓńŰ„CÚ ëîéÉ}~)­Ňq<7gx™3•MŁă{ţTŠđŘ3#9ö„! ‘žpĐ{ mżö6ܑ˙ţ4Áż‘=Ż&œ@(@•§Č´ö;Ž›FÇwœSB2ŃsRj˝ăę˘áŐdÝűˇšęUvĚٴŸí-hŸ:ŃŒî/‚'N´nÝÚŮŮůÚľkŢŢޏjVż~}‹,ËÄŽűxçN/˛ WQ”ęŐŤÔ!„c € ďŕ- €Fω&šiŚ Â~Ď8ýkúĺŮ†;˛9[.ßJżgfĘŮ5éąbŠvTśÉ2ăĒU´„(|Şë˛âE €˘PţaŁT/š˝[‚Ü΅ˇS† Ŕť’–ĘŕUDçÂŤ8‚–“L•á[GŔÉG…Ő¨B|„‰ă !H¸`vôVŮry„PľÔ_ܚ%™)'Ž'ŠDˇ|˜`5*žÁšěD‰pĹ@-gçüdď>ů˛•Re*-ÇŤaɒ9ŽHŜ}Ďá"œ@ÔzžĺŐ%*kĚY˛`ÇQ<ÉČrX…HlllPP$Iťwď._ž|>Żţ͛6őéÓ§áňĺ5J–ŹęíÍ­|$„ˆE’ĹĆŢČČ(_žüĄC‡^LŸFBBBĽJ•RSSç͛׳gĎ'Œ]'Íôž,•-€"çz%Š [Ď !Ě€›żÚˇŽn×ÔçŇBĘ5ků–zuem|„9>ܤ÷ŇoŠśšˇ((źTĽŞÚíř<ÉŠ”nŽýž+UŕZVž1K´ b'GSş˛ylźs'ŹŰb­w\ěœx˝ťP˘’vďŹGo!1ŇŇôcwY¤’EÉ;N[ż!ÉB Tv\ôaCô!¤\ľ6ľ×:qĽŞÚ횖l¸#Ԗ\ăŐDeÇ힞Ňh´[÷\-I÷ލÉI’8řTłS$ˆfĽ€§š˝ŐِHOO÷đđeůďż˙n׎ÝS­k6›{÷î˝oß>I’˜%ó'YDŤŐ>|ʔ)/f %K–°bŊAƒَĄdeťĆş?j>,ACdkî G8p<‘E*h‰lĄ”‚pŕ"ß­Č/„œ;’Ł— ‰Od+5eĘނ"RJq˙–LĹŢ#ˇˆ5[Q;pŠDA ¨‰1U`çĘç՚P`ĘTô^źM(y5ąmůţ#áՄĘÁşÁqoýZ*'Eâ"hUއáŽěŕ)P@‘)•Á °ä(j;ŽRđ*’“"Ű9qše<áM4§r‹™yX/”Y–÷îÝŰ´iÓ§]WŤŐnÚ´Éh4 öDÉ_ňŠsrrR˝¨éoŢźŕŔ5ĘçZ÷ߢTŹP יĘ]bĽ˙iIPP+/ÝýI‘)áĄsť§8÷oh9›ZŮňG‚QlľŠ’…Şő€ű+ăŠZ'.o;÷˙šw$ś…wKŽ ˛ăňÖ…"ÁÎůŢAP$¨´œíâ•EjçĚŮŢöŻ"ł°Č™™Yž|ů¤¤¤… @­ňĐét:ŽŮł¨qâĉ:uę‚°yóćüŤŐ3Aóąä…@ŘĚ^‘^ÚC” Öó§zőęIIIK—.}ď˝÷˜5^1>ܰaCžç?^ŁF×íϧ ŞôpĘóŕ^‚+Í.Áçv.)PĽJ•čččůóç3ľzőŘźysăƍííí###_Cľ*ą?3ÁóB–ĺzőꅇ‡7nřđáĚ ŻŤV­ęÜšłłłóéÓ§óŮçË`‚UtéĐĄĂącÇ&Nœříˇß2kźb̚5Ť˙ţćŇĽKÁÁÁĚ L°Š7íھ۹cÇťďž;mÚ4fWŒ/żüňÓO? 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'""R|6“ŹC]Ą6łr3k6łĄłd‹Jľd•ťˇšű€j’Ç›~üŻ™]¨r?1ž°DDJH´…:̀@eč ŮSŠŽIoRÜ}‡ťšäIeÍ$#Řż#Y%ä"•ëźˆî„%"R"b/ÔQŠŚTť{­ť×†Î!]š{đ’őŹ›s€€ föe•k‘.T¨‹T4ĽZ —ťr÷%Ŕ‡k?g+€?™Ů?™™FSE$„6’+j—†"‚ uQSŠ–źq÷wÜýg$ĺúj`0¸xŮĚLO 2§ˆ”ŽôęEuî~č,Rň´ĘG‘SŠ–źs÷wż | X 8đ’Š!{ÍěV3ű¤ śˆˆ”€LĄŢ:Hž¸{ 0:Kś¨TK0îŢîî˙éîŁ€ë€ŔŠŔ5ŔŔA3ű/3ű–™M13ýŸíĽOX""zŽ+ÔîŢěîűBçȖăBČ3Ťp÷ËÂ&‘ţp÷ýŔ­Ŕ­föq’5Ž?M˛4ßgŇŔ3[ 4ŰŇ[Łťˇç?uás÷ćĐDD¤Gϑ̡.šB#s÷вÂĚŔÝľšDDĚl0¸ ˝ífˇwüĽdďŢŢL˙xäĎßÉyčŇăőőőo ż[ÉžÖT*5Ä̆„"ń¨ŻŻ‡Â8_ŠPG&š‘j‰Sú˛Đňô†™}„äqč“HnrœœNňhôł€™A‚–śV`Xč'3 C˘rBč¨PGIĽZŠŠťď •>ĚĚNÎ$)Řg*z؆<E˛§%t‰Z'ÉŐ§\1ŕ4’›Ľ_ÉáqD2T¨#ĽR-EĎÝқĐĐĐ Ëó’îţ&9|*hzjÉ;@›ťk˝üř|ĽBffĺŔ. ĹÝÇŽ“*Ő"‘Šń„%"RÄT¨ť2`ÉÂ(ÄTŞkB)0ѝ°DDŠ” u ˆŚTť{mč """"ďąę’MŠé‡6`.Đ:ˆDI…ş„¨T‹ˆHÉr÷N .t‰RŚPkU™ĄR-"""’]*ÔÇŕî-f6’d9Ë(¨T‹D*Ć–ˆHPĄî%wo!›˘)ŐfV ŕM"R8b;a‰ˆ8ę6(t€,šŸŢDDDDňM…şÄĹTŞEDDúÄĚ›Y™Ý:‹5jQŠ‘’VĚf…"EëO¨P *Ő""""ýő'`ş uߙYš™5›ŮÎĐY˛%šE¤+3+v-î>6p‘بPŒ#€ÖĐA˛%ŚR]:€H‰î„%"R T¨ĺ(єjwŻ ADDD˘§9ÔŇ­hJľˆˆH?´sŽĐA¤(d őžĐA¤đ¨T‹ˆHÉr÷N .t) *ÔňžTŞEDDDޟ u–š{‹™` for more information. .. note:: If you are running QuTiP from a python script you must use the :func:`print` function to view the Qobj attributes. .. _basics-qobj-states: States and operators --------------------- Manually specifying the data for each quantum object is inefficient. Even more so when most objects correspond to commonly used types such as the ladder operators of a harmonic oscillator, the Pauli spin operators for a two-level system, or state vectors such as Fock states. Therefore, QuTiP includes predefined objects for a variety of states and operators: .. cssclass:: table-striped +--------------------------+----------------------------------+----------------------------------------+ | States | Command (# means optional) | Inputs | +==========================+==================================+========================================+ | Fock state ket vector | ``basis(N,#m)``/``fock(N,#m)`` | N = number of levels in Hilbert space, | | | | m = level containing excitation | | | | (0 if no m given) | +--------------------------+----------------------------------+----------------------------------------+ | Empty ket vector | ``zero_ket(N)`` | N = number of levels in Hilbert space, | +--------------------------+----------------------------------+----------------------------------------+ | Fock density matrix | ``fock_dm(N,#p)`` | same as basis(N,m) / fock(N,m) | | (outer product of basis) | | | +--------------------------+----------------------------------+----------------------------------------+ | Coherent state | ``coherent(N,alpha)`` | alpha = complex number (eigenvalue) | | | | for requested coherent state | +--------------------------+----------------------------------+----------------------------------------+ | Coherent density matrix | ``coherent_dm(N,alpha)`` | same as coherent(N,alpha) | | (outer product) | | | +--------------------------+----------------------------------+----------------------------------------+ | Thermal density matrix | ``thermal_dm(N,n)`` | n = particle number expectation value | | (for n particles) | | | +--------------------------+----------------------------------+----------------------------------------+ | Maximally mixed density | ``maximally_mixed_dm(N)`` | N = number of levels in Hilbert space | | matrix | | | +--------------------------+----------------------------------+----------------------------------------+ .. cssclass:: table-striped +--------------------------+----------------------------+----------------------------------------+ | Operators | Command (# means optional) | Inputs | +==========================+============================+========================================+ | Charge operator | ``charge(N,M=-N)`` | Diagonal operator with entries | | | | from M..0..N. | +--------------------------+----------------------------+----------------------------------------+ | Commutator | ``commutator(A, B, kind)`` | Kind = 'normal' or 'anti'. | +--------------------------+----------------------------+----------------------------------------+ | Diagonals operator | ``qdiags(N)`` | Quantum object created from arrays of | | | | diagonals at given offsets. | +--------------------------+----------------------------+----------------------------------------+ | Displacement operator | ``displace(N,alpha)`` | N=number of levels in Hilbert space, | | (Single-mode) | | alpha = complex displacement amplitude.| +--------------------------+----------------------------+----------------------------------------+ | Higher spin operators | ``jmat(j,#s)`` | j = integer or half-integer | | | | representing spin, s = 'x', 'y', 'z', | | | | '+', or '-' | +--------------------------+----------------------------+----------------------------------------+ | Identity | ``qeye(N)`` | N = number of levels in Hilbert space. | +--------------------------+----------------------------+----------------------------------------+ | Identity-like | ``qeye_like(qobj)`` | qobj = Object to copy dimensions from. | +--------------------------+----------------------------+----------------------------------------+ | Lowering (destruction) | ``destroy(N)`` | same as above | | operator | | | +--------------------------+----------------------------+----------------------------------------+ | Momentum operator | ``momentum(N)`` | same as above | +--------------------------+----------------------------+----------------------------------------+ | Number operator | ``num(N)`` | same as above | +--------------------------+----------------------------+----------------------------------------+ | Phase operator | ``phase(N, phi0)`` | Single-mode Pegg-Barnett phase | | (Single-mode) | | operator with ref phase phi0. | +--------------------------+----------------------------+----------------------------------------+ | Position operator | ``position(N)`` | same as above | +--------------------------+----------------------------+----------------------------------------+ | Raising (creation) | ``create(N)`` | same as above | | operator | | | +--------------------------+----------------------------+----------------------------------------+ | Squeezing operator | ``squeeze(N, sp)`` | N=number of levels in Hilbert space, | | (Single-mode) | | sp = squeezing parameter. | +--------------------------+----------------------------+----------------------------------------+ | Squeezing operator | ``squeezing(q1, q2, sp)`` | q1,q2 = Quantum operators (Qobj) | | (Generalized) | | sp = squeezing parameter. | +--------------------------+----------------------------+----------------------------------------+ | Sigma-X | ``sigmax()`` | | +--------------------------+----------------------------+----------------------------------------+ | Sigma-Y | ``sigmay()`` | | +--------------------------+----------------------------+----------------------------------------+ | Sigma-Z | ``sigmaz()`` | | +--------------------------+----------------------------+----------------------------------------+ | Sigma plus | ``sigmap()`` | | +--------------------------+----------------------------+----------------------------------------+ | Sigma minus | ``sigmam()`` | | +--------------------------+----------------------------+----------------------------------------+ | Tunneling operator | ``tunneling(N,m)`` | Tunneling operator with elements of the| | | | form :math:`|N>>> basis(5,3) Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [0.] [1.] [0.]] >>> coherent(5,0.5-0.5j) Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[ 0.7788017 +0.j ] [ 0.38939142-0.38939142j] [ 0. -0.27545895j] [-0.07898617-0.07898617j] [-0.04314271+0.j ]] >>> destroy(4) Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False Qobj data = [[0. 1. 0. 0. ] [0. 0. 1.41421356 0. ] [0. 0. 0. 1.73205081] [0. 0. 0. 0. ]] >>> sigmaz() Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[ 1. 0.] [ 0. -1.]] >>> jmat(5/2.0,'+') Quantum object: dims = [[6], [6]], shape = (6, 6), type = oper, isherm = False Qobj data = [[0. 2.23606798 0. 0. 0. 0. ] [0. 0. 2.82842712 0. 0. 0. ] [0. 0. 0. 3. 0. 0. ] [0. 0. 0. 0. 2.82842712 0. ] [0. 0. 0. 0. 0. 2.23606798] [0. 0. 0. 0. 0. 0. ]] .. _basics-qobj-props: Qobj attributes --------------- We have seen that a quantum object has several internal attributes, such as data, dims, and shape. These can be accessed in the following way: .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> q = destroy(4) >>> q.dims [[4], [4]] >>> q.shape (4, 4) In general, the attributes (properties) of a ``Qobj`` object (or any Python object) can be retrieved using the `Q.attribute` notation. In addition to the those shown with the ``print`` function, an instance of the ``Qobj`` class also has the following attributes: .. cssclass:: table-striped +---------------+---------------+----------------------------------------+ | Property | Attribute | Description | +===============+===============+========================================+ | Data | ``Q.data`` | Matrix representing state or operator | +---------------+---------------+----------------------------------------+ | Dimensions | ``Q.dims`` | List keeping track of shapes for | | | | individual components of a | | | | multipartite system (for tensor | | | | products and partial traces). | +---------------+---------------+----------------------------------------+ | Shape | ``Q.shape`` | Dimensions of underlying data matrix. | +---------------+---------------+----------------------------------------+ | is Hermitian? | ``Q.isherm`` | Is the operator Hermitian or not? | +---------------+---------------+----------------------------------------+ | Type | ``Q.type`` | Is object of type 'ket, 'bra', | | | | 'oper', or 'super'? | +---------------+---------------+----------------------------------------+ .. figure:: quide-basics-qobj-box.png :align: center :width: 3.5in The ``Qobj`` Class viewed as a container for the properties needed to characterize a quantum operator or state vector. For the destruction operator above: .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> q.type 'oper' >>> q.isherm False >>> q.data Dia(shape=(4, 4), num_diag=1) The ``data`` attribute returns a Qutip diagonal matrix. ``Qobj`` instances store their data in Qutip matrix format. In the core qutip module, the ``Dense``, ``CSR`` and ``Dia`` formats are available, but other packages can add other formats. For example, the ``qutip-jax`` module adds the ``Jax`` and ``JaxDia`` formats. One can always access the underlying matrix as a numpy array using :meth:`.Qobj.full`. It is also possible to access the underlying data in a common format using :meth:`.Qobj.data_as`. .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> q.data_as("dia_matrix") <4x4 sparse matrix of type '' with 3 stored elements (1 diagonals) in DIAgonal format> Conversion between storage type is done using the :meth:`.Qobj.to` method. .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> q.to("CSR").data CSR(shape=(4, 4), nnz=3) >>> q.to("CSR").data_as("csr_matrix") <4x4 sparse matrix of type '' with 3 stored elements in Compressed Sparse Row format> Note that :meth:`.Qobj.data_as` does not do the conversion. QuTiP will do conversion when needed to keep everything working in any format. However these conversions could slow down computation and it is recommended to keep to one format family where possible. For example, core QuTiP ``Dense`` and ``CSR`` work well together and binary operations between these formats is efficient. However binary operations between ``Dense`` and ``Jax`` should be avoided since it is not always clear whether the operation will be executed by Jax (possibly on a GPU if present) or numpy. .. _basics-qobj-math: Qobj Math ---------- The rules for mathematical operations on ``Qobj`` instances are similar to standard matrix arithmetic: .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> q = destroy(4) >>> x = sigmax() >>> q + 5 Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False Qobj data = [[5. 1. 0. 0. ] [0. 5. 1.41421356 0. ] [0. 0. 5. 1.73205081] [0. 0. 0. 5. ]] >>> x * x Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[1. 0.] [0. 1.]] >>> q ** 3 Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False Qobj data = [[0. 0. 0. 2.44948974] [0. 0. 0. 0. ] [0. 0. 0. 0. ] [0. 0. 0. 0. ]] >>> x / np.sqrt(2) Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.70710678] [0.70710678 0. ]] Of course, like matrices, multiplying two objects of incompatible shape throws an error: .. doctest:: [basics] :options: +SKIP >>> print(q * x) ------------------------------------------------------------------ TypeError Traceback (most recent call last) in ----> 1 print(q * x) ~/Documents/qutip_dev/qutip/qutip/qobj.py in __mul__(self, other) 553 554 else: --> 555 raise TypeError("Incompatible Qobj shapes") 556 557 elif isinstance(other, np.ndarray): TypeError: Incompatible Qobj shapes In addition, the logic operators "is equal" `==` and "is not equal" `!=` are also supported. .. _basics-functions: Functions operating on Qobj class ================================= Like attributes, the quantum object class has defined functions (methods) that operate on ``Qobj`` class instances. For a general quantum object ``Q``: .. cssclass:: table-striped +-----------------+-------------------------------+----------------------------------------+ | Function | Command | Description | +=================+===============================+========================================+ | Check Hermicity | ``Q.check_herm()`` | Check if quantum object is Hermitian | +-----------------+-------------------------------+----------------------------------------+ | Conjugate | ``Q.conj()`` | Conjugate of quantum object. | +-----------------+-------------------------------+----------------------------------------+ | Cosine | ``Q.cosm()`` | Cosine of quantum object. | +-----------------+-------------------------------+----------------------------------------+ | Dagger (adjoint)| ``Q.dag()`` | Returns adjoint (dagger) of object. | +-----------------+-------------------------------+----------------------------------------+ | Diagonal | ``Q.diag()`` | Returns the diagonal elements. | +-----------------+-------------------------------+----------------------------------------+ | Diamond Norm | ``Q.dnorm()`` | Returns the diamond norm. | +-----------------+-------------------------------+----------------------------------------+ | Eigenenergies | ``Q.eigenenergies()`` | Eigenenergies (values) of operator. | +-----------------+-------------------------------+----------------------------------------+ | Eigenstates | ``Q.eigenstates()`` | Returns eigenvalues and eigenvectors. | +-----------------+-------------------------------+----------------------------------------+ | Exponential | ``Q.expm()`` | Matrix exponential of operator. | +-----------------+-------------------------------+----------------------------------------+ | Full | ``Q.full()`` | Returns full (not sparse) array of | | | | Q's data. | +-----------------+-------------------------------+----------------------------------------+ | Groundstate | ``Q.groundstate()`` | Eigenval & eigket of Qobj groundstate. | +-----------------+-------------------------------+----------------------------------------+ | Matrix inverse | ``Q.inv()`` | Matrix inverse of the Qobj. | +-----------------+-------------------------------+----------------------------------------+ | Matrix Element | ``Q.matrix_element(bra,ket)`` | Matrix element | +-----------------+-------------------------------+----------------------------------------+ | Norm | ``Q.norm()`` | Returns L2 norm for states, | | | | trace norm for operators. | +-----------------+-------------------------------+----------------------------------------+ | Overlap | ``Q.overlap(state)`` | Overlap between current Qobj and a | | | | given state. | +-----------------+-------------------------------+----------------------------------------+ | Partial Trace | ``Q.ptrace(sel)`` | Partial trace returning components | | | | selected using 'sel' parameter. | +-----------------+-------------------------------+----------------------------------------+ | Permute | ``Q.permute(order)`` | Permutes the tensor structure of a | | | | composite object in the given order. | +-----------------+-------------------------------+----------------------------------------+ | Projector | ``Q.proj()`` | Form projector operator from given | | | | ket or bra vector. | +-----------------+-------------------------------+----------------------------------------+ | Sine | ``Q.sinm()`` | Sine of quantum operator. | +-----------------+-------------------------------+----------------------------------------+ | Sqrt | ``Q.sqrtm()`` | Matrix sqrt of operator. | +-----------------+-------------------------------+----------------------------------------+ | Tidyup | ``Q.tidyup()`` | Removes small elements from Qobj. | +-----------------+-------------------------------+----------------------------------------+ | Trace | ``Q.tr()`` | Returns trace of quantum object. | +-----------------+-------------------------------+----------------------------------------+ | Conversion | ``Q.to(dtype)`` | Convert the matrix format CSR / Dense. | +-----------------+-------------------------------+----------------------------------------+ | Transform | ``Q.transform(inpt)`` | A basis transformation defined by | | | | matrix or list of kets 'inpt' . | +-----------------+-------------------------------+----------------------------------------+ | Transpose | ``Q.trans()`` | Transpose of quantum object. | +-----------------+-------------------------------+----------------------------------------+ | Truncate Neg | ``Q.trunc_neg()`` | Truncates negative eigenvalues | +-----------------+-------------------------------+----------------------------------------+ | Unit | ``Q.unit()`` | Returns normalized (unit) | | | | vector Q/Q.norm(). | +-----------------+-------------------------------+----------------------------------------+ .. doctest:: [basics] :options: +NORMALIZE_WHITESPACE >>> basis(5, 3) Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [0.] [1.] [0.]] >>> basis(5, 3).dag() Quantum object: dims = [[1], [5]], shape = (1, 5), type = bra Qobj data = [[0. 0. 0. 1. 0.]] >>> coherent_dm(5, 1) Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0.36791117 0.36774407 0.26105441 0.14620658 0.08826704] [0.36774407 0.36757705 0.26093584 0.14614018 0.08822695] [0.26105441 0.26093584 0.18523331 0.10374209 0.06263061] [0.14620658 0.14614018 0.10374209 0.05810197 0.035077 ] [0.08826704 0.08822695 0.06263061 0.035077 0.0211765 ]] >>> coherent_dm(5, 1).diag() array([0.36791117, 0.36757705, 0.18523331, 0.05810197, 0.0211765 ]) >>> coherent_dm(5, 1).full() array([[0.36791117+0.j, 0.36774407+0.j, 0.26105441+0.j, 0.14620658+0.j, 0.08826704+0.j], [0.36774407+0.j, 0.36757705+0.j, 0.26093584+0.j, 0.14614018+0.j, 0.08822695+0.j], [0.26105441+0.j, 0.26093584+0.j, 0.18523331+0.j, 0.10374209+0.j, 0.06263061+0.j], [0.14620658+0.j, 0.14614018+0.j, 0.10374209+0.j, 0.05810197+0.j, 0.035077 +0.j], [0.08826704+0.j, 0.08822695+0.j, 0.06263061+0.j, 0.035077 +0.j, 0.0211765 +0.j]]) >>> coherent_dm(5, 1).norm() 1.0000000175063126 >>> coherent_dm(5, 1).sqrtm() Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = False Qobj data = [[0.36791117+3.66778589e-09j 0.36774407-2.13388761e-09j 0.26105441-1.51480558e-09j 0.14620658-8.48384618e-10j 0.08826704-5.12182118e-10j] [0.36774407-2.13388761e-09j 0.36757705+2.41479965e-09j 0.26093584-1.11446422e-09j 0.14614018+8.98971115e-10j 0.08822695+6.40705133e-10j] [0.26105441-1.51480558e-09j 0.26093584-1.11446422e-09j 0.18523331+4.02032413e-09j 0.10374209-3.39161017e-10j 0.06263061-3.71421368e-10j] [0.14620658-8.48384618e-10j 0.14614018+8.98971115e-10j 0.10374209-3.39161017e-10j 0.05810197+3.36300708e-10j 0.035077 +2.36883273e-10j] [0.08826704-5.12182118e-10j 0.08822695+6.40705133e-10j 0.06263061-3.71421368e-10j 0.035077 +2.36883273e-10j 0.0211765 +1.71630348e-10j]] >>> coherent_dm(5, 1).tr() 1.0 >>> (basis(4, 2) + basis(4, 1)).unit() Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket Qobj data = [[0. ] [0.70710678] [0.70710678] [0. ]] qutip-5.1.1/doc/guide/guide-bloch.rst000066400000000000000000000400361474175217300174540ustar00rootroot00000000000000.. _bloch: ****************************** Plotting on the Bloch Sphere ****************************** .. _bloch-intro: Introduction ============ When studying the dynamics of a two-level system, it is often convenient to visualize the state of the system by plotting the state-vector or density matrix on the Bloch sphere. In QuTiP, there is a class to allow for easy creation and manipulation of data sets, both vectors and data points, on the Bloch sphere. .. _bloch-class: The Bloch Class =============== In QuTiP, creating a Bloch sphere is accomplished by calling either: .. plot:: :context: reset b = qutip.Bloch() which will load an instance of the :class:`~qutip.bloch.Bloch` class. Before getting into the details of these objects, we can simply plot the blank Bloch sphere associated with these instances via: .. plot:: :context: b.render() In addition to the ``show`` command, see the API documentation for :class:`~qutip.bloch.Bloch` for a full list of other available functions. As an example, we can add a single data point: .. plot:: :context: close-figs pnt = [1/np.sqrt(3), 1/np.sqrt(3), 1/np.sqrt(3)] b.add_points(pnt) b.render() and then a single vector: .. plot:: :context: close-figs b.fig.clf() vec = [0, 1, 0] b.add_vectors(vec) b.render() and then add another vector corresponding to the :math:`\left|\rm up \right>` state: .. plot:: :context: close-figs up = qutip.basis(2, 0) b.add_states(up) b.render() Notice that when we add more than a single vector (or data point), a different color will automatically be applied to the later data set (mod 4). In total, the code for constructing our Bloch sphere with one vector, one state, and a single data point is: .. plot:: :context: close-figs b = qutip.Bloch() pnt = [1./np.sqrt(3), 1./np.sqrt(3), 1./np.sqrt(3)] b.add_points(pnt) vec = [0, 1, 0] b.add_vectors(vec) up = qutip.basis(2, 0) b.add_states(up) b.render() where we have removed the extra ``show()`` commands. We can also plot multiple points, vectors, and states at the same time by passing list or arrays instead of individual elements. Before giving an example, we can use the `clear()` command to remove the current data from our Bloch sphere instead of creating a new instance: .. plot:: :context: close-figs b.clear() b.render() Now on the same Bloch sphere, we can plot the three states associated with the x, y, and z directions: .. plot:: :context: close-figs x = (qutip.basis(2, 0) + (1+0j)*qutip.basis(2, 1)).unit() y = (qutip.basis(2, 0) + (0+1j)*qutip.basis(2, 1)).unit() z = (qutip.basis(2, 0) + (0+0j)*qutip.basis(2, 1)).unit() b.add_states([x, y, z]) b.render() a similar method works for adding vectors: .. plot:: :context: close-figs b.clear() vec = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] b.add_vectors(vec) b.render() You can also add lines and arcs: .. plot:: :context: close-figs b.add_line(x, y) b.add_arc(y, z) b.render() Adding multiple points to the Bloch sphere works slightly differently than adding multiple states or vectors. For example, lets add a set of 20 points around the equator (after calling `clear()`): .. plot:: :context: close-figs b.clear() th = np.linspace(0, 2*np.pi, 20) xp = np.cos(th) yp = np.sin(th) zp = np.zeros(20) pnts = [xp, yp, zp] b.add_points(pnts) b.render() Notice that, in contrast to states or vectors, each point remains the same color as the initial point. This is because adding multiple data points using the ``add_points`` function is interpreted, by default, to correspond to a single data point (single qubit state) plotted at different times. This is very useful when visualizing the dynamics of a qubit. An example of this is given in the example . If we want to plot additional qubit states we can call additional ``add_points`` functions: .. plot:: :context: close-figs xz = np.zeros(20) yz = np.sin(th) zz = np.cos(th) b.add_points([xz, yz, zz]) b.render() The color and shape of the data points is varied automatically by the Bloch class. Notice how the color and point markers change for each set of data. Again, we have had to call ``add_points`` twice because adding more than one set of multiple data points is *not* supported by the ``add_points`` function. What if we want to vary the color of our points. We can tell the :class:`qutip.bloch.Bloch` class to vary the color of each point according to the colors listed in the ``b.point_color`` list (see :ref:`bloch-config` below). Again after ``clear()``: .. plot:: :context: close-figs b.clear() xp = np.cos(th) yp = np.sin(th) zp = np.zeros(20) pnts = [xp, yp, zp] b.add_points(pnts, 'm') # <-- add a 'm' string to signify 'multi' colored points b.render() Now, the data points cycle through a variety of predefined colors. Now lets add another set of points, but this time we want the set to be a single color, representing say a qubit going from the :math:`\left|\rm up\right>` state to the :math:`\left|\rm down\right>` state in the y-z plane: .. plot:: :context: close-figs xz = np.zeros(20) yz = np.sin(th) zz = np.cos(th) b.add_points([xz, yz, zz]) # no 'm' b.render() A more slick way of using this 'multi' color feature is also given in the example, where we set the color of the markers as a function of time. .. _bloch-config: Configuring the Bloch sphere ============================ Bloch Class Options -------------------- At the end of the last section we saw that the colors and marker shapes of the data plotted on the Bloch sphere are automatically varied according to the number of points and vectors added. But what if you want a different choice of color, or you want your sphere to be purple with different axes labels? Well then you are in luck as the Bloch class has 22 attributes which one can control. Assuming ``b=Bloch()``: .. tabularcolumns:: | p{3cm} | p{7cm} | p{7cm} | .. cssclass:: table-striped +---------------+---------------------------------------------------------+-------------------------------------------------+ | Attribute | Function | Default Setting | +===============+=========================================================+=================================================+ | b.axes | Matplotlib axes instance for animations. Set by ``axes``| ``None`` | | | keyword arg. | | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.fig | User supplied Matplotlib Figure instance. Set by ``fig``| ``None`` | | | keyword arg. | | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.font_color | Color of fonts | 'black' | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.font_size | Size of fonts | 20 | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.frame_alpha | Transparency of wireframe | 0.1 | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.frame_color | Color of wireframe | 'gray' | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.frame_width | Width of wireframe | 1 | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.point_color | List of colors for Bloch point markers to cycle through | ``['b', 'r', 'g', '#CC6600']`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.point_marker| List of point marker shapes to cycle through | ``['o', 's', 'd', '^']`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.point_size | List of point marker sizes (not all markers look the | ``[55, 62, 65, 75]`` | | | same size when plotted) | | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.sphere_alpha| Transparency of Bloch sphere | 0.2 | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.sphere_color| Color of Bloch sphere | ``'#FFDDDD'`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.size | Sets size of figure window | ``[7, 7]`` (700x700 pixels) | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.vector_color| List of colors for Bloch vectors to cycle through | ``['g', '#CC6600', 'b', 'r']`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.vector_width| Width of Bloch vectors | 4 | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.view | Azimuthal and Elevation viewing angles | ``[-60,30]`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.xlabel | Labels for x-axis | ``['$x$', '']`` +x and -x (labels use LaTeX) | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.xlpos | Position of x-axis labels | ``[1.1, -1.1]`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.ylabel | Labels for y-axis | ``['$y$', '']`` +y and -y (labels use LaTeX) | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.ylpos | Position of y-axis labels | ``[1.2, -1.2]`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.zlabel | Labels for z-axis | ``['$\left|0\right>$', '$\left|1\right>$']`` | | | | +z and -z (labels use LaTeX) | +---------------+---------------------------------------------------------+-------------------------------------------------+ | b.zlpos | Position of z-axis labels | ``[1.2, -1.2]`` | +---------------+---------------------------------------------------------+-------------------------------------------------+ These properties can also be accessed via the print command: .. doctest:: >>> b = qutip.Bloch() >>> print(b) # doctest: +NORMALIZE_WHITESPACE Bloch data: ----------- Number of points: 0 Number of vectors: 0 Bloch sphere properties: ------------------------ font_color: black font_size: 20 frame_alpha: 0.2 frame_color: gray frame_width: 1 point_color: ['b', 'r', 'g', '#CC6600'] point_marker: ['o', 's', 'd', '^'] point_size: [25, 32, 35, 45] sphere_alpha: 0.2 sphere_color: #FFDDDD figsize: [5, 5] vector_color: ['g', '#CC6600', 'b', 'r'] vector_width: 3 vector_style: -|> vector_mutation: 20 view: [-60, 30] xlabel: ['$x$', ''] xlpos: [1.2, -1.2] ylabel: ['$y$', ''] ylpos: [1.2, -1.2] zlabel: ['$\\left|0\\right>$', '$\\left|1\\right>$'] zlpos: [1.2, -1.2] .. _bloch-animate: Animating with the Bloch sphere =============================== The Bloch class was designed from the outset to generate animations. To animate a set of vectors or data points the basic idea is: plot the data at time t1, save the sphere, clear the sphere, plot data at t2,... The Bloch sphere will automatically number the output file based on how many times the object has been saved (this is stored in b.savenum). The easiest way to animate data on the Bloch sphere is to use the ``save()`` method and generate a series of images to convert into an animation. However, as of Matplotlib version 1.1, creating animations is built-in. We will demonstrate both methods by looking at the decay of a qubit on the bloch sphere. .. _bloch-animate-decay: Example: Qubit Decay -------------------- The code for calculating the expectation values for the Pauli spin operators of a qubit decay is given below. This code is common to both animation examples. .. literalinclude:: scripts/ex_bloch_animation.py .. _bloch-animate-decay-images: Generating Images for Animation ++++++++++++++++++++++++++++++++ An example of generating images for generating an animation outside of Python is given below:: import numpy as np b = qutip.Bloch() b.vector_color = ['r'] b.view = [-40, 30] for i in range(len(sx)): b.clear() b.add_vectors([np.sin(theta), 0, np.cos(theta)]) b.add_points([sx[:i+1], sy[:i+1], sz[:i+1]]) b.save(dirc='temp') # saving images to temp directory in current working directory Generating an animation using FFmpeg (for example) is fairly simple:: ffmpeg -i temp/bloch_%01d.png bloch.mp4 .. _bloch-animate-decay-direct: Directly Generating an Animation ++++++++++++++++++++++++++++++++ .. important:: Generating animations directly from Matplotlib requires installing either MEncoder or FFmpeg. While either choice works on linux, it is best to choose FFmpeg when running on the Mac. If using macports just do: ``sudo port install ffmpeg``. The code to directly generate an mp4 movie of the Qubit decay is as follows :: from matplotlib import pyplot, animation fig = pyplot.figure() ax = fig.add_subplot(azim=-40, elev=30, projection="3d") sphere = qutip.Bloch(axes=ax) def animate(i): sphere.clear() sphere.add_vectors([np.sin(theta), 0, np.cos(theta)], ["r"]) sphere.add_points([sx[:i+1], sy[:i+1], sz[:i+1]]) sphere.render() return ax ani = animation.FuncAnimation(fig, animate, np.arange(len(sx)), blit=False, repeat=False) ani.save('bloch_sphere.mp4', fps=20) The resulting movie may be viewed here: `bloch_decay.mp4 `_ qutip-5.1.1/doc/guide/guide-control.rst000066400000000000000000000313701474175217300200460ustar00rootroot00000000000000.. _control: ********************************************* Quantum Optimal Control ********************************************* Introduction ============= In quantum control we look to prepare some specific state, effect some state-to-state transfer, or effect some transformation (or gate) on a quantum system. For a given quantum system there will always be factors that effect the dynamics that are outside of our control. As examples, the interactions between elements of the system or a magnetic field required to trap the system. However, there may be methods of affecting the dynamics in a controlled way, such as the time varying amplitude of the electric component of an interacting laser field. And so this leads to some questions; given a specific quantum system with known time-independent dynamics generator (referred to as the *drift* dynamics generators) and set of externally controllable fields for which the interaction can be described by *control* dynamics generators: 1. What states or transformations can we achieve (if any)? 2. What is the shape of the control pulse required to achieve this? These questions are addressed as *controllability* and *quantum optimal control* [dAless08]_. The answer to question of *controllability* is determined by the commutability of the dynamics generators and is formalised as the *Lie Algebra Rank Criterion* and is discussed in detail in [dAless08]_. The solutions to the second question can be determined through optimal control algorithms, or control pulse optimisation. .. figure:: figures/quant_optim_ctrl.png :align: center :width: 2.5in Schematic showing the principle of quantum control. Quantum Control has many applications including NMR, *quantum metrology*, *control of chemical reactions*, and *quantum information processing*. To explain the physics behind these algorithms we will first consider only finite-dimensional, closed quantum systems. Closed Quantum Systems ====================== In closed quantum systems the states can be represented by kets, and the transformations on these states are unitary operators. The dynamics generators are Hamiltonians. The combined Hamiltonian for the system is given by .. math:: H(t) = H_0 + \sum_{j=1} u_j(t) H_j where :math:`H_0` is the drift Hamiltonian and the :math:`H_j` are the control Hamiltonians. The :math:`u_j` are time varying amplitude functions for the specific control. The dynamics of the system are governed by *SchrĂśdingers equation*. .. math:: \tfrac{d}{dt} \ket{\psi} = -i H(t)\ket{\psi} Note we use units where :math:`\hbar=1` throughout. The solutions to SchrĂśdinger's equation are of the form: .. math:: \ket{\psi(t)} = U(t)\ket{\psi_0} where :math:`\psi_0` is the state of the system at :math:`t=0` and :math:`U(t)` is a unitary operator on the Hilbert space containing the states. :math:`U(t)` is a solution to the *SchrĂśdinger operator equation* .. math:: \tfrac{d}{dt}U = -i H(t)U ,\quad U(0) = \mathbb{1} We can use optimal control algorithms to determine a set of :math:`u_j` that will drive our system from :math:`\ket{\psi_0}` to :math:`\ket{\psi_1}`, this is state-to-state transfer, or drive the system from some arbitary state to a given state :math:`\ket{\psi_1}`, which is state preparation, or effect some unitary transformation :math:`U_{target}`, called gate synthesis. The latter of these is most important in quantum computation. The GRAPE algorithm =================== The **GR**\ adient **A**\ scent **P**\ ulse **E**\ ngineering was first proposed in [NKanej]_. Solutions to SchrĂśdinger's equation for a time-dependent Hamiltonian are not generally possible to obtain analytically. Therefore, a piecewise constant approximation to the pulse amplitudes is made. Time allowed for the system to evolve :math:`T` is split into :math:`M` timeslots (typically these are of equal duration), during which the control amplitude is assumed to remain constant. The combined Hamiltonian can then be approximated as: .. math:: H(t) \approx H(t_k) = H_0 + \sum_{j=1}^N u_{jk} H_j\quad where :math:`k` is a timeslot index, :math:`j` is the control index, and :math:`N` is the number of controls. Hence :math:`t_k` is the evolution time at the start of the timeslot, and :math:`u_{jk}` is the amplitude of control :math:`j` throughout timeslot :math:`k`. The time evolution operator, or propagator, within the timeslot can then be calculated as: .. math:: X_k:=e^{-iH(t_k)\Delta t_k} where :math:`\Delta t_k` is the duration of the timeslot. The evolution up to (and including) any timeslot :math:`k` (including the full evolution :math:`k=M`) can the be calculated as .. math:: X(t_k):=X_k X_{k-1}\cdots X_1 X_0 If the objective is state-to-state transfer then :math:`X_0=\ket{\psi_0}` and the target :math:`X_{targ}=\ket{\psi_1}`, for gate synthesis :math:`X_0 = U(0) = \mathbb{1}` and the target :math:`X_{targ}=U_{targ}`. A *figure of merit* or *fidelity* is some measure of how close the evolution is to the target, based on the control amplitudes in the timeslots. The typical figure of merit for unitary systems is the normalised overlap of the evolution and the target. .. math:: f_{PSU} = \tfrac{1}{d} \big| \tr \{X_{targ}^{\dagger} X(T)\} \big| where :math:`d` is the system dimension. In this figure of merit the absolute value is taken to ignore any differences in global phase, and :math:`0 \le f \le 1`. Typically the fidelity error (or *infidelity*) is more useful, in this case defined as :math:`\varepsilon = 1 - f_{PSU}`. There are many other possible objectives, and hence figures of merit. As there are now :math:`N \times M` variables (the :math:`u_{jk}`) and one parameter to minimise :math:`\varepsilon`, then the problem becomes a finite multi-variable optimisation problem, for which there are many established methods, often referred to as 'hill-climbing' methods. The simplest of these to understand is that of steepest ascent (or descent). The gradient of the fidelity with respect to all the variables is calculated (or approximated) and a step is made in the variable space in the direction of steepest ascent (or descent). This method is a first order gradient method. In two dimensions this describes a method of climbing a hill by heading in the direction where the ground rises fastest. This analogy also clearly illustrates one of the main challenges in multi-variable optimisation, which is that all methods have a tendency to get stuck in local maxima. It is hard to determine whether one has found a global maximum or not - a local peak is likely not to be the highest mountain in the region. In quantum optimal control we can typically define an infidelity that has a lower bound of zero. We can then look to minimise the infidelity (from here on we will only consider optimising for infidelity minima). This means that we can terminate any pulse optimisation when the infidelity reaches zero (to a sufficient precision). This is however only possible for fully controllable systems; otherwise it is hard (if not impossible) to know that the minimum possible infidelity has been achieved. In the hill walking analogy the step size is roughly fixed to a stride, however, in computations the step size must be chosen. Clearly there is a trade-off here between the number of steps (or iterations) required to reach the minima and the possibility that we might step over a minima. In practice it is difficult to determine an efficient and effective step size. The second order differentials of the infidelity with respect to the variables can be used to approximate the local landscape to a parabola. This way a step (or jump) can be made to where the minima would be if it were parabolic. This typically vastly reduces the number of iterations, and removes the need to guess a step size. The method where all the second differentials are calculated explicitly is called the *Newton-Raphson* method. However, calculating the second-order differentials (the Hessian matrix) can be computationally expensive, and so there are a class of methods known as *quasi-Newton* that approximate the Hessian based on successive iterations. The most popular of these (in quantum optimal control) is the Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS). The default method in the QuTiP Qtrl GRAPE implementation is the L-BFGS-B method in Scipy, which is a wrapper to the implementation described in [Byrd95]_. This limited memory and bounded method does not need to store the entire Hessian, which reduces the computer memory required, and allows bounds to be set for variable values, which considering these are field amplitudes is often physical. The pulse optimisation is typically far more efficient if the gradients can be calculated exactly, rather than approximated. For simple fidelity measures such as :math:`f_{PSU}` this is possible. Firstly the propagator gradient for each timeslot with respect to the control amplitudes is calculated. For closed systems, with unitary dynamics, a method using the eigendecomposition is used, which is efficient as it is also used in the propagator calculation (to exponentiate the combined Hamiltonian). More generally (for example open systems and symplectic dynamics) the Frechet derivative (or augmented matrix) method is used, which is described in [Flo12]_. For other optimisation goals it may not be possible to calculate analytic gradients. In these cases it is necessary to approximate the gradients, but this can be very expensive, and can lead to other algorithms out-performing GRAPE. The CRAB Algorithm =================== It has been shown [Lloyd14]_, the dimension of a quantum optimal control problem is a polynomial function of the dimension of the manifold of the time-polynomial reachable states, when allowing for a finite control precision and evolution time. You can think of this as the information content of the pulse (as being the only effective input) being very limited e.g. the pulse is compressible to a few bytes without loosing the target. This is where the **C**\ hopped **RA**\ ndom **B**\ asis (CRAB) algorithm [Doria11]_, [Caneva11]_ comes into play: Since the pulse complexity is usually very low, it is sufficient to transform the optimal control problem to a few parameter search by introducing a physically motivated function basis that builds up the pulse. Compared to the number of time slices needed to accurately simulate quantum dynamics (often equals basis dimension for Gradient based algorithms), this number is lower by orders of magnitude, allowing CRAB to efficiently optimize smooth pulses with realistic experimental constraints. It is important to point out, that CRAB does not make any suggestion on the basis function to be used. The basis must be chosen carefully considered, taking into account a priori knowledge of the system (such as symmetries, magnitudes of scales,...) and solution (e.g. sign, smoothness, bang-bang behavior, singularities, maximum excursion or rate of change,....). By doing so, this algorithm allows for native integration of experimental constraints such as maximum frequencies allowed, maximum amplitude, smooth ramping up and down of the pulse and many more. Moreover initial guesses, if they are available, can (however not have to) be included to speed up convergence. As mentioned in the GRAPE paragraph, for CRAB local minima arising from algorithmic design can occur, too. However, for CRAB a 'dressed' version has recently been introduced [Rach15]_ that allows to escape local minima. For some control objectives and/or dynamical quantum descriptions, it is either not possible to derive the gradient for the cost functional with respect to each time slice or it is computationally expensive to do so. The same can apply for the necessary (reverse) propagation of the co-state. All this trouble does not occur within CRAB as those elements are not in use here. CRAB, instead, takes the time evolution as a black-box where the pulse goes as an input and the cost (e.g. infidelity) value will be returned as an output. This concept, on top, allows for direct integration in a closed loop experimental environment where both the preliminarily open loop optimization, as well as the final adoption, and integration to the lab (to account for modeling errors, experimental systematic noise, ...) can be done all in one, using this algorithm. Optimal Quantum Control in QuTiP ================================ The Quantum Control part of qutip has been moved to its own project. The previously available implementation is now located in the `qutip-qtrl `_ module. If the ``qutip-qtrl`` package is installed, it can also be imported under the name ``qutip.control`` to ease porting code developed for QuTiP 4 to QuTiP 5. A newer interface with upgraded capacities is being developped in `qutip-qoc `_. Please give these modules a try. qutip-5.1.1/doc/guide/guide-correlation.rst000066400000000000000000000221241474175217300207040ustar00rootroot00000000000000.. _correlation: ****************************** Two-time correlation functions ****************************** With the QuTiP time-evolution functions (for example :func:`.mesolve` and :func:`.mcsolve`), a state vector or density matrix can be evolved from an initial state at :math:`t_0` to an arbitrary time :math:`t`, :math:`\rho(t)=V(t, t_0)\left\{\rho(t_0)\right\}`, where :math:`V(t, t_0)` is the propagator defined by the equation of motion. The resulting density matrix can then be used to evaluate the expectation values of arbitrary combinations of *same-time* operators. To calculate *two-time* correlation functions on the form :math:`\left`, we can use the quantum regression theorem (see, e.g., [Gar03]_) to write .. math:: \left = {\rm Tr}\left[A V(t+\tau, t)\left\{B\rho(t)\right\}\right] = {\rm Tr}\left[A V(t+\tau, t)\left\{BV(t, 0)\left\{\rho(0)\right\}\right\}\right] We therefore first calculate :math:`\rho(t)=V(t, 0)\left\{\rho(0)\right\}` using one of the QuTiP evolution solvers with :math:`\rho(0)` as initial state, and then again use the same solver to calculate :math:`V(t+\tau, t)\left\{B\rho(t)\right\}` using :math:`B\rho(t)` as initial state. Note that if the initial state is the steady state, then :math:`\rho(t)=V(t, 0)\left\{\rho_{\rm ss}\right\}=\rho_{\rm ss}` and .. math:: \left = {\rm Tr}\left[A V(t+\tau, t)\left\{B\rho_{\rm ss}\right\}\right] = {\rm Tr}\left[A V(\tau, 0)\left\{B\rho_{\rm ss}\right\}\right] = \left, which is independent of :math:`t`, so that we only have one time coordinate :math:`\tau`. QuTiP provides a family of functions that assists in the process of calculating two-time correlation functions. The available functions and their usage is shown in the table below. Each of these functions can use one of the following evolution solvers: Master-equation, Exponential series and the Monte-Carlo. The choice of solver is defined by the optional argument ``solver``. .. cssclass:: table-striped +----------------------------------+--------------------------------------------------+ | QuTiP function | Correlation function | +==================================+==================================================+ | | :math:`\left` or | | :func:`qutip.correlation_2op_2t` | :math:`\left`. | +----------------------------------+--------------------------------------------------+ | | :math:`\left` or | | :func:`qutip.correlation_2op_1t` | :math:`\left`. | +----------------------------------+--------------------------------------------------+ | :func:`qutip.correlation_3op_1t` | :math:`\left`. | +----------------------------------+--------------------------------------------------+ | :func:`qutip.correlation_3op_2t` | :math:`\left`. | +----------------------------------+--------------------------------------------------+ | :func:`qutip.correlation_3op` | :math:`\left`. | +----------------------------------+--------------------------------------------------+ The most common use-case is to calculate the two time correlation function :math:`\left`. :func:`.correlation_2op_1t` performs this task with sensible default values, but only allows using the :func:`.mesolve` solver. From QuTiP 5.0 we added :func:`.correlation_3op`. This function can also calculate correlation functions with two or three operators and with one or two times. Most importantly, this function accepts alternative solvers such as :func:`.brmesolve`. .. _correlation-steady: Steadystate correlation function ================================ The following code demonstrates how to calculate the :math:`\left` correlation for a leaky cavity with three different relaxation rates. .. plot:: :context: close-figs times = np.linspace(0,10.0,200) a = destroy(10) x = a.dag() + a H = a.dag() * a corr1 = correlation_2op_1t(H, None, times, [np.sqrt(0.5) * a], x, x) corr2 = correlation_2op_1t(H, None, times, [np.sqrt(1.0) * a], x, x) corr3 = correlation_2op_1t(H, None, times, [np.sqrt(2.0) * a], x, x) plt.figure() plt.plot(times, np.real(corr1)) plt.plot(times, np.real(corr2)) plt.plot(times, np.real(corr3)) plt.legend(['0.5','1.0','2.0']) plt.xlabel(r'Time $t$') plt.ylabel(r'Correlation $\left$') plt.show() Emission spectrum ================= Given a correlation function :math:`\left` we can define the corresponding power spectrum as .. math:: S(\omega) = \int_{-\infty}^{\infty} \left e^{-i\omega\tau} d\tau. In QuTiP, we can calculate :math:`S(\omega)` using either :func:`.spectrum`, which first calculates the correlation function using one of the time-dependent solvers and then performs the Fourier transform semi-analytically, or we can use the function :func:`.spectrum_correlation_fft` to numerically calculate the Fourier transform of a given correlation data using FFT. The following example demonstrates how these two functions can be used to obtain the emission power spectrum. .. plot:: guide/scripts/spectrum_ex1.py :width: 5.0in :include-source: .. _correlation-spectrum: Non-steadystate correlation function ==================================== More generally, we can also calculate correlation functions of the kind :math:`\left`, i.e., the correlation function of a system that is not in its steady state. In QuTiP, we can evaluate such correlation functions using the function :func:`.correlation_2op_2t`. The default behavior of this function is to return a matrix with the correlations as a function of the two time coordinates (:math:`t_1` and :math:`t_2`). .. plot:: guide/scripts/correlation_ex2.py :width: 5.0in :include-source: However, in some cases we might be interested in the correlation functions on the form :math:`\left`, but only as a function of time coordinate :math:`t_2`. In this case we can also use the :func:`.correlation_2op_2t` function, if we pass the density matrix at time :math:`t_1` as second argument, and `None` as third argument. The :func:`.correlation_2op_2t` function then returns a vector with the correlation values corresponding to the times in `taulist` (the fourth argument). Example: first-order optical coherence function ----------------------------------------------- This example demonstrates how to calculate a correlation function on the form :math:`\left` for a non-steady initial state. Consider an oscillator that is interacting with a thermal environment. If the oscillator initially is in a coherent state, it will gradually decay to a thermal (incoherent) state. The amount of coherence can be quantified using the first-order optical coherence function :math:`g^{(1)}(\tau) = \frac{\left}{\sqrt{\left\left}}`. For a coherent state :math:`|g^{(1)}(\tau)| = 1`, and for a completely incoherent (thermal) state :math:`g^{(1)}(\tau) = 0`. The following code calculates and plots :math:`g^{(1)}(\tau)` as a function of :math:`\tau`. .. plot:: guide/scripts/correlation_ex3.py :width: 5.0in :include-source: For convenience, the steps for calculating the first-order coherence function have been collected in the function :func:`.coherence_function_g1`. Example: second-order optical coherence function ------------------------------------------------ The second-order optical coherence function, with time-delay :math:`\tau`, is defined as .. math:: \displaystyle g^{(2)}(\tau) = \frac{\langle a^\dagger(0)a^\dagger(\tau)a(\tau)a(0)\rangle}{\langle a^\dagger(0)a(0)\rangle^2} For a coherent state :math:`g^{(2)}(\tau) = 1`, for a thermal state :math:`g^{(2)}(\tau=0) = 2` and it decreases as a function of time (bunched photons, they tend to appear together), and for a Fock state with :math:`n` photons :math:`g^{(2)}(\tau = 0) = n(n - 1)/n^2 < 1` and it increases with time (anti-bunched photons, more likely to arrive separated in time). To calculate this type of correlation function with QuTiP, we can use :func:`.correlation_3op_1t`, which computes a correlation function on the form :math:`\left` (three operators, one delay-time vector). We first have to combine the central two operators into one single one as they are evaluated at the same time, e.g. here we do :math:`a^\dagger(\tau)a(\tau) = (a^\dagger a)(\tau)`. The following code calculates and plots :math:`g^{(2)}(\tau)` as a function of :math:`\tau` for a coherent, thermal and Fock state. .. plot:: guide/scripts/correlation_ex4.py :width: 5.0in :include-source: For convenience, the steps for calculating the second-order coherence function have been collected in the function :func:`.coherence_function_g2`. qutip-5.1.1/doc/guide/guide-dynamics.rst000066400000000000000000000011331474175217300201670ustar00rootroot00000000000000.. _dynamics: ****************************************** Time Evolution and Quantum System Dynamics ****************************************** .. toctree:: :maxdepth: 2 dynamics/dynamics-intro.rst dynamics/dynamics-data.rst dynamics/dynamics-master.rst dynamics/dynamics-monte.rst dynamics/dynamics-krylov.rst dynamics/dynamics-stochastic.rst dynamics/dynamics-time.rst dynamics/dynamics-class.rst dynamics/dynamics-bloch-redfield.rst dynamics/dynamics-floquet.rst dynamics/dynamics-nmmonte.rst dynamics/dynamics-options.rst dynamics/dynamics-propagator.rst qutip-5.1.1/doc/guide/guide-environments.rst000066400000000000000000000536231474175217300211220ustar00rootroot00000000000000.. _environments guide: ************************************ Environments of Open Quantum Systems ************************************ *written by* |pm|_ *and* |gs|_ .. _pm: https://www.menczel.net/ .. |pm| replace:: *Paul Menczel* .. _gs: https://gsuarezr.github.io/ .. |gs| replace:: *Gerardo Suarez* .. (this is a workaround for italic links in rst) QuTiP can describe environments of open quantum systems. They can be passed to various solvers, where their influence is taken into account exactly or approximately. In the following, we will discuss bosonic and fermionic thermal environments. In our definitions, we follow [BoFiN23]_. Note that currently, we only support a single coupling term per environment. If a more generalized coupling would be useful to you, please let us know on GitHub. .. _bosonic environments guide: Bosonic Environments -------------------- A bosonic environment is described by a continuum of harmonic oscillators. The open quantum system and its environment are thus described by the Hamiltonian .. math:: H = H_{\rm s} + Q \otimes X + \sum_k \hbar\omega_k\, a_k^\dagger a_k , \qquad X = \sum_k g_k (a_k + a_k^\dagger) (in the case of a single bosonic environment). Here, :math:`H_{\rm s}` is the Hamiltonian of the open system and :math:`Q` a system coupling operator. The sums enumerate the environment modes with frequencies :math:`\omega_k` and couplings :math:`g_k`. The couplings are described by the spectral density .. math:: J(\omega) = \pi \sum_k g_k^2 \delta(\omega - \omega_k) . Equivalently, a bosonic environment can be described by its auto-correlation function .. math:: C(t) = \langle X(t) X \rangle = \sum_{k} g_{k}^{2} \Big( \cos(\omega_{k} t) \underbrace{( 2 n_{k}+1)}_{\coth(\frac{\beta \omega_{k}}{2})} - i \sin(\omega_{k} t) \Big) (where :math:`X(t)` is the interaction picture operator) or its power spectrum .. math:: S(\omega) = \int_{-\infty}^\infty \mathrm dt\, C(t)\, \mathrm e^{\mathrm i\omega t} , which is the inverse Fourier transform of the correlation function. The correlation function satisfies the symmetry relation :math:`C(-t) = C(t)^\ast`. Assuming that the initial state is thermal with inverse temperature :math:`\beta`, in the continuum limit the correlation function and the power spectrum can be calculated from the spectral density via .. math:: :label: cfandps \begin{aligned} C(t) &= \int_0^\infty \frac{\mathrm d\omega}{\pi}\, J(\omega) \Bigl[ \coth\Bigl( \frac{\beta\omega}{2} \Bigr) \cos\bigl( \omega t \bigr) - \mathrm i \sin\bigl( \omega t \bigr) \Bigr] , \\ S(\omega) &= \operatorname{sign}(\omega)\, J(|\omega|) \Bigl[ \coth\Bigl( \frac{\beta\omega}{2} \Bigr) + 1 \Bigr] . \end{aligned} Here, :math:`\operatorname{sign}(\omega) = \pm 1` depending on the sign of :math:`\omega`. At zero temperature, these equations become :math:`C(t) = \int_0^\infty \frac{\mathrm d\omega}{\pi} J(\omega) \mathrm e^{-\mathrm i\omega t}` and :math:`S(\omega) = 2 \Theta(\omega) J(|\omega|)`, where :math:`\Theta` is the Heaviside function. If the environment is coupled weakly to the open system, the environment induces quantum jumps with transition rates :math:`\gamma \propto S(-\Delta\omega)`, where :math:`\Delta\omega` is the energy change in the system corresponding to the quantum jump. In the strong coupling case, QuTiP provides exact integration methods based on multi-exponential decompositions of the correlation function, see below. .. note:: We generally assume that the frequencies :math:`\omega_k` are all positive and hence :math:`J(\omega) = 0` for :math:`\omega \leq 0`. To handle a spectral density :math:`J(\omega)` with support at negative frequencies, one can use an effective spectral density :math:`J'(\omega) = J(\omega) - J(-\omega)`. This process might result in the desired correlation function, because .. math:: \int_0^\infty \frac{\mathrm d\omega}{\pi}\, J'(\omega) \bigl[ \cdots \bigr] = \int_{-\infty}^\infty \frac{\mathrm d\omega}{\pi}\, J(\omega) \bigl[ \cdots \bigr] , where :math:`[\cdots]` stands for the square brackets in Eq. :eq:`cfandps`. Note however that the derivation of Eq. :eq:`cfandps` is not valid in this situation, since the environment does not have a thermal state. .. note:: Note that the expressions provided above for :math:`S(\omega)` are ill-defined at :math:`\omega=0`. For zero temperature, we simply have :math:`S(0) = 0`. For non-zero temperature, one obtains .. math:: S(0) = 2\beta^{-1}\, J'(0) . Hence, :math:`S(0)` diverges if the spectral density is sub-ohmic. Pre-defined Environments ------------------------ Ohmic Environment ^^^^^^^^^^^^^^^^^ Ohmic environments can be constructed in QuTiP using the class :class:`.OhmicEnvironment`. They are characterized by spectral densities of the form .. math:: :label: ohmicf J(\omega) = \alpha \frac{\omega^s}{\omega_c^{s-1}} e^{-\omega / \omega_c} , where :math:`\alpha` is a dimensionless parameter that indicates the coupling strength, :math:`\omega_{c}` is the cutoff frequency, and :math:`s` is a parameter that determines the low-frequency behaviour. Ohmic environments are usually classified according to this parameter as * Sub-Ohmic (:math:`s<1`) * Ohmic (:math:`s=1`) * Super-Ohmic (:math:`s>1`). .. note:: In the literature, the Ohmic spectral density can often be found as :math:`J(\omega) = \alpha \frac{\omega^s}{\omega_c^{s-1}} f(\omega)`, where :math:`f(\omega)` with :math:`\lim\limits_{\omega \to \infty} f(\omega) = 0` is known as the cutoff function. The cutoff function ensures that the spectral density and its integrals (for example :eq:`cfandps`) do not diverge. Sometimes, with sub-Ohmic spectral densities, an infrared cutoff is used as well so that :math:`\lim\limits_{\omega \to 0} J(\omega) = 0`. This pre-defined Ohmic environment class is restricted to an exponential cutoff function, which is one of the most commonly used in the literature. Other cutoff functions can be used in QuTiP with user-defined environments as explained below. Substituting the Ohmic spectral density :eq:`ohmicf` into :eq:`cfandps`, the correlation function can be computed analytically: .. math:: C(t)= \frac{\alpha}{\pi} w_{c}^{1-s} \beta^{-(s+1)} \Gamma(s+1) \left[ \zeta\left(s+1,\frac{1+\beta w_{c} -i w_{c} t}{\beta w_{c}} \right) +\zeta\left(s+1,\frac{1+ i w_{c} t}{\beta w_{c}}\right) \right] , where :math:`\beta` is the inverse temperature, :math:`\Gamma` the Gamma function, and :math:`\zeta` the Hurwitz zeta function. The zero temperature case can be obtained by taking the limit :math:`\beta \to \infty`, which results in .. math:: C(t) = \frac{\alpha}{\pi} \omega_c^2\, \Gamma(s+1) (1+ i \omega_{c} t)^{-(s+1)} . The evaluation of the zeta function for complex arguments requires `mpmath`, so certain features of the Ohmic enviroment are only available if `mpmath` is installed. Multi-exponential approximations to Ohmic environments can be obtained through the fitting procedures :meth:`approx_by_cf_fit<.BosonicEnvironment.approx_by_cf_fit>` and :meth:`approx_by_sd_fit<.BosonicEnvironment.approx_by_sd_fit>`. The following example shows how to create a sub-Ohmic environment, and how to use :meth:`approx_by_cf_fit<.BosonicEnvironment.approx_by_cf_fit>` to fit the real and imaginary parts of the correlation function with two exponential terms each. .. plot:: :context: reset :nofigs: import numpy as np import qutip as qt import matplotlib.pyplot as plt # Define a sub-Ohmic environment with the given temperature, coupling strength and cutoff env = qt.OhmicEnvironment(T=0.1, alpha=1, wc=3, s=0.7) # Fit the correlation function with three exponential terms tlist = np.linspace(0, 3, 250) approx_env, info = env.approx_by_cf_fit(tlist, target_rsme=None, Nr_max=3, Ni_max=3, maxfev=1e8) The environment `approx_env` created here could be used, for example, with the :ref:`HEOM solver`. The variable `info` contains info about the convergence of the fit; here, we will just plot the fit together with the analytical correlation function. Note that a larger number of exponential terms would have yielded a better result. .. plot:: :context: plt.plot(tlist, np.real(env.correlation_function(tlist)), label='Real part (analytic)') plt.plot(tlist, np.real(approx_env.correlation_function(tlist)), '--', label='Real part (fit)') plt.plot(tlist, np.imag(env.correlation_function(tlist)), label='Imag part (analytic)') plt.plot(tlist, np.imag(approx_env.correlation_function(tlist)), '--', label='Imag part (fit)') plt.xlabel('Time') plt.ylabel('Correlation function') plt.tight_layout() plt.legend() .. _dl env guide: Drude-Lorentz Environment ^^^^^^^^^^^^^^^^^^^^^^^^^ Drude-Lorentz environments, also known as overdamped environments, can be constructed in QuTiP using the class :class:`.DrudeLorentzEnvironment`. They are characterized by spectral densities of the form .. math:: J(\omega) = \frac{2 \lambda \gamma \omega}{\gamma^{2}+\omega^{2}} , where :math:`\lambda` is a coupling strength (with the dimension of energy) and :math:`\gamma` the cutoff frequency. To compute the corresponding correlation function, one can apply the Matsubara expansion: .. math:: C(t) = \sum_{k=0}^{\infty} c_k e^{- \nu_k t} The coefficients of this expansion are .. math:: \nu_{k} = \begin{cases} \gamma & k = 0\\ {2 \pi k} / {\beta} & k \geq 1\\ \end{cases} \;, \qquad c_k = \begin{cases} \lambda \gamma [\cot(\beta \gamma / 2) - i] & k = 0\\ \frac{4 \lambda \gamma \nu_k }{ (\nu_k^2 - \gamma^2)\beta} & k \geq 1\\ \end{cases} \;. The function :meth:`approx_by_matsubara<.DrudeLorentzEnvironment.approx_by_matsubara>` creates a multi-exponential approximation to the Drude-Lorentz environment by truncating this series at a finite index :math:`N_k`. This approximation can then be used with the HEOM solver, for example. The :ref:`HEOM section` of this guide contains further examples using the Drude-Lorentz enviroment. Similarly, the function :meth:`approx_by_pade<.DrudeLorentzEnvironment.approx_by_pade>` can be used to apply and truncate the numerically more efficient PadĂŠ expansion. Underdamped Environment ^^^^^^^^^^^^^^^^^^^^^^^ Underdamped environments can be constructed in QuTiP using the class :class:`.UnderDampedEnvironment`. They are characterized by spectral densities of the form .. math:: J(\omega) = \frac{\lambda^{2} \Gamma \omega}{(\omega_0^{2}- \omega^{2})^{2}+ \Gamma^{2} \omega^{2}} , where :math:`\lambda`, :math:`\Gamma` and :math:`\omega_0` are the coupling strength (with dimension :math:`(\text{energy})^{3/2}`), the cutoff frequency and the resonance frequency. Similar to the Drude-Lorentz environment, the correlation function can be approximated by a Matsubara expansion. This functionality is available with the :meth:`approx_by_matsubara<.UnderDampedEnvironment.approx_by_matsubara>` function. For small temperatures, the Matsubara expansion converges slowly. It is recommended to instead use a fitting procedure for the Matsubara contribution as described in [Lambert19]_. User-Defined Environments ------------------------- As stated in the introduction, a bosonic environment is fully characterized by its temperature and spectral density (SD), or alternatively by its correlation function (CF) or its power spectrum (PS). QuTiP allows for the creation of an user-defined environment by specifying either the spectral density, the correlation function, or the power spectrum. QuTiP then computes the other two functions based on the provided one. To do so, it converts between the SD and the PS using the formula :math:`S(\omega) = \operatorname{sign}(\omega)\, J(|\omega|) \bigl[ \coth( \beta\omega / 2 ) + 1 \bigr]` introduced earlier, and between the PS and the CF using the fast Fourier transform. The former conversion requires the bath temperature to be specified; the latter requires a cutoff frequency (or cutoff time) to be provided together with the specified function (SD, CF or PS). In this way, all characteristic functions can be computed from the specified one. The following example manually creates an environment with an underdamped spectral density. It then compares the correlation function obtained via fast Fourier transformation with the Matsubara expansion. The slow convergence of the Matsubara expansion is visible around :math:`t=0`. .. plot:: :context: close-figs # Define underdamped environment parameters T = 0.1 lam = 1 gamma = 2 w0 = 5 # User-defined environment based on SD def underdamped_sd(w): return lam**2 * gamma * w / ((w**2 - w0**2)**2 + (gamma*w)**2) env = qt.BosonicEnvironment.from_spectral_density(underdamped_sd, wMax=50, T=T) tlist = np.linspace(-2, 2, 250) plt.plot(tlist, np.real(env.correlation_function(tlist)), label='FFT') # Pre-defined environment and Matsubara approximations env2 = qt.UnderDampedEnvironment(T, lam, gamma, w0) for Nk in range(0, 11, 2): approx_env = env2.approx_by_matsubara(Nk) plt.plot(tlist, np.real(approx_env.correlation_function(tlist)), label=f'Nk={Nk}') plt.xlabel('Time') plt.ylabel('Correlation function (real part)') plt.tight_layout() plt.legend() Multi-Exponential Approximations -------------------------------- Many approaches to simulating the dynamics of an open quantum system strongly coupled to an environment assume that the environment correlation function can be approximated by a multi-exponential expansion like .. math:: C(t) = C_R(t) + \mathrm i C_I(t) , \qquad C_{R,I}(t) = \sum_{k=1}^{N_{R,I}} c^{R,I}_k \exp[-\nu^{R,I}_k t] with small numbers :math:`N_{R,I}` of exponents. Note that :math:`C_R(t)` and :math:`C_I(t)` are the real and imaginary parts of the correlation function, but the coefficients :math:`c^{R,I}_k` and exponents :math:`\nu^{R,I}_k` are not required to be real in general. In the previous sections, various methods of obtaining multi-exponential approximations were introduced. The output of these approximation functions are :class:`.ExponentialBosonicEnvironment` objects. An :class:`.ExponentialBosonicEnvironment` is basically a collection of :class:`.CFExponent` s, which store (in the bosonic case) the coefficient, the exponent, and whether the exponent contributes to the real part, the imaginary part, or both. As we have already seen above, one can then compute the spectral density, correlation function and power spectrum corresponding to the exponents, in order to compare them to the original, exact environment. Let :math:`c_k \mathrm e^{-\nu_k t}` be a term in the correlation function (i.e., :math:`c_k = c^R_k` or :math:`c_k = \mathrm i c^I_k`). The corresponding term in the power spectrum is .. math:: S_k(\omega) = 2\Re\Bigr[ \frac{c_k}{\nu_k - \mathrm i\omega} \Bigr] and, if a temperature has been specified, the corresponding term in the spectral density can be computed as described above. The following example shows how to manually create an :class:`.ExponentialBosonicEnvironment` for the simple example :math:`C(t) = c \mathrm e^{-\nu t}` with real :math:`c`, :math:`\nu`. The power spectrum then is a Lorentzian, :math:`S(\omega) = 2c\nu / (\nu^2 + \omega^2)`. .. plot:: :context: close-figs c = 1 nu = 2 wlist = np.linspace(-3, 3, 250) env = qt.ExponentialBosonicEnvironment([c], [nu], [], []) plt.figure(figsize=(4, 3)) plt.plot(wlist, env.power_spectrum(wlist)) plt.plot(wlist, 2 * c * nu / (nu**2 + wlist**2), '--') plt.xlabel('Frequency') plt.ylabel('Power spectrum') plt.tight_layout() .. _fermionic environments guide: Fermionic environments ---------------------- The implementation of fermionic environments in QuTiP is not yet as advanced as the bosonic environments. Currently, user-defined fermionic environments and fitting are not implemented. However, the overall structure of fermionic environments in QuTiP is analogous to the bosonic environments. There is one pre-defined fermionic environment, the Lorentzian environment, and multi-exponential fermionic environments. Lorentzian environments can be approximated by multi-exponential Matsubara or PadĂŠ expansions. In the fermionic case, we consider the number-conserving Hamiltonian .. math:: H = H_s + (B^\dagger c + c^\dagger B) + \sum_k \hbar\omega_k\, b^\dagger_k b_k , \qquad B = \sum_k f_k b_k , where the bath operators :math:`b_k` and the system operator :math:`c` obey fermionic anti-commutation relations. In analogy to the bosonic case, we define the spectral density .. math:: J(\omega) = 2\pi \sum_k f_k^2\, \delta[\omega - \omega_k] , which may however now be defined for all (including negative) frequencies, since the spectrum of each mode is bounded. The fermionic environment is characterized either by its spectral density, inverse temperature :math:`\beta` and chemical potential :math:`\mu`, or equivalently by two correlation functions or by two power spectra. The correlation functions are .. math:: C^\sigma(t) = \langle B^\sigma(t) B^{-\sigma} \rangle = \int_{-\infty}^\infty \frac{\mathrm d\omega}{2\pi}\, J(\omega)\, \mathrm e^{\sigma \mathrm i\omega t}\, f_F(\sigma \beta[\omega - \mu]) , where :math:`\sigma = \pm 1`, :math:`B^+ = B^\dagger` and :math:`B^- = B`. Further, :math:`f_F(x) = (\mathrm e^x + 1)^{-1}` is the Fermi-Dirac function. Note that we still have :math:`C^\sigma(-t) = C^\sigma(t)^\ast`. The power spectra are the Fourier transformed correlation functions, .. math:: S^\sigma(\omega) = \int_{-\infty}^\infty \mathrm dt\, C^\sigma(t)\, \mathrm e^{-\sigma \mathrm i\omega t} = J(\omega) f_F(\sigma\beta[\omega - \mu]) . Since :math:`f_F(x) + f_F(-x) = 1`, we have :math:`S^+(\omega) + S^-(\omega) = J(\omega)`. .. note:: The relationship between the spectral density and the two power spectra (or the two correlation functions) is not one-to-one. A pair of functions :math:`S^\pm(\omega)` is physical if they satisfy the condition .. math:: S^-(\omega) = \mathrm e^{\beta(\omega - \mu)}\, S^+(\omega) . For the correlation functions, the condition becomes :math:`C^-(t) = \mathrm e^{-\beta\mu}\, C^+(t - \mathrm i\beta)^\ast`. For flexibility, we do not enforce the power spectra / correlation functions to be physical in this sense. .. _lorentzian env guide: Lorentzian Environment ^^^^^^^^^^^^^^^^^^^^^^ Fermionic Lorentzian environments are represented by the class :class:`.LorentzianEnvironment`. They are characterized by spectral densities of the form .. math:: J(\omega) = \frac{\gamma W^2}{(\omega - \omega_0)^2 + W^2} , where :math:`\gamma` is the coupling strength, :math:`W` the spectral width and :math:`\omega_0` the resonance frequency. Often, the resonance frequency is taken to be equal to the chemical potential of the environment. As with the bosonic Drude-Lorentz environments, multi-exponential approximations of the correlation functions, .. math:: C^\sigma(t) \approx \sum_{k=0}^{N_k} c^\sigma_k e^{- \nu^\sigma_k t} , can be obtained using the Matsubara or PadĂŠ expansions. The functions :meth:`approx_by_matsubara<.LorentzianEnvironment.approx_by_matsubara>` and :meth:`approx_by_pade<.LorentzianEnvironment.approx_by_pade>` implement these approximations in QuTiP, yielding approximated environments that can be used, for example, with the HEOM solver. Note that for this type of environment, the Matsubara expansion is very inefficient, converging much more slowly than the PadĂŠ expansion. Typically, at least :math:`N_k \geq 20` is required for good convergence. For reference, we tabulate the values of the coefficients and exponents in the following. For the Matsubara expansion, they are .. math:: \nu^\sigma_{k} = \begin{cases} W - \mathrm i \sigma\, \omega_0 & k = 0\\ \frac{(2k - 1) \pi}{\beta} - \mathrm i \sigma\, \mu & k \geq 1\\ \end{cases} \;, \qquad c^\sigma_k = \begin{cases} \frac{\gamma W}{2} f_F[\sigma\beta(\omega_0 - \mu) + \mathrm i\, \beta W] & k = 0\\ \frac{\mathrm i \gamma W^2}{\beta} \frac{1}{[\mathrm i \sigma (\omega_0 - \mu) + (2k - 1) \pi / \beta]^2 - W^2} & k \geq 1\\ \end{cases} \;. The PadĂŠ decomposition approximates the Fermi distribution as: .. math:: f_F(x) \approx f_F^{\mathrm{approx}}(x) = \frac{1}{2} - \sum_{k=0}^{N_k} \frac{2\kappa_k x}{x^2 + \epsilon_k^2} where :math:`\kappa_k` and :math:`\epsilon_k` are coefficients that depend on :math:`N_k` and are defined in `J. Chem Phys 133, "Efficient on the fly calculation of time correlation functions in computer simulations" `_. This approach results in the exponents .. math:: \nu^\sigma_{k} = \begin{cases} W - \mathrm i \sigma\, \omega_0 & k = 0\\ \frac{\epsilon_k}{\beta} - \mathrm i \sigma\, \mu & k \geq 1\\ \end{cases} \;, \qquad c^\sigma_k = \begin{cases} \frac{\gamma W}{2} f_F^{\mathrm{approx}}[\sigma\beta(\omega_0 - \mu) + \mathrm i\, \beta W] & k = 0\\ \frac{\mathrm i\, \kappa_k \gamma W^2}{\beta} \frac{1}{[\mathrm i\sigma(\omega_0 - \mu) + \epsilon_k / \beta]^2 - W^2} & k \geq 1\\ \end{cases} \;. Multi-Exponential Fermionic Environment ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Analogous to the :class:`.ExponentialBosonicEnvironment` in the bosonic case, the :class:`.ExponentialFermionicEnvironment` describes fermionic environments where the correlation functions are given by multi-exponential decompositions, .. math:: C^\sigma(t) \approx \sum_{k=0}^{N_k^\sigma} c^\sigma_k e^{-\nu^\sigma_k t} . Like in the bosonic case, the class allows us to automatically compute the spectral density and power spectra that correspond to the multi-exponential correlation functions. In this case, they are .. math:: S^\sigma(\omega) = \sum_{k=0}^{N_k^\sigma} 2\Re\Bigr[ \frac{c_k^\sigma}{\nu_k^\sigma + \mathrm i \sigma\, \omega} \Bigr] and :math:`J(\omega) = S^+(\omega) + S^-(\omega)`. .. plot:: :context: reset :include-source: false :nofigs:qutip-5.1.1/doc/guide/guide-heom.rst000066400000000000000000000003641474175217300173150ustar00rootroot00000000000000.. _heom: ******************************** Hierarchical Equations of Motion ******************************** .. toctree:: :maxdepth: 2 heom/intro.rst heom/bosonic.rst heom/fermionic.rst heom/history.rst heom/references.rst qutip-5.1.1/doc/guide/guide-measurement.rst000066400000000000000000000301001474175217300207010ustar00rootroot00000000000000.. _measurement: ****************************** Measurement of Quantum Objects ****************************** .. note:: New in QuTiP 4.6 .. _measurement-intro: Introduction ------------ Measurement is a fundamental part of the standard formulation of quantum mechanics and is the process by which classical readings are obtained from a quantum object. Although the interpretation of the procedure is at times contentious, the procedure itself is mathematically straightforward and is described in many good introductory texts. Here we will show you how to perform simple measurement operations on QuTiP objects. The same functions :func:`~qutip.measurement.measure` and :func:`~qutip.measurement.measurement_statistics` can be used to handle both observable-style measurements and projective style measurements. .. _measurement-basic: Performing a basic measurement (Observable) ------------------------------------------- First we need to select some states to measure. For now, let us create an *up* state and a *down* state: .. testcode:: up = basis(2, 0) down = basis(2, 1) which represent spin-1/2 particles with their spin pointing either up or down along the z-axis. We choose what to measure (in this case) by selecting a **measurement operator**. For example, we could select :func:`.sigmaz` which measures the z-component of the spin of a spin-1/2 particle, or :func:`.sigmax` which measures the x-component: .. testcode:: spin_z = sigmaz() spin_x = sigmax() How do we know what these operators measure? The answer lies in the measurement procedure itself: * A quantum measurement transforms the state being measured by projecting it into one of the eigenvectors of the measurement operator. * Which eigenvector to project onto is chosen probabilistically according to the square of the amplitude of the state in the direction of the eigenvector. * The value returned by the measurement is the eigenvalue corresponding to the chosen eigenvector. .. note:: How to interpret this "random choosing" is the famous "quantum measurement problem". The eigenvectors of `spin_z` are the states with their spin pointing either up or down, so it measures the component of the spin along the z-axis. The eigenvectors of `spin_x` are the states with their spin pointing either left or right, so it measures the component of the spin along the x-axis. When we measure our `up` and `down` states using the operator `spin_z`, we always obtain: .. testcode:: from qutip.measurement import measure, measurement_statistics measure(up, spin_z) == (1.0, up) measure(down, spin_z) == (-1.0, down) because `up` is the eigenvector of `spin_z` with eigenvalue `1.0` and `down` is the eigenvector with eigenvalue `-1.0`. The minus signs are just an arbitrary global phase -- `up` and `-up` represent the same quantum state. Neither eigenvector has any component in the direction of the other (they are orthogonal), so `measure(spin_z, up)` returns the state `up` 100% percent of the time and `measure(spin_z, down)` returns the state `down` 100% of the time. Note how :func:`~qutip.measurement.measure` returns a pair of values. The first is the measured value, i.e. an eigenvalue of the operator (e.g. `1.0`), and the second is the state of the quantum system after the measurement, i.e. an eigenvector of the operator (e.g. `up`). Now let us consider what happens if we measure the x-component of the spin of `up`: .. testcode:: measure(up, spin_x) The `up` state is not an eigenvector of `spin_x`. `spin_x` has two eigenvectors which we will call `left` and `right`. The `up` state has equal components in the direction of these two vectors, so measurement will select each of them 50% of the time. These `left` and `right` states are: .. testcode:: left = (up - down).unit() right = (up + down).unit() When `left` is chosen, the result of the measurement will be `(-1.0, -left)`. When `right` is chosen, the result of measurement with be `(1.0, right)`. .. note:: When :func:`~qutip.measurement.measure` is invoked with the second argument being an observable, it acts as an alias to :func:`~qutip.measurement.measure_observable`. Performing a basic measurement (Projective) ------------------------------------------- We can also choose what to measure by specifying a *list of projection operators*. For example, we could select the projection operators :math:`\ket{0} \bra{0}` and :math:`\ket{1} \bra{1}` which measure the state in the :math:`\ket{0}, \ket{1}` basis. Note that these projection operators are simply the projectors determined by the eigenstates of the :func:`~qutip.operators.sigmaz` operator. .. testcode:: Z0, Z1 = ket2dm(basis(2, 0)), ket2dm(basis(2, 1)) The probabilities and respective output state are calculated for each projection operator. .. testcode:: measure(up, [Z0, Z1]) == (0, up) measure(down, [Z0, Z1]) == (1, down) In this case, the projection operators are conveniently eigenstates corresponding to subspaces of dimension :math:`1`. However, this might not be the case, in which case it is not possible to have unique eigenvalues for each eigenstate. Suppose we want to measure only the first qubit in a two-qubit system. Consider the two qubit state :math:`\ket{0+}` .. testcode:: state_0 = basis(2, 0) state_plus = (basis(2, 0) + basis(2, 1)).unit() state_0plus = tensor(state_0, state_plus) Now, suppose we want to measure only the first qubit in the computational basis. We can do that by measuring with the projection operators :math:`\ket{0}\bra{0} \otimes I` and :math:`\ket{1}\bra{1} \otimes I`. .. testcode:: PZ1 = [tensor(Z0, identity(2)), tensor(Z1, identity(2))] PZ2 = [tensor(identity(2), Z0), tensor(identity(2), Z1)] Now, as in the previous example, we can measure by supplying a list of projection operators and the state. .. testcode:: measure(state_0plus, PZ1) == (0, state_0plus) The output of the measurement is the index of the measurement outcome as well as the output state on the full Hilbert space of the input state. It is crucial to note that we do not discard the measured qubit after measurement (as opposed to when measuring on quantum hardware). .. note:: When :func:`~qutip.measurement.measure` is invoked with the second argument being a list of projectors, it acts as an alias to :func:`~qutip.measurement.measure_povm`. The :func:`~qutip.measurement.measure` function can perform measurements on density matrices too. You can read about these and other details at :func:`~qutip.measurement.measure_povm` and :func:`~qutip.measurement.measure_observable`. Now you know how to measure quantum states in QuTiP! .. _measurement-statistics: Obtaining measurement statistics(Observable) -------------------------------------------- You've just learned how to perform measurements in QuTiP, but you've also learned that measurements are probabilistic. What if instead of just making a single measurement, we want to determine the probability distribution of a large number of measurements? One way would be to repeat the measurement many times -- and this is what happens in many quantum experiments. In QuTiP one could simulate this using: .. testcode:: :hide: np.random.seed(42) .. testcode:: results = {1.0: 0, -1.0: 0} # 1 and -1 are the possible outcomes for _ in range(1000): value, new_state = measure(up, spin_x) results[round(value)] += 1 print(results) **Output**: .. testoutput:: {1.0: 497, -1.0: 503} which measures the x-component of the spin of the `up` state `1000` times and stores the results in a dictionary. Afterwards we expect to have seen the result `1.0` (i.e. left) roughly 500 times and the result `-1.0` (i.e. right) roughly 500 times, but, of course, the number of each will vary slightly each time we run it. But what if we want to know the distribution of results precisely? In a physical system, we would have to perform the measurement many many times, but in QuTiP we can peak at the state itself and determine the probability distribution of the outcomes exactly in a single line: .. doctest:: :hide: >>> np.random.seed(42) .. doctest:: >>> eigenvalues, eigenstates, probabilities = measurement_statistics(up, spin_x) >>> eigenvalues # doctest: +NORMALIZE_WHITESPACE array([-1., 1.]) >>> eigenstates # doctest: +NORMALIZE_WHITESPACE array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[ 0.70710678] [-0.70710678]], Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.70710678] [0.70710678]]], dtype=object) >>> probabilities # doctest: +NORMALIZE_WHITESPACE [0.5000000000000001, 0.4999999999999999] The :func:`~qutip.measurement.measurement_statistics` function then returns three values when called with a single observable: - `eigenvalues` is an array of eigenvalues of the measurement operator, i.e. a list of the possible measurement results. In our example the value is `array([-1., -1.])`. - `eigenstates` is an array of the eigenstates of the measurement operator, i.e. a list of the possible final states after the measurement is complete. Each element of the array is a :obj:`.Qobj`. - `probabilities` is a list of the probabilities of each measurement result. In our example the value is `[0.5, 0.5]` since the `up` state has equal probability of being measured to be in the left (`-1.0`) or right (`1.0`) eigenstates. All three lists are in the same order -- i.e. the first eigenvalue is `eigenvalues[0]`, its corresponding eigenstate is `eigenstates[0]`, and its probability is `probabilities[0]`, and so on. .. note:: When :func:`~qutip.measurement.measurement_statistics` is invoked with the second argument being an observable, it acts as an alias to :func:`~qutip.measurement.measurement_statistics_observable`. Obtaining measurement statistics(Projective) -------------------------------------------- Similarly, when we want to obtain measurement statistics for projection operators, we can use the `measurement_statistics` function with the second argument being a list of projectors. Consider again, the state :math:`\ket{0+}`. Suppose, now we want to obtain the measurement outcomes for the second qubit. We must use the projectors specified earlier by `PZ2` which allow us to measure only on the second qubit. Since the second qubit has the state :math:`\ket{+}`, we get the following result. .. testcode:: collapsed_states, probabilities = measurement_statistics(state_0plus, PZ2) print(collapsed_states) **Output**: .. testoutput:: :options: +NORMALIZE_WHITESPACE [Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket Qobj data = [[1.] [0.] [0.] [0.]], Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket Qobj data = [[0.] [1.] [0.] [0.]]] .. testcode:: print(probabilities) **Output**: .. testoutput:: :options: +NORMALIZE_WHITESPACE [0.4999999999999999, 0.4999999999999999] The function :func:`~qutip.measurement.measurement_statistics` then returns two values: * `collapsed_states` is an array of the possible final states after the measurement is complete. Each element of the array is a :obj:`.Qobj`. * `probabilities` is a list of the probabilities of each measurement outcome. Note that the collapsed_states are exactly :math:`\ket{00}` and :math:`\ket{01}` with equal probability, as expected. The two lists are in the same order. .. note:: When :func:`~qutip.measurement.measurement_statistics` is invoked with the second argument being a list of projectors, it acts as an alias to :func:`~qutip.measurement.measurement_statistics_povm`. The :func:`~qutip.measurement.measurement_statistics` function can provide statistics for measurements of density matrices too. You can read about these and other details at :func:`~qutip.measurement.measurement_statistics_observable` and :func:`~qutip.measurement.measurement_statistics_povm`. Furthermore, the :func:`~qutip.measurement.measure_povm` and :func:`~qutip.measurement.measurement_statistics_povm` functions can handle POVM measurements which are more general than projective measurements. qutip-5.1.1/doc/guide/guide-overview.rst000066400000000000000000000010371474175217300202310ustar00rootroot00000000000000.. _overview: ****************** Guide Overview ****************** The goal of this guide is to introduce you to the basic structures and functions that make up QuTiP. This guide is divided up into several sections, each highlighting a specific set of functionalities. In combination with the examples that can be found on the project web page `https://qutip.org/tutorials.html `_, this guide should provide a more or less complete overview of QuTip. We also provide the API documentation in :ref:`apidoc`. qutip-5.1.1/doc/guide/guide-piqs.rst000066400000000000000000000157641474175217300173530ustar00rootroot00000000000000.. _master-piqs: ********************************* Permutational Invariance ********************************* .. _master-unitary-piqs: Permutational Invariant Quantum Solver (PIQS) ============================================= The *Permutational Invariant Quantum Solver (PIQS)* is a QuTiP module that allows to study the dynamics of an open quantum system consisting of an ensemble of identical qubits that can dissipate through local and collective baths according to a Lindblad master equation. The Liouvillian of an ensemble of :math:`N` qubits, or two-level systems (TLSs), :math:`\mathcal{D}_{TLS}(\rho)`, can be built using only polynomial – instead of exponential – resources. This has many applications for the study of realistic quantum optics models of many TLSs and in general as a tool in cavity QED. Consider a system evolving according to the equation .. math:: \dot{\rho} = \mathcal{D}_\text{TLS}(\rho)=-\frac{i}{\hbar}\lbrack H,\rho \rbrack +\frac{\gamma_\text{CE}}{2}\mathcal{L}_{J_{-}}[\rho] +\frac{\gamma_\text{CD}}{2}\mathcal{L}_{J_{z}}[\rho] +\frac{\gamma_\text{CP}}{2}\mathcal{L}_{J_{+}}[\rho] +\sum_{n=1}^{N}\left( \frac{\gamma_\text{E}}{2}\mathcal{L}_{J_{-,n}}[\rho] +\frac{\gamma_\text{D}}{2}\mathcal{L}_{J_{z,n}}[\rho] +\frac{\gamma_\text{P}}{2}\mathcal{L}_{J_{+,n}}[\rho]\right) where :math:`J_{\alpha,n}=\frac{1}{2}\sigma_{\alpha,n}` are SU(2) Pauli spin operators, with :math:`{\alpha=x,y,z}` and :math:`J_{\pm,n}=\sigma_{\pm,n}`. The collective spin operators are :math:`J_{\alpha} = \sum_{n}J_{\alpha,n}` . The Lindblad super-operators are :math:`\mathcal{L}_{A} = 2A\rho A^\dagger - A^\dagger A \rho - \rho A^\dagger A`. The inclusion of local processes in the dynamics lead to using a Liouvillian space of dimension :math:`4^N`. By exploiting the permutational invariance of identical particles [2-8], the Liouvillian :math:`\mathcal{D}_\text{TLS}(\rho)` can be built as a block-diagonal matrix in the basis of Dicke states :math:`|j, m \rangle`. The system under study is defined by creating an object of the :class:`~qutip.piqs.piqs.Dicke` class, e.g. simply named :code:`system`, whose first attribute is - :code:`system.N`, the number of TLSs of the system :math:`N`. The rates for collective and local processes are simply defined as - :code:`collective_emission` defines :math:`\gamma_\text{CE}`, collective (superradiant) emission - :code:`collective_dephasing` defines :math:`\gamma_\text{CD}`, collective dephasing - :code:`collective_pumping` defines :math:`\gamma_\text{CP}`, collective pumping. - :code:`emission` defines :math:`\gamma_\text{E}`, incoherent emission (losses) - :code:`dephasing` defines :math:`\gamma_\text{D}`, local dephasing - :code:`pumping` defines :math:`\gamma_\text{P}`, incoherent pumping. Then the :code:`system.lindbladian()` creates the total TLS Lindbladian superoperator matrix. Similarly, :code:`system.hamiltonian` defines the TLS hamiltonian of the system :math:`H_\text{TLS}`. The system's Liouvillian can be built using :code:`system.liouvillian()`. The properties of a Piqs object can be visualized by simply calling :code:`system`. We give two basic examples on the use of *PIQS*. In the first example the incoherent emission of N driven TLSs is considered. .. code-block:: python from qutip import piqs N = 10 system = piqs.Dicke(N, emission = 1, pumping = 2) L = system.liouvillian() steady = steadystate(L) For more example of use, see the "Permutational Invariant Lindblad Dynamics" section in the tutorials section of the website, `https://qutip.org/tutorials.html `_. .. list-table:: Useful PIQS functions. :widths: 25 25 50 :header-rows: 1 * - Operators - Command - Description * - Collective spin algebra :math:`J_x,\ J_y,\ J_z` - ``jspin(N)`` - The collective spin algebra :math:`J_x,\ J_y,\ J_z` for :math:`N` TLSs * - Collective spin :math:`J_x` - ``jspin(N, "x")`` - The collective spin operator :math:`Jx`. Requires :math:`N` number of TLSs * - Collective spin :math:`J_y` - ``jspin(N, "y")`` - The collective spin operator :math:`J_y`. Requires :math:`N` number of TLSs * - Collective spin :math:`J_z` - ``jspin(N, "z")`` - The collective spin operator :math:`J_z`. Requires :math:`N` number of TLSs * - Collective spin :math:`J_+` - ``jspin(N, "+")`` - The collective spin operator :math:`J_+`. * - Collective spin :math:`J_-` - ``jspin(N, "-")`` - The collective spin operator :math:`J_-`. * - Collective spin :math:`J_z` in uncoupled basis - ``jspin(N, "z", basis='uncoupled')`` - The collective spin operator :math:`J_z` in the uncoupled basis of dimension :math:`2^N`. * - Dicke state :math:`|j,m\rangle` density matrix - ``dicke(N, j, m)`` - The density matrix for the Dicke state given by :math:`|j,m\rangle` * - Excited-state density matrix in Dicke basis - ``excited(N)`` - The excited state in the Dicke basis * - Excited-state density matrix in uncoupled basis - ``excited(N, basis="uncoupled")`` - The excited state in the uncoupled basis * - Ground-state density matrix in Dicke basis - ``ground(N)`` - The ground state in the Dicke basis * - GHZ-state density matrix in the Dicke basis - ``ghz(N)`` - The GHZ-state density matrix in the Dicke (default) basis for N number of TLS * - Collapse operators of the ensemble - ``Dicke.c_ops()`` - The collapse operators for the ensemble can be called by the `c_ops` method of the Dicke class. Note that the mathematical object representing the density matrix of the full system that is manipulated (or obtained from `steadystate`) in the Dicke-basis formalism used here is a *representative of the density matrix*. This *representative object* is of linear size N^2, whereas the full density matrix is defined over a 2^N Hilbert space. In order to calculate nonlinear functions of such density matrix, such as the Von Neumann entropy or the purity, it is necessary to take into account the degeneracy of each block of such block-diagonal density matrix. Note that as long as one calculates expected values of operators, being Tr[A*rho] a *linear* function of `rho`, the *representative density matrix* give straightforwardly the correct result. When a *nonlinear* function of the density matrix needs to be calculated, one needs to weigh each degenerate block correctly; this is taken care by the `dicke_function_trace` in :obj:`.piqs`, and the user can use it to define general nonlinear functions that can be described as the trace of a Taylor expandable function. Two nonlinear functions that use `dicke_function_trace` and are already implemented are `purity_dicke`, to calculate the purity of a density matrix in the Dicke basis, and `entropy_vn_dicke`, which can be used to calculate the Von Neumann entropy. More functions relative to the :obj:`qutip.piqs` module can be found at :ref:`apidoc`. Attributes to the :class:`.piqs.Dicke` and :class:`.piqs.Pim` class can also be found there. qutip-5.1.1/doc/guide/guide-random.rst000066400000000000000000000230221474175217300176410ustar00rootroot00000000000000.. _random: ******************************************** Generating Random Quantum States & Operators ******************************************** .. testsetup:: [random] from qutip import rand_herm, rand_dm, rand_super_bcsz, rand_dm_ginibre QuTiP includes a collection of random state, unitary and channel generators for simulations, Monte Carlo evaluation, theorem evaluation, and code testing. Each of these objects can be sampled from one of several different distributions. For example, a random Hermitian operator can be sampled by calling :func:`.rand_herm` function: .. doctest:: [random] :hide: >>> np.random.seed(42) .. doctest:: [random] >>> rand_herm(5) # doctest: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[-0.25091976+0.j 0. +0.j 0. +0.j -0.21793701+0.47037633j -0.23212846-0.61607187j] [ 0. +0.j -0.88383278+0.j 0.836086 -0.23956218j -0.09464275+0.45370863j -0.15243356+0.65392096j] [ 0. +0.j 0.836086 +0.23956218j 0.66488528+0.j -0.26290446+0.64984451j -0.52603038-0.07991553j] [-0.21793701-0.47037633j -0.09464275-0.45370863j -0.26290446-0.64984451j -0.13610996+0.j -0.34240902-0.2879303j ] [-0.23212846+0.61607187j -0.15243356-0.65392096j -0.52603038+0.07991553j -0.34240902+0.2879303j 0. +0.j ]] .. tabularcolumns:: | p{2cm} | p{3cm} | c | .. cssclass:: table-striped +-------------------------------+-----------------------------------------------+------------------------------------------+ | Random Variable Type | Sampling Functions | Dimensions | +===============================+===============================================+==========================================+ | State vector (``ket``) | :func:`.rand_ket` | :math:`N \times 1` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | Hermitian operator (``oper``) | :func:`.rand_herm` | :math:`N \times N` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | Density operator (``oper``) | :func:`.rand_dm` | :math:`N \times N` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | Unitary operator (``oper``) | :func:`.rand_unitary` | :math:`N \times N` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | stochastic matrix (``oper``) | :func:`.rand_stochastic` | :math:`N \times N` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | CPTP channel (``super``) | :func:`.rand_super`, :func:`.rand_super_bcsz` | :math:`(N \times N) \times (N \times N)` | +-------------------------------+-----------------------------------------------+------------------------------------------+ | CPTP map (list of ``oper``) | :func:`.rand_kraus_map` | :math:`N \times N` (N**2 operators) | +-------------------------------+-----------------------------------------------+------------------------------------------+ In all cases, these functions can be called with a single parameter :math:`dimensions` that can be the size of the relevant Hilbert space or the dimensions of a random state, unitary or channel. .. doctest:: [random] >>> rand_super_bcsz(7).dims [[[7], [7]], [[7], [7]]] >>> rand_super_bcsz([[2, 3], [2, 3]]).dims [[[2, 3], [2, 3]], [[2, 3], [2, 3]]] Several of the random :class:`.Qobj` function in QuTiP support additional parameters as well, namely *density* and *distribution*. :func:`.rand_dm`, :func:`.rand_herm`, :func:`.rand_unitary` and :func:`.rand_ket` can be created using multiple method controlled by *distribution*. The :func:`.rand_ket`, :func:`.rand_herm` and :func:`.rand_unitary` functions can return quantum objects such that a fraction of the elements are identically equal to zero. The ratio of nonzero elements is passed as the ``density`` keyword argument. By contrast, `rand_super_bcsz` take as an argument the rank of the generated object, such that passing ``rank=1`` returns a random pure state or unitary channel, respectively. Passing ``rank=None`` specifies that the generated object should be full-rank for the given dimension. `rand_dm` can support *density* or *rank* depending on the chosen distribution. For example, .. doctest:: [random] :hide: >>> np.random.seed(42) .. doctest:: [random] >>> rand_dm(5, density=0.5, distribution="herm") Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[ 0.298+0.j , 0. +0.j , -0.095+0.1j , 0. +0.j ,-0.105+0.122j], [ 0. +0.j , 0.088+0.j , 0. +0.j , -0.018-0.001j, 0. +0.j ], [-0.095-0.1j , 0. +0.j , 0.328+0.j , 0. +0.j ,-0.077-0.033j], [ 0. +0.j , -0.018+0.001j, 0. +0.j , 0.084+0.j , 0. +0.j ], [-0.105-0.122j, 0. +0.j , -0.077+0.033j, 0. +0.j , 0.201+0.j ]] >>> rand_dm_ginibre(5, rank=2) Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[ 0.307+0.j , -0.258+0.039j, -0.039+0.184j, 0.041-0.054j, 0.016+0.045j], [-0.258-0.039j, 0.239+0.j , 0.075-0.15j , -0.053+0.008j,-0.057-0.078j], [-0.039-0.184j, 0.075+0.15j , 0.136+0.j , -0.05 -0.052j,-0.028-0.058j], [ 0.041+0.054j, -0.053-0.008j, -0.05 +0.052j, 0.083+0.j , 0.101-0.056j], [ 0.016-0.045j, -0.057+0.078j, -0.028+0.058j, 0.101+0.056j, 0.236+0.j ]] See the API documentation: :ref:`api-rand` for details. .. warning:: When using the ``density`` keyword argument, setting the density too low may result in not enough diagonal elements to satisfy trace constraints. Random objects with a given eigen spectrum ========================================== It is also possible to generate random Hamiltonian (:func:`.rand_herm`) and densitiy matrices (:func:`.rand_dm`) with a given eigen spectrum. This is done by passing an array to eigenvalues argument to either function and choosing the "eigen" distribution. For example, .. doctest:: [random] :hide: >>> np.random.seed(42) .. doctest:: [random] >>> eigs = np.arange(5) >>> H = rand_herm(5, density=0.5, eigenvalues=eigs, distribution="eigen") >>> H # doctest: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[ 0.5 +0.j , 0.228+0.27j, 0. +0.j , 0. +0.j ,-0.228-0.27j], [ 0.228-0.27j, 1.75 +0.j , 0.456+0.54j, 0. +0.j , 1.25 +0.j ], [ 0. +0.j , 0.456-0.54j, 3. +0.j , 0. +0.j , 0.456-0.54j], [ 0. +0.j , 0. +0.j , 0. +0.j , 3. +0.j , 0. +0.j ], [-0.228+0.27j, 1.25 +0.j , 0.456+0.54j, 0. +0.j , 1.75 +0.j ]] >>> H.eigenenergies() # doctest: +NORMALIZE_WHITESPACE array([7.70647994e-17, 1.00000000e+00, 2.00000000e+00, 3.00000000e+00, 4.00000000e+00]) In order to generate a random object with a given spectrum QuTiP applies a series of random complex Jacobi rotations. This technique requires many steps to build the desired quantum object, and is thus suitable only for objects with Hilbert dimensionality :math:`\lesssim 1000`. Composite random objects ======================== In many cases, one is interested in generating random quantum objects that correspond to composite systems generated using the :func:`.tensor` function. Specifying the tensor structure of a quantum object is done passing a list for the first argument. The resulting quantum objects size will be the product of the elements in the list and the resulting :class:`.Qobj` dimensions will be ``[dims, dims]``: .. doctest:: [random] :hide: >>> np.random.seed(42) .. doctest:: [random] >>> rand_unitary([2, 2], density=0.5) # doctest: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True Qobj data = [[ 0.887+0.061j, 0. +0.j , 0. +0.j , -0.191-0.416j], [ 0. +0.j , 0.604+0.116j, -0.32 -0.721j, 0. +0.j ], [ 0. +0.j , 0.768+0.178j, 0.227+0.572j, 0. +0.j ], [ 0.412-0.2j , 0. +0.j , 0. +0.j , 0.724+0.516j]] Controlling the random number generator ======================================= Qutip uses numpy random number generator to create random quantum objects. To control the random number, a seed as an `int` or `numpy.random.SeedSequence` or a `numpy.random.Generator` can be passed to the `seed` keyword argument: .. doctest:: [random] >>> rng = np.random.default_rng(12345) >>> rand_ket(2, seed=rng) # doctest: +NORMALIZE_WHITESPACE Quantum object: dims=[[2], [1]], shape=(2, 1), type='ket' Qobj data = [[-0.697+0.618j], [-0.326-0.163j]] Internal matrix format ====================== The internal storage type of the generated random quantum objects can be set with the *dtype* keyword. .. doctest:: [random] >>> rand_ket(2, dtype="dense").data Dense(shape=(2, 1), fortran=True) >>> rand_ket(2, dtype="CSR").data CSR(shape=(2, 1), nnz=2) .. TODO: add a link to a page explaining data-types. qutip-5.1.1/doc/guide/guide-saving.rst000066400000000000000000000175321474175217300176610ustar00rootroot00000000000000.. _saving: ********************************** Saving QuTiP Objects and Data Sets ********************************** With time-consuming calculations it is often necessary to store the results to files on disk, so it can be post-processed and archived. In QuTiP there are two facilities for storing data: Quantum objects can be stored to files and later read back as python pickles, and numerical data (vectors and matrices) can be exported as plain text files in for example CSV (comma-separated values), TSV (tab-separated values), etc. The former method is preferred when further calculations will be performed with the data, and the latter when the calculations are completed and data is to be imported into a post-processing tool (e.g. for generating figures). Storing and loading QuTiP objects ================================= To store and load arbitrary QuTiP related objects (:class:`.Qobj`, :class:`.Result`, etc.) there are two functions: :func:`qutip.fileio.qsave` and :func:`qutip.fileio.qload`. The function :func:`qutip.fileio.qsave` takes an arbitrary object as first parameter and an optional filename as second parameter (default filename is `qutip_data.qu`). The filename extension is always `.qu`. The function :func:`qutip.fileio.qload` takes a mandatory filename as first argument and loads and returns the objects in the file. To illustrate how these functions can be used, consider a simple calculation of the steadystate of the harmonic oscillator :: >>> a = destroy(10); H = a.dag() * a >>> c_ops = [np.sqrt(0.5) * a, np.sqrt(0.25) * a.dag()] >>> rho_ss = steadystate(H, c_ops) The steadystate density matrix `rho_ss` is an instance of :class:`.Qobj`. It can be stored to a file `steadystate.qu` using :: >>> qsave(rho_ss, 'steadystate') >>> !ls *.qu density_matrix_vs_time.qu steadystate.qu and it can later be loaded again, and used in further calculations :: >>> rho_ss_loaded = qload('steadystate') Loaded Qobj object: Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isHerm = True >>> a = destroy(10) >>> np.testing.assert_almost_equal(expect(a.dag() * a, rho_ss_loaded), 0.9902248289345061) The nice thing about the :func:`qutip.fileio.qsave` and :func:`qutip.fileio.qload` functions is that almost any object can be stored and load again later on. We can for example store a list of density matrices as returned by :func:`.mesolve` :: >>> a = destroy(10); H = a.dag() * a ; c_ops = [np.sqrt(0.5) * a, np.sqrt(0.25) * a.dag()] >>> psi0 = rand_ket(10) >>> times = np.linspace(0, 10, 10) >>> dm_list = mesolve(H, psi0, times, c_ops, []) >>> qsave(dm_list, 'density_matrix_vs_time') And it can then be loaded and used again, for example in an other program :: >>> dm_list_loaded = qload('density_matrix_vs_time') Loaded Result object: Result object with mesolve data. -------------------------------- states = True num_collapse = 0 >>> a = destroy(10) >>> expect(a.dag() * a, dm_list_loaded.states) # doctest: +SKIP array([4.63317086, 3.59150315, 2.90590183, 2.41306641, 2.05120716, 1.78312503, 1.58357995, 1.4346382 , 1.32327398, 1.23991233]) Storing and loading datasets ============================ The :func:`qutip.fileio.qsave` and :func:`qutip.fileio.qload` are great, but the file format used is only understood by QuTiP (python) programs. When data must be exported to other programs the preferred method is to store the data in the commonly used plain-text file formats. With the QuTiP functions :func:`qutip.fileio.file_data_store` and :func:`qutip.fileio.file_data_read` we can store and load **numpy** arrays and matrices to files on disk using a deliminator-separated value format (for example comma-separated values CSV). Almost any program can handle this file format. The :func:`qutip.fileio.file_data_store` takes two mandatory and three optional arguments: >>> file_data_store(filename, data, numtype="complex", numformat="decimal", sep=",") # doctest: +SKIP where `filename` is the name of the file, `data` is the data to be written to the file (must be a *numpy* array), `numtype` (optional) is a flag indicating numerical type that can take values `complex` or `real`, `numformat` (optional) specifies the numerical format that can take the values `exp` for the format `1.0e1` and `decimal` for the format `10.0`, and `sep` (optional) is an arbitrary single-character field separator (usually a tab, space, comma, semicolon, etc.). A common use for the :func:`qutip.fileio.file_data_store` function is to store the expectation values of a set of operators for a sequence of times, e.g., as returned by the :func:`.mesolve` function, which is what the following example does .. plot:: :context: >>> a = destroy(10); H = a.dag() * a ; c_ops = [np.sqrt(0.5) * a, np.sqrt(0.25) * a.dag()] >>> psi0 = rand_ket(10) >>> times = np.linspace(0, 100, 100) >>> medata = mesolve(H, psi0, times, c_ops, e_ops=[a.dag() * a, a + a.dag(), -1j * (a - a.dag())]) >>> np.shape(medata.expect) (3, 100) >>> times.shape (100,) >>> output_data = np.vstack((times, medata.expect)) # join time and expt data >>> file_data_store('expect.dat', output_data.T) # Note the .T for transpose! >>> with open("expect.dat", "r") as f: ... print('\n'.join(f.readlines()[:10])) # Generated by QuTiP: 100x4 complex matrix in decimal format [',' separated values]. 0.0000000000+0.0000000000j,3.2109553666+0.0000000000j,0.3689771549+0.0000000000j,0.0185002867+0.0000000000j 1.0101010101+0.0000000000j,2.6754598872+0.0000000000j,0.1298251132+0.0000000000j,-0.3303672956+0.0000000000j 2.0202020202+0.0000000000j,2.2743186810+0.0000000000j,-0.2106241300+0.0000000000j,-0.2623894277+0.0000000000j 3.0303030303+0.0000000000j,1.9726633457+0.0000000000j,-0.3037311621+0.0000000000j,0.0397330921+0.0000000000j 4.0404040404+0.0000000000j,1.7435892209+0.0000000000j,-0.1126550232+0.0000000000j,0.2497182058+0.0000000000j 5.0505050505+0.0000000000j,1.5687324121+0.0000000000j,0.1351622725+0.0000000000j,0.2018398581+0.0000000000j 6.0606060606+0.0000000000j,1.4348632045+0.0000000000j,0.2143080535+0.0000000000j,-0.0067820038+0.0000000000j 7.0707070707+0.0000000000j,1.3321818015+0.0000000000j,0.0950352763+0.0000000000j,-0.1630920429+0.0000000000j 8.0808080808+0.0000000000j,1.2533244850+0.0000000000j,-0.0771210981+0.0000000000j,-0.1468923919+0.0000000000j In this case we didn't really need to store both the real and imaginary parts, so instead we could use the ``numtype="real"`` option .. plot:: :context: >>> file_data_store('expect.dat', output_data.T, numtype="real") >>> with open("expect.dat", "r") as f: ... print('\n'.join(f.readlines()[:5])) # Generated by QuTiP: 100x4 real matrix in decimal format [',' separated values]. 0.0000000000,3.2109553666,0.3689771549,0.0185002867 1.0101010101,2.6754598872,0.1298251132,-0.3303672956 2.0202020202,2.2743186810,-0.2106241300,-0.2623894277 3.0303030303,1.9726633457,-0.3037311621,0.0397330921 and if we prefer scientific notation we can request that using the ``numformat="exp"`` option .. plot:: :context: >>> file_data_store('expect.dat', output_data.T, numtype="real", numformat="exp") Loading data previously stored using :func:`qutip.fileio.file_data_store` (or some other software) is a even easier. Regardless of which deliminator was used, if data was stored as complex or real numbers, if it is in decimal or exponential form, the data can be loaded using the :func:`qutip.fileio.file_data_read`, which only takes the filename as mandatory argument. .. plot:: :context: input_data = file_data_read('expect.dat') plt.plot(input_data[:,0], input_data[:,1]); # plot the data (If a particularly obscure choice of deliminator was used it might be necessary to use the optional second argument, for example ``sep="_"`` if ``_`` is the deliminator). qutip-5.1.1/doc/guide/guide-settings.rst000066400000000000000000000276761474175217300202440ustar00rootroot00000000000000.. _settings: ************** QuTiP settings ************** QuTiP has multiple settings that control it's behaviour: * ``qutip.settings`` contains installation and runtime information. Most of these parameters are readonly. But systems paths used by QuTiP are also included here and could need updating in none standard environment. * ``qutip.settings.core`` contains options for operations with ``Qobj`` and other qutip's class. All options are writable. * ``qutip.settings.compile`` has options that control compilation of string coefficients to cython modules. All options are writable. .. _settings-install: ******************** Environment settings ******************** ``qutip.settings`` has information about the run time environment: .. tabularcolumns:: | p{3cm} | p{2cm} | p{10cm} | .. cssclass:: table-striped +-------------------+-----------+----------------------------------------------------------+ | Setting | Read Only | Description | +===================+===========+==========================================================+ | `has_mkl` | True | Whether qutip can find mkl libraries. | | | | mkl sparse linear equation solver can be used when True. | +-------------------+-----------+----------------------------------------------------------+ | `mkl_lib_location`| False | Path of the mkl library. | +-------------------+-----------+----------------------------------------------------------+ | `mkl_lib` | True | Mkl libraries loaded with ctypes. | +-------------------+-----------+----------------------------------------------------------+ | `ipython` | True | Whether running in IPython. | +-------------------+-----------+----------------------------------------------------------+ | `eigh_unsafe` | True | When true, SciPy's `eigh` and `eigvalsh` are replaced | | | | with custom implementations that call `eig` and | | | | `eigvals` instead. This setting exists because in some | | | | environments SciPy's `eigh` segfaults or gives invalid | | | | results. | +-------------------+-----------+----------------------------------------------------------+ | `coeffroot` | False | Directory in which QuTiP creates cython modules for | | | | string coefficient. | +-------------------+-----------+----------------------------------------------------------+ | `coeff_write_ok` | True | Whether QuTiP has write permission for `coeffroot`. | +-------------------+-----------+----------------------------------------------------------+ | `idxint_size` | True | Whether QuTiP's sparse matrix indices use 32 or 64 bits. | | | | Sparse matrices' size are limited to 2**(idxint_size-1) | | | | rows and columns. | +-------------------+-----------+----------------------------------------------------------+ | `num_cpus` | True | Detected number of cpus. | +-------------------+-----------+----------------------------------------------------------+ | `colorblind_safe` | False | Control the default cmap in visualization functions. | +-------------------+-----------+----------------------------------------------------------+ It may be needed to update ``coeffroot`` if the default HOME is not writable. It can be done with: >>> qutip.settings.coeffroot = "path/to/string/coeff/directory" In QuTiP version 5 and later, strings compiled in a session are kept for future sessions. As long as the same ``coeffroot`` is used, each string will only be compiled once. ********************************* Modifying Internal QuTiP Settings ********************************* .. _settings-params: User Accessible Parameters ========================== In this section we show how to modify a few of the internal parameters used by ``Qobj``. The settings that can be modified are given in the following table: .. tabularcolumns:: | p{3cm} | p{5cm} | p{5cm} | .. cssclass:: table-striped +------------------------------+----------------------------------------------+--------------------------------+ | Options | Description | type [default] | +==============================+==============================================+================================+ | `auto_tidyup` | Automatically tidyup sparse quantum objects. | bool [True] | +------------------------------+----------------------------------------------+--------------------------------+ | `auto_tidyup_atol` | Tolerance used by tidyup. (sparse only) | float [1e-14] | +------------------------------+----------------------------------------------+--------------------------------+ | `auto_tidyup_dims` | Whether the scalar dimension are contracted | bool [False] | +------------------------------+----------------------------------------------+--------------------------------+ | `atol` | General absolute tolerance. | float [1e-12] | +------------------------------+----------------------------------------------+--------------------------------+ | `rtol` | General relative tolerance. | float [1e-12] | +------------------------------+----------------------------------------------+--------------------------------+ | `function_coefficient_style` | Signature expected by function coefficients. | {["auto"], "pythonic", "dict"} | +------------------------------+----------------------------------------------+--------------------------------+ | `default_dtype` | Data format used when creating Qobj from | {[None], "CSR", "Dense", | | | QuTiP functions, such as ``qeye``. | "Dia"} + other from plugins | +------------------------------+----------------------------------------------+--------------------------------+ See also :class:`.CoreOptions`. .. _settings-usage: Example: Changing Settings ========================== The two most important settings are ``auto_tidyup`` and ``auto_tidyup_atol`` as they control whether the small elements of a quantum object should be removed, and what number should be considered as the cut-off tolerance. Modifying these, or any other parameters, is quite simple:: >>> qutip.settings.core["auto_tidyup"] = False The settings can also be changed for a code block:: >>> with qutip.CoreOptions(atol=1e-5): >>> assert qutip.qeye(2) * 1e-9 == qutip.qzero(2) .. _settings-compile: String Coefficient Parameters ============================= String based coefficient used for time dependent system are compiled using Cython when available. Speeding the simulations, it tries to set c types to passed variables. ``qutip.settings.compile`` has multiple options for compilation. There are options are about to whether to compile. .. tabularcolumns:: | p{3cm} | p{10cm} | .. cssclass:: table-striped +--------------------------+-----------------------------------------------------------+ | Options | Description | +==========================+===========================================================+ | `use_cython` | Whether to compile string using cython or using ``eval``. | +--------------------------+-----------------------------------------------------------+ | `recompile` | Whether to force recompilation or use a previously | | | constructed coefficient if available. | +--------------------------+-----------------------------------------------------------+ Some options passed to cython and the compiler (for advanced user). .. tabularcolumns:: | p{3cm} | p{10cm} | .. cssclass:: table-striped +--------------------------+-----------------------------------------------------------+ | Options | Description | +==========================+===========================================================+ | `compiler_flags` | C++ compiler flags. | +--------------------------+-----------------------------------------------------------+ | `link_flags` | C++ linker flags. | +--------------------------+-----------------------------------------------------------+ | `build_dir` | cythonize's build_dir. | +--------------------------+-----------------------------------------------------------+ | `extra_import` | import or cimport line of code to add to the cython file. | +--------------------------+-----------------------------------------------------------+ | `clean_on_error` | Whether to erase the created file if compilation failed. | +--------------------------+-----------------------------------------------------------+ Lastly some options control how qutip tries to detect C types (for advanced user). .. tabularcolumns:: | p{3cm} | p{10cm} | .. cssclass:: table-striped +--------------------------+-----------------------------------------------------------------------------------------+ | Options | Description | +==========================+=========================================================================================+ | `try_parse` | Whether QuTiP parses the string to detect common patterns. | | | | | | When True, "cos(w * t)" and "cos(a * t)" will use the same compiled coefficient. | +--------------------------+-----------------------------------------------------------------------------------------+ | `static_types` | If False, every variable will be typed as ``object``, (except ``t`` which is double). | | | | | | If True, scalar (int, float, complex), string and Data types are detected. | +--------------------------+-----------------------------------------------------------------------------------------+ | `accept_int` | Whether to type ``args`` values which are Python ints as int or float/complex. | | | | | | Per default it is True when subscription (``a[i]``) is used. | +--------------------------+-----------------------------------------------------------------------------------------+ | `accept_float` | Whether to type ``args`` values which are Python floats as int or float/complex. | | | | | | Per default it is True when comparison (``a > b``) is used. | +--------------------------+-----------------------------------------------------------------------------------------+ These options can be set at a global level in ``qutip.settings.compile`` or by passing a :class:`.CompilationOptions` instance to the :func:`.coefficient` functions. >>> qutip.coefficient("cos(t)", compile_opt=CompilationOptions(recompile=True)) qutip-5.1.1/doc/guide/guide-states.rst000066400000000000000000001375571474175217300177070ustar00rootroot00000000000000.. _states: ************************************* Manipulating States and Operators ************************************* .. _states-intro: Introduction ================= In the previous guide section :ref:`basics`, we saw how to create states and operators, using the functions built into QuTiP. In this portion of the guide, we will look at performing basic operations with states and operators. For more detailed demonstrations on how to use and manipulate these objects, see the examples on the `tutorials `_ web page. .. _states-vectors: State Vectors (kets or bras) ============================== Here we begin by creating a Fock :func:`.basis` vacuum state vector :math:`\left|0\right>` with in a Hilbert space with 5 number states, from 0 to 4: .. testcode:: [states] vac = basis(5, 0) print(vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[1.] [0.] [0.] [0.] [0.]] and then create a lowering operator :math:`\left(\hat{a}\right)` corresponding to 5 number states using the :func:`.destroy` function: .. testcode:: [states] a = destroy(5) print(a) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = False Qobj data = [[0. 1. 0. 0. 0. ] [0. 0. 1.41421356 0. 0. ] [0. 0. 0. 1.73205081 0. ] [0. 0. 0. 0. 2. ] [0. 0. 0. 0. 0. ]] Now lets apply the destruction operator to our vacuum state ``vac``, .. testcode:: [states] print(a * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [0.] [0.] [0.]] We see that, as expected, the vacuum is transformed to the zero vector. A more interesting example comes from using the adjoint of the lowering operator, the raising operator :math:`\hat{a}^\dagger`: .. testcode:: [states] print(a.dag() * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [1.] [0.] [0.] [0.]] The raising operator has in indeed raised the state `vec` from the vacuum to the :math:`\left| 1\right>` state. Instead of using the dagger ``Qobj.dag()`` method to raise the state, we could have also used the built in :func:`.create` function to make a raising operator: .. testcode:: [states] c = create(5) print(c * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [1.] [0.] [0.] [0.]] which does the same thing. We can raise the vacuum state more than once by successively apply the raising operator: .. testcode:: [states] print(c * c * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0. ] [0. ] [1.41421356] [0. ] [0. ]] or just taking the square of the raising operator :math:`\left(\hat{a}^\dagger\right)^{2}`: .. testcode:: [states] print(c ** 2 * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0. ] [0. ] [1.41421356] [0. ] [0. ]] Applying the raising operator twice gives the expected :math:`\sqrt{n + 1}` dependence. We can use the product of :math:`c * a` to also apply the number operator to the state vector ``vac``: .. testcode:: [states] print(c * a * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [0.] [0.] [0.]] or on the :math:`\left| 1\right>` state: .. testcode:: [states] print(c * a * (c * vac)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [1.] [0.] [0.] [0.]] or the :math:`\left| 2\right>` state: .. testcode:: [states] print(c * a * (c**2 * vac)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0. ] [0. ] [2.82842712] [0. ] [0. ]] Notice how in this last example, application of the number operator does not give the expected value :math:`n=2`, but rather :math:`2\sqrt{2}`. This is because this last state is not normalized to unity as :math:`c\left| n\right> = \sqrt{n+1}\left| n+1\right>`. Therefore, we should normalize our vector first: .. testcode:: [states] print(c * a * (c**2 * vac).unit()) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [2.] [0.] [0.]] Since we are giving a demonstration of using states and operators, we have done a lot more work than we should have. For example, we do not need to operate on the vacuum state to generate a higher number Fock state. Instead we can use the :func:`.basis` (or :func:`.fock`) function to directly obtain the required state: .. testcode:: [states] ket = basis(5, 2) print(ket) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [1.] [0.] [0.]] Notice how it is automatically normalized. We can also use the built in :func:`.num` operator: .. testcode:: [states] n = num(5) print(n) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0. 0. 0. 0. 0.] [0. 1. 0. 0. 0.] [0. 0. 2. 0. 0.] [0. 0. 0. 3. 0.] [0. 0. 0. 0. 4.]] Therefore, instead of ``c * a * (c ** 2 * vac).unit()`` we have: .. testcode:: [states] print(n * ket) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.] [0.] [2.] [0.] [0.]] We can also create superpositions of states: .. testcode:: [states] ket = (basis(5, 0) + basis(5, 1)).unit() print(ket) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0.70710678] [0.70710678] [0. ] [0. ] [0. ]] where we have used the :meth:`.Qobj.unit` method to again normalize the state. Operating with the number function again: .. testcode:: [states] print(n * ket) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[0. ] [0.70710678] [0. ] [0. ] [0. ]] We can also create coherent states and squeezed states by applying the :func:`.displace` and :func:`.squeeze` functions to the vacuum state: .. testcode:: [states] vac = basis(5, 0) d = displace(5, 1j) s = squeeze(5, np.complex(0.25, 0.25)) print(d * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[ 0.60655682+0.j ] [ 0. +0.60628133j] [-0.4303874 +0.j ] [ 0. -0.24104351j] [ 0.14552147+0.j ]] .. testcode:: [states] print(d * s * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket Qobj data = [[ 0.65893786+0.08139381j] [ 0.10779462+0.51579735j] [-0.37567217-0.01326853j] [-0.02688063-0.23828775j] [ 0.26352814+0.11512178j]] Of course, displacing the vacuum gives a coherent state, which can also be generated using the built in :func:`.coherent` function. .. _states-dm: Density matrices ================= One of the main purpose of QuTiP is to explore the dynamics of **open** quantum systems, where the most general state of a system is no longer a state vector, but rather a density matrix. Since operations on density matrices operate identically to those of vectors, we will just briefly highlight creating and using these structures. The simplest density matrix is created by forming the outer-product :math:`\left|\psi\right>\left<\psi\right|` of a ket vector: .. testcode:: [states] ket = basis(5, 2) print(ket * ket.dag()) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 1. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.]] A similar task can also be accomplished via the :func:`.fock_dm` or :func:`.ket2dm` functions: .. testcode:: [states] print(fock_dm(5, 2)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 1. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.]] .. testcode:: [states] print(ket2dm(ket)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 1. 0. 0.] [0. 0. 0. 0. 0.] [0. 0. 0. 0. 0.]] If we want to create a density matrix with equal classical probability of being found in the :math:`\left|2\right>` or :math:`\left|4\right>` number states we can do the following: .. testcode:: [states] print(0.5 * ket2dm(basis(5, 4)) + 0.5 * ket2dm(basis(5, 2))) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0. 0. 0. 0. 0. ] [0. 0. 0. 0. 0. ] [0. 0. 0.5 0. 0. ] [0. 0. 0. 0. 0. ] [0. 0. 0. 0. 0.5]] or use ``0.5 * fock_dm(5, 2) + 0.5 * fock_dm(5, 4)``. There are also several other built-in functions for creating predefined density matrices, for example :func:`.coherent_dm` and :func:`.thermal_dm` which create coherent state and thermal state density matrices, respectively. .. testcode:: [states] print(coherent_dm(5, 1.25)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0.20980701 0.26141096 0.23509686 0.15572585 0.13390765] [0.26141096 0.32570738 0.29292109 0.19402805 0.16684347] [0.23509686 0.29292109 0.26343512 0.17449684 0.1500487 ] [0.15572585 0.19402805 0.17449684 0.11558499 0.09939079] [0.13390765 0.16684347 0.1500487 0.09939079 0.0854655 ]] .. testcode:: [states] print(thermal_dm(5, 1.25)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True Qobj data = [[0.46927974 0. 0. 0. 0. ] [0. 0.26071096 0. 0. 0. ] [0. 0. 0.14483942 0. 0. ] [0. 0. 0. 0.08046635 0. ] [0. 0. 0. 0. 0.04470353]] QuTiP also provides a set of distance metrics for determining how close two density matrix distributions are to each other. Included are the trace distance :func:`.tracedist`, fidelity :func:`.fidelity`, Hilbert-Schmidt distance :func:`.hilbert_dist`, Bures distance :func:`.bures_dist`, Bures angle :func:`.bures_angle`, and quantum Hellinger distance :func:`.hellinger_dist`. .. testcode:: [states] x = coherent_dm(5, 1.25) y = coherent_dm(5, np.complex(0, 1.25)) # <-- note the 'j' z = thermal_dm(5, 0.125) np.testing.assert_almost_equal(fidelity(x, x), 1) np.testing.assert_almost_equal(hellinger_dist(x, y), 1.3819080728932833) We also know that for two pure states, the trace distance (T) and the fidelity (F) are related by :math:`T = \sqrt{1 - F^{2}}`, while the quantum Hellinger distance (QHE) between two pure states :math:`\left|\psi\right>` and :math:`\left|\phi\right>` is given by :math:`QHE = \sqrt{2 - 2\left|\left<\psi | \phi\right>\right|^2}`. .. testcode:: [states] np.testing.assert_almost_equal(tracedist(y, x), np.sqrt(1 - fidelity(y, x) ** 2)) For a pure state and a mixed state, :math:`1 - F^{2} \le T` which can also be verified: .. testcode:: [states] assert 1 - fidelity(x, z) ** 2 < tracedist(x, z) .. _states-qubit: Qubit (two-level) systems ========================= Having spent a fair amount of time on basis states that represent harmonic oscillator states, we now move on to qubit, or two-level quantum systems (for example a spin-1/2). To create a state vector corresponding to a qubit system, we use the same :func:`.basis`, or :func:`.fock`, function with only two levels: .. testcode:: [states] spin = basis(2, 0) Now at this point one may ask how this state is different than that of a harmonic oscillator in the vacuum state truncated to two energy levels? .. testcode:: [states] vac = basis(2, 0) At this stage, there is no difference. This should not be surprising as we called the exact same function twice. The difference between the two comes from the action of the spin operators :func:`.sigmax`, :func:`.sigmay`, :func:`.sigmaz`, :func:`.sigmap`, and :func:`.sigmam` on these two-level states. For example, if ``vac`` corresponds to the vacuum state of a harmonic oscillator, then, as we have already seen, we can use the raising operator to get the :math:`\left|1\right>` state: .. testcode:: [states] print(vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[1.] [0.]] .. testcode:: [states] c = create(2) print(c * vac) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.] [1.]] For a spin system, the operator analogous to the raising operator is the sigma-plus operator :func:`.sigmap`. Operating on the ``spin`` state gives: .. testcode:: [states] print(spin) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[1.] [0.]] .. testcode:: [states] print(sigmap() * spin) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.] [0.]] Now we see the difference! The :func:`.sigmap` operator acting on the ``spin`` state returns the zero vector. Why is this? To see what happened, let us use the :func:`.sigmaz` operator: .. testcode:: [states] print(sigmaz()) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[ 1. 0.] [ 0. -1.]] .. testcode:: [states] print(sigmaz() * spin) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[1.] [0.]] .. testcode:: [states] spin2 = basis(2, 1) print(spin2) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[0.] [1.]] .. testcode:: [states] print(sigmaz() * spin2) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[ 0.] [-1.]] The answer is now apparent. Since the QuTiP :func:`.sigmaz` function uses the standard z-basis representation of the sigma-z spin operator, the ``spin`` state corresponds to the :math:`\left|\uparrow\right>` state of a two-level spin system while ``spin2`` gives the :math:`\left|\downarrow\right>` state. Therefore, in our previous example ``sigmap() * spin``, we raised the qubit state out of the truncated two-level Hilbert space resulting in the zero state. While at first glance this convention might seem somewhat odd, it is in fact quite handy. For one, the spin operators remain in the conventional form. Second, when the spin system is in the :math:`\left|\uparrow\right>` state: .. testcode:: [states] print(sigmaz() * spin) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket Qobj data = [[1.] [0.]] the non-zero component is the zeroth-element of the underlying matrix (remember that python uses c-indexing, and matrices start with the zeroth element). The :math:`\left|\downarrow\right>` state therefore has a non-zero entry in the first index position. This corresponds nicely with the quantum information definitions of qubit states, where the excited :math:`\left|\uparrow\right>` state is label as :math:`\left|0\right>`, and the :math:`\left|\downarrow\right>` state by :math:`\left|1\right>`. If one wants to create spin operators for higher spin systems, then the :func:`.jmat` function comes in handy. .. _quantum_gates: Gates ===== The pre-defined gates are shown in the table below: .. cssclass:: table-striped +------------------------------------------------+-------------------------------------------------------+ | Gate function | Description | +================================================+=======================================================+ | :func:`~qutip.core.gates.rx` | Rotation around x axis | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.ry` | Rotation around y axis | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.rz` | Rotation around z axis | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.sqrtnot` | Square root of not gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.sqrtnot` | Square root of not gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.snot` | Hardmard gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.phasegate` | Phase shift gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.qrot` | A qubit rotation under a Rabi pulse | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.cy_gate` | Controlled y gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.cz_gate` | Controlled z gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.s_gate` | Single-qubit rotation | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.t_gate` | Square root of s gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.cs_gate` | Controlled s gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.ct_gate` | Controlled t gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.cphase` | Controlled phase gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.cnot` | Controlled not gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.csign` | Same as cphase | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.berkeley` | Berkeley gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.swapalpha` | Swapalpha gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.swap` | Swap the states of two qubits | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.iswap` | Swap gate with additional phase for 01 and 10 states | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.sqrtswap` | Square root of the swap gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.sqrtiswap` | Square root of the iswap gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.fredkin` | Fredkin gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.molmer_sorensen` | Molmer Sorensen gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.toffoli` | Toffoli gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.hadamard_transform` | Hadamard gate | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.qubit_clifford_group` | Generates the Clifford group on a single qubit | +------------------------------------------------+-------------------------------------------------------+ | :func:`~qutip.core.gates.globalphase` | Global phase gate | +------------------------------------------------+-------------------------------------------------------+ To load this qutip module, first you have to import gates: .. code-block:: Python from qutip import gates For example to use the Hadamard Gate: .. testcode:: [basics] H = gates.hadamard_transform() print(H) **Output**: .. testoutput:: [basics] :options: +NORMALIZE_WHITESPACE Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=True Qobj data = [[ 0.70710678 0.70710678] [0.70710678 -0.70710678]] .. _states-expect: Expectation values =================== Some of the most important information about quantum systems comes from calculating the expectation value of operators, both Hermitian and non-Hermitian, as the state or density matrix of the system varies in time. Therefore, in this section we demonstrate the use of the :func:`.expect` function. To begin: .. testcode:: [states] vac = basis(5, 0) one = basis(5, 1) c = create(5) N = num(5) np.testing.assert_almost_equal(expect(N, vac), 0) np.testing.assert_almost_equal(expect(N, one), 1) coh = coherent_dm(5, 1.0j) np.testing.assert_almost_equal(expect(N, coh), 0.9970555745806597) cat = (basis(5, 4) + 1.0j * basis(5, 3)).unit() np.testing.assert_almost_equal(expect(c, cat), 0.9999999999999998j) The :func:`.expect` function also accepts lists or arrays of state vectors or density matrices for the second input: .. testcode:: [states] states = [(c**k * vac).unit() for k in range(5)] # must normalize print(expect(N, states)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [0. 1. 2. 3. 4.] .. testcode:: [states] cat_list = [(basis(5, 4) + x * basis(5, 3)).unit() for x in [0, 1.0j, -1.0, -1.0j]] print(expect(c, cat_list)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [ 0.+0.j 0.+1.j -1.+0.j 0.-1.j] Notice how in this last example, all of the return values are complex numbers. This is because the :func:`.expect` function looks to see whether the operator is Hermitian or not. If the operator is Hermitian, then the output will always be real. In the case of non-Hermitian operators, the return values may be complex. Therefore, the :func:`.expect` function will return an array of complex values for non-Hermitian operators when the input is a list/array of states or density matrices. Of course, the :func:`.expect` function works for spin states and operators: .. testcode:: [states] up = basis(2, 0) down = basis(2, 1) np.testing.assert_almost_equal(expect(sigmaz(), up), 1) np.testing.assert_almost_equal(expect(sigmaz(), down), -1) as well as the composite objects discussed in the next section :ref:`tensor`: .. testcode:: [states] spin1 = basis(2, 0) spin2 = basis(2, 1) two_spins = tensor(spin1, spin2) sz1 = tensor(sigmaz(), qeye(2)) sz2 = tensor(qeye(2), sigmaz()) np.testing.assert_almost_equal(expect(sz1, two_spins), 1) np.testing.assert_almost_equal(expect(sz2, two_spins), -1) .. _states-super: Superoperators and Vectorized Operators ======================================= In addition to state vectors and density operators, QuTiP allows for representing maps that act linearly on density operators using the Kraus, Liouville supermatrix and Choi matrix formalisms. This support is based on the correspondence between linear operators acting on a Hilbert space, and vectors in two copies of that Hilbert space, :math:`\mathrm{vec} : \mathcal{L}(\mathcal{H}) \to \mathcal{H} \otimes \mathcal{H}` [Hav03]_, [Wat13]_. This isomorphism is implemented in QuTiP by the :obj:`.operator_to_vector` and :obj:`.vector_to_operator` functions: .. testcode:: [states] psi = basis(2, 0) rho = ket2dm(psi) print(rho) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[1. 0.] [0. 0.]] .. testcode:: [states] vec_rho = operator_to_vector(rho) print(vec_rho) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [1]], shape = (4, 1), type = operator-ket Qobj data = [[1.] [0.] [0.] [0.]] .. testcode:: [states] rho2 = vector_to_operator(vec_rho) np.testing.assert_almost_equal((rho - rho2).norm(), 0) The :attr:`.Qobj.type` attribute indicates whether a quantum object is a vector corresponding to an operator (``operator-ket``), or its Hermitian conjugate (``operator-bra``). Note that QuTiP uses the *column-stacking* convention for the isomorphism between :math:`\mathcal{L}(\mathcal{H})` and :math:`\mathcal{H} \otimes \mathcal{H}`: .. testcode:: [states] A = Qobj(np.arange(4).reshape((2, 2))) print(A) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False Qobj data = [[0. 1.] [2. 3.]] .. testcode:: [states] print(operator_to_vector(A)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [1]], shape = (4, 1), type = operator-ket Qobj data = [[0.] [2.] [1.] [3.]] Since :math:`\mathcal{H} \otimes \mathcal{H}` is a vector space, linear maps on this space can be represented as matrices, often called *superoperators*. Using the :obj:`.Qobj`, the :obj:`.spre` and :obj:`.spost` functions, supermatrices corresponding to left- and right-multiplication respectively can be quickly constructed. .. testcode:: [states] X = sigmax() S = spre(X) * spost(X.dag()) # Represents conjugation by X. Note that this is done automatically by the :obj:`.to_super` function when given ``type='oper'`` input. .. testcode:: [states] S2 = to_super(X) np.testing.assert_almost_equal((S - S2).norm(), 0) Quantum objects representing superoperators are denoted by ``type='super'``: .. testcode:: [states] print(S) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True Qobj data = [[0. 0. 0. 1.] [0. 0. 1. 0.] [0. 1. 0. 0.] [1. 0. 0. 0.]] Information about superoperators, such as whether they represent completely positive maps, is exposed through the :attr:`.Qobj.iscp`, :attr:`.Qobj.istp` and :attr:`.Qobj.iscptp` attributes: .. testcode:: [states] print(S.iscp, S.istp, S.iscptp) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE True True True In addition, dynamical generators on this extended space, often called *Liouvillian superoperators*, can be created using the :func:`.liouvillian` function. Each of these takes a Hamiltonian along with a list of collapse operators, and returns a ``type="super"`` object that can be exponentiated to find the superoperator for that evolution. .. testcode:: [states] H = 10 * sigmaz() c1 = destroy(2) L = liouvillian(H, [c1]) print(L) S = (12 * L).expm() **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = False Qobj data = [[ 0. +0.j 0. +0.j 0. +0.j 1. +0.j] [ 0. +0.j -0.5+20.j 0. +0.j 0. +0.j] [ 0. +0.j 0. +0.j -0.5-20.j 0. +0.j] [ 0. +0.j 0. +0.j 0. +0.j -1. +0.j]] For qubits, a particularly useful way to visualize superoperators is to plot them in the Pauli basis, such that :math:`S_{\mu,\nu} = \langle\!\langle \sigma_{\mu} | S[\sigma_{\nu}] \rangle\!\rangle`. Because the Pauli basis is Hermitian, :math:`S_{\mu,\nu}` is a real number for all Hermitian-preserving superoperators :math:`S`, allowing us to plot the elements of :math:`S` as a `Hinton diagram `_. In such diagrams, positive elements are indicated by white squares, and negative elements by black squares. The size of each element is indicated by the size of the corresponding square. For instance, let :math:`S[\rho] = \sigma_x \rho \sigma_x^{\dagger}`. Then :math:`S[\sigma_{\mu}] = \sigma_{\mu} \cdot \begin{cases} +1 & \mu = 0, x \\ -1 & \mu = y, z \end{cases}`. We can quickly see this by noting that the :math:`Y` and :math:`Z` elements of the Hinton diagram for :math:`S` are negative: .. plot:: from qutip import * settings.colorblind_safe = True import matplotlib.pyplot as plt plt.rcParams['savefig.transparent'] = True X = sigmax() S = spre(X) * spost(X.dag()) hinton(S) Choi, Kraus, Stinespring and :math:`\chi` Representations ========================================================= In addition to the superoperator representation of quantum maps, QuTiP supports several other useful representations. First, the Choi matrix :math:`J(\Lambda)` of a quantum map :math:`\Lambda` is useful for working with ancilla-assisted process tomography (AAPT), and for reasoning about properties of a map or channel. Up to normalization, the Choi matrix is defined by acting :math:`\Lambda` on half of an entangled pair. In the column-stacking convention, .. math:: J(\Lambda) = (\mathbb{1} \otimes \Lambda) [|\mathbb{1}\rangle\!\rangle \langle\!\langle \mathbb{1}|]. In QuTiP, :math:`J(\Lambda)` can be found by calling the :func:`.to_choi` function on a ``type="super"`` :obj:`.Qobj`. .. testcode:: [states] X = sigmax() S = sprepost(X, X) J = to_choi(S) print(J) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True, superrep = choi Qobj data = [[0. 0. 0. 0.] [0. 1. 1. 0.] [0. 1. 1. 0.] [0. 0. 0. 0.]] .. testcode:: [states] print(to_choi(spre(qeye(2)))) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True, superrep = choi Qobj data = [[1. 0. 0. 1.] [0. 0. 0. 0.] [0. 0. 0. 0.] [1. 0. 0. 1.]] If a :obj:`.Qobj` instance is already in the Choi :attr:`.Qobj.superrep`, then calling :func:`.to_choi` does nothing: .. testcode:: [states] print(to_choi(J)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True, superrep = choi Qobj data = [[0. 0. 0. 0.] [0. 1. 1. 0.] [0. 1. 1. 0.] [0. 0. 0. 0.]] To get back to the superoperator representation, simply use the :func:`.to_super` function. As with :func:`.to_choi`, :func:`.to_super` is idempotent: .. testcode:: [states] print(to_super(J) - S) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True Qobj data = [[0. 0. 0. 0.] [0. 0. 0. 0.] [0. 0. 0. 0.] [0. 0. 0. 0.]] .. testcode:: [states] print(to_super(S)) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True Qobj data = [[0. 0. 0. 1.] [0. 0. 1. 0.] [0. 1. 0. 0.] [1. 0. 0. 0.]] We can quickly obtain another useful representation from the Choi matrix by taking its eigendecomposition. In particular, let :math:`\{A_i\}` be a set of operators such that :math:`J(\Lambda) = \sum_i |A_i\rangle\!\rangle \langle\!\langle A_i|`. We can write :math:`J(\Lambda)` in this way for any hermicity-preserving map; that is, for any map :math:`\Lambda` such that :math:`J(\Lambda) = J^\dagger(\Lambda)`. These operators then form the Kraus representation of :math:`\Lambda`. In particular, for any input :math:`\rho`, .. math:: \Lambda(\rho) = \sum_i A_i \rho A_i^\dagger. Notice using the column-stacking identity that :math:`(C^\mathrm{T} \otimes A) |B\rangle\!\rangle = |ABC\rangle\!\rangle`, we have that .. math:: \sum_i (\mathbb{1} \otimes A_i) (\mathbb{1} \otimes A_i)^\dagger |\mathbb{1}\rangle\!\rangle \langle\!\langle\mathbb{1}| = \sum_i |A_i\rangle\!\rangle \langle\!\langle A_i| = J(\Lambda). The Kraus representation of a hermicity-preserving map can be found in QuTiP using the :func:`.to_kraus` function. .. testcode:: [states] del sum # np.sum overwrote sum and caused a bug. .. testcode:: [states] I, X, Y, Z = qeye(2), sigmax(), sigmay(), sigmaz() .. testcode:: [states] S = sum([sprepost(P, P) for P in (I, X, Y, Z)]) / 4 print(S) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True Qobj data = [[0.5 0. 0. 0.5] [0. 0. 0. 0. ] [0. 0. 0. 0. ] [0.5 0. 0. 0.5]] .. testcode:: [states] J = to_choi(S) print(J) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True, superrep = choi Qobj data = [[0.5 0. 0. 0. ] [0. 0.5 0. 0. ] [0. 0. 0.5 0. ] [0. 0. 0. 0.5]] .. testcode:: [states] print(J.eigenstates()[1]) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [Quantum object: dims = [[[2], [2]], [1, 1]], shape = (4, 1), type = operator-ket Qobj data = [[1.] [0.] [0.] [0.]] Quantum object: dims = [[[2], [2]], [1, 1]], shape = (4, 1), type = operator-ket Qobj data = [[0.] [1.] [0.] [0.]] Quantum object: dims = [[[2], [2]], [1, 1]], shape = (4, 1), type = operator-ket Qobj data = [[0.] [0.] [1.] [0.]] Quantum object: dims = [[[2], [2]], [1, 1]], shape = (4, 1), type = operator-ket Qobj data = [[0.] [0.] [0.] [1.]]] .. testcode:: [states] K = to_kraus(S) print(K) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0.70710678 0. ] [0. 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False Qobj data = [[0. 0. ] [0.70710678 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False Qobj data = [[0. 0.70710678] [0. 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0. ] [0. 0.70710678]]] As with the other representation conversion functions, :func:`.to_kraus` checks the :attr:`.Qobj.superrep` attribute of its input, and chooses an appropriate conversion method. Thus, in the above example, we can also call :func:`.to_kraus` on ``J``. .. testcode:: [states] KJ = to_kraus(J) print(KJ) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0.70710678 0. ] [0. 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False Qobj data = [[0. 0. ] [0.70710678 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False Qobj data = [[0. 0.70710678] [0. 0. ]], Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0. ] [0. 0.70710678]]] .. testcode:: [states] for A, AJ in zip(K, KJ): print(A - AJ) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.] [0. 0.]] Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.] [0. 0.]] Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.] [0. 0.]] Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.] [0. 0.]] The Stinespring representation is closely related to the Kraus representation, and consists of a pair of operators :math:`A` and :math:`B` such that for all operators :math:`X` acting on :math:`\mathcal{H}`, .. math:: \Lambda(X) = \operatorname{Tr}_2(A X B^\dagger), where the partial trace is over a new index that corresponds to the index in the Kraus summation. Conversion to Stinespring is handled by the :func:`.to_stinespring` function. .. testcode:: [states] a = create(2).dag() S_ad = sprepost(a * a.dag(), a * a.dag()) + sprepost(a, a.dag()) S = 0.9 * sprepost(I, I) + 0.1 * S_ad print(S) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = False Qobj data = [[1. 0. 0. 0.1] [0. 0.9 0. 0. ] [0. 0. 0.9 0. ] [0. 0. 0. 0.9]] .. testcode:: [states] A, B = to_stinespring(S) print(A) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 3], [2]], shape = (6, 2), type = oper, isherm = False Qobj data = [[-0.98845443 0. ] [ 0. 0.31622777] [ 0.15151842 0. ] [ 0. -0.93506452] [ 0. 0. ] [ 0. -0.16016975]] .. testcode:: [states] print(B) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 3], [2]], shape = (6, 2), type = oper, isherm = False Qobj data = [[-0.98845443 0. ] [ 0. 0.31622777] [ 0.15151842 0. ] [ 0. -0.93506452] [ 0. 0. ] [ 0. -0.16016975]] Notice that a new index has been added, such that :math:`A` and :math:`B` have dimensions ``[[2, 3], [2]]``, with the length-3 index representing the fact that the Choi matrix is rank-3 (alternatively, that the map has three Kraus operators). .. testcode:: [states] to_kraus(S) print(to_choi(S).eigenenergies()) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [0. 0.04861218 0.1 1.85138782] Finally, the last superoperator representation supported by QuTiP is the :math:`\chi`-matrix representation, .. math:: \Lambda(\rho) = \sum_{\alpha,\beta} \chi_{\alpha,\beta} B_{\alpha} \rho B_{\beta}^\dagger, where :math:`\{B_\alpha\}` is a basis for the space of matrices acting on :math:`\mathcal{H}`. In QuTiP, this basis is taken to be the Pauli basis :math:`B_\alpha = \sigma_\alpha / \sqrt{2}`. Conversion to the :math:`\chi` formalism is handled by the :func:`.to_chi` function. .. testcode:: [states] chi = to_chi(S) print(chi) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True, superrep = chi Qobj data = [[3.7+0.j 0. +0.j 0. +0.j 0.1+0.j ] [0. +0.j 0.1+0.j 0. +0.1j 0. +0.j ] [0. +0.j 0. -0.1j 0.1+0.j 0. +0.j ] [0.1+0.j 0. +0.j 0. +0.j 0.1+0.j ]] One convenient property of the :math:`\chi` matrix is that the average gate fidelity with the identity map can be read off directly from the :math:`\chi_{00}` element: .. testcode:: [states] np.testing.assert_almost_equal(average_gate_fidelity(S), 0.9499999999999998) print(chi[0, 0] / 4) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE (0.925+0j) Here, the factor of 4 comes from the dimension of the underlying Hilbert space :math:`\mathcal{H}`. As with the superoperator and Choi representations, the :math:`\chi` representation is denoted by the :attr:`.Qobj.superrep`, such that :func:`.to_super`, :func:`.to_choi`, :func:`.to_kraus`, :func:`.to_stinespring` and :func:`.to_chi` all convert from the :math:`\chi` representation appropriately. Properties of Quantum Maps ========================== In addition to converting between the different representations of quantum maps, QuTiP also provides attributes to make it easy to check if a map is completely positive, trace preserving and/or hermicity preserving. Each of these attributes uses :attr:`.Qobj.superrep` to automatically perform any needed conversions. In particular, a quantum map is said to be positive (but not necessarily completely positive) if it maps all positive operators to positive operators. For instance, the transpose map :math:`\Lambda(\rho) = \rho^{\mathrm{T}}` is a positive map. We run into problems, however, if we tensor :math:`\Lambda` with the identity to get a partial transpose map. .. testcode:: [states] rho = ket2dm(bell_state()) rho_out = partial_transpose(rho, [0, 1]) print(rho_out.eigenenergies()) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE [-0.5 0.5 0.5 0.5] Notice that even though we started with a positive map, we got an operator out with negative eigenvalues. Complete positivity addresses this by requiring that a map returns positive operators for all positive operators, and does so even under tensoring with another map. The Choi matrix is very useful here, as it can be shown that a map is completely positive if and only if its Choi matrix is positive [Wat13]_. QuTiP implements this check with the :attr:`.Qobj.iscp` attribute. As an example, notice that the snippet above already calculates the Choi matrix of the transpose map by acting it on half of an entangled pair. We simply need to manually set the ``dims`` and ``superrep`` attributes to reflect the structure of the underlying Hilbert space and the chosen representation. .. testcode:: [states] J = rho_out J.dims = [[[2], [2]], [[2], [2]]] J.superrep = 'choi' print(J.iscp) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE False This confirms that the transpose map is not completely positive. On the other hand, the transpose map does satisfy a weaker condition, namely that it is hermicity preserving. That is, :math:`\Lambda(\rho) = (\Lambda(\rho))^\dagger` for all :math:`\rho` such that :math:`\rho = \rho^\dagger`. To see this, we note that :math:`(\rho^{\mathrm{T}})^\dagger = \rho^*`, the complex conjugate of :math:`\rho`. By assumption, :math:`\rho = \rho^\dagger = (\rho^*)^{\mathrm{T}}`, though, such that :math:`\Lambda(\rho) = \Lambda(\rho^\dagger) = \rho^*`. We can confirm this by checking the :attr:`.Qobj.ishp` attribute: .. testcode:: [states] print(J.ishp) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE True Next, we note that the transpose map does preserve the trace of its inputs, such that :math:`\operatorname{Tr}(\Lambda[\rho]) = \operatorname{Tr}(\rho)` for all :math:`\rho`. This can be confirmed by the :attr:`.Qobj.istp` attribute: .. testcode:: [states] print(J.istp) **Output**: .. testoutput:: [states] :options: +NORMALIZE_WHITESPACE False Finally, a map is called a quantum channel if it always maps valid states to valid states. Formally, a map is a channel if it is both completely positive and trace preserving. Thus, QuTiP provides a single attribute to quickly check that this is true. .. doctest:: [states] >>> print(J.iscptp) False >>> print(to_super(qeye(2)).iscptp) True qutip-5.1.1/doc/guide/guide-steady.rst000066400000000000000000000222161474175217300176560ustar00rootroot00000000000000.. _steady: ************************************* Solving for Steady-State Solutions ************************************* .. _steady-intro: Introduction ============ For time-independent open quantum systems with decay rates larger than the corresponding excitation rates, the system will tend toward a steady state as :math:`t\rightarrow\infty` that satisfies the equation .. math:: \frac{d\hat{\rho}_{ss}}{dt}=\mathcal{L}\hat{\rho}_{ss}=0. Although the requirement for time-independence seems quite resitrictive, one can often employ a transformation to the interaction picture that yields a time-independent Hamiltonian. For many these systems, solving for the asymptotic density matrix :math:`\hat{\rho}_{ss}` can be achieved using direct or iterative solution methods faster than using master equation or Monte Carlo simulations. Although the steady state equation has a simple mathematical form, the properties of the Liouvillian operator are such that the solutions to this equation are anything but straightforward to find. Steady State solvers in QuTiP ============================= In QuTiP, the steady-state solution for a system Hamiltonian or Liouvillian is given by :func:`.steadystate`. This function implements a number of different methods for finding the steady state, each with their own pros and cons, where the method used can be chosen using the ``method`` keyword argument. .. cssclass:: table-striped .. list-table:: :widths: 10 15 30 :header-rows: 1 * - Method - Keyword - Description * - Direct (default) - 'direct' - Direct solution solving :math:`Ax=b`. * - Eigenvalue - 'eigen' - Iteratively find the zero eigenvalue of :math:`\mathcal{L}`. * - Inverse-Power - 'power' - Solve using the inverse-power method. * - SVD - 'svd' - Steady-state solution via the **dense** SVD of the Liouvillian. The function :func:`.steadystate` can take either a Hamiltonian and a list of collapse operators as input, generating internally the corresponding Liouvillian super operator in Lindblad form, or alternatively, a Liouvillian passed by the user. Both the ``"direct"`` and ``"power"`` method need to solve a linear equation system. To do so, there are multiple solvers available: `` .. cssclass:: table-striped .. list-table:: :widths: 10 15 20 :header-rows: 1 * - Solver - Original function - Description * - "solve" - ``numpy.linalg.solve`` - Dense solver from numpy. * - "lstsq" - ``numpy.linalg.lstsq`` - Dense least-squares solver. * - "spsolve" - ``scipy.sparse.linalg.spsolve`` - Sparse solver from scipy. * - "gmres" - ``scipy.sparse.linalg.gmres`` - Generalized Minimal RESidual iterative solver. * - "lgmres" - ``scipy.sparse.linalg.lgmres`` - LGMRES iterative solver. * - "bicgstab" - ``scipy.sparse.linalg.bicgstab`` - BIConjugate Gradient STABilized iterative solver. * - "mkl_spsolve" - ``pardiso`` - Intel Pardiso LU solver from MKL QuTiP can take advantage of the Intel Pardiso LU solver in the Intel Math Kernel library that comes with the Anacoda (2.5+) and Intel Python distributions. This gives a substantial increase in performance compared with the standard SuperLU method used by SciPy. To verify that QuTiP can find the necessary libraries, one can check for ``INTEL MKL Ext: True`` in the QuTiP about box (:func:`.about`). .. _steady-usage: Using the Steadystate Solver ============================= Solving for the steady state solution to the Lindblad master equation for a general system with :func:`.steadystate` can be accomplished using:: >>> rho_ss = steadystate(H, c_ops) where ``H`` is a quantum object representing the system Hamiltonian, and ``c_ops`` is a list of quantum objects for the system collapse operators. The output, labelled as ``rho_ss``, is the steady-state solution for the systems. If no other keywords are passed to the solver, the default 'direct' method is used with ``numpy.linalg.solve``, generating a solution that is exact to machine precision at the expense of a large memory requirement. However Liouvillians are often quite sparse and using a sparse solver may be preferred: .. code-block:: python rho_ss = steadystate(H, c_ops, method="power", solver="spsolve") where ``method='power'`` indicates that we are using the inverse-power solution method, and ``solver="spsolve"`` indicate to use the sparse solver. Sparse solvers may still use quite a large amount of memory when they factorize the matrix since the Liouvillian usually has a large bandwidth. To address this, :func:`.steadystate` allows one to use the bandwidth minimization algorithms listed in :ref:`steady-args`. For example: .. code-block:: python rho_ss = steadystate(H, c_ops, solver="spsolve", use_rcm=True) where ``use_rcm=True`` turns on a bandwidth minimization routine. Although it is not obvious, the ``'direct'``, ``'eigen'``, and ``'power'`` methods all use an LU decomposition internally and thus can have a large memory overhead. In contrast, iterative solvers such as the ``'gmres'``, ``'lgmres'``, and ``'bicgstab'`` do not factor the matrix and thus take less memory than the LU methods and allow, in principle, for extremely large system sizes. The downside is that these methods can take much longer than the direct method as the condition number of the Liouvillian matrix is large, indicating that these iterative methods require a large number of iterations for convergence. To overcome this, one can use a preconditioner :math:`M` that solves for an approximate inverse for the (modified) Liouvillian, thus better conditioning the problem, leading to faster convergence. The use of a preconditioner can actually make these iterative methods faster than the other solution methods. The problem with precondioning is that it is only well defined for Hermitian matrices. Since the Liouvillian is non-Hermitian, the ability to find a good preconditioner is not guaranteed. And moreover, if a preconditioner is found, it is not guaranteed to have a good condition number. QuTiP can make use of an incomplete LU preconditioner when using the iterative ``'gmres'``, ``'lgmres'``, and ``'bicgstab'`` solvers by setting ``use_precond=True``. The preconditioner optionally makes use of a combination of symmetric and anti-symmetric matrix permutations that attempt to improve the preconditioning process. These features are discussed in the :ref:`steady-args` section. Even with these state-of-the-art permutations, the generation of a successful preconditoner for non-symmetric matrices is currently a trial-and-error process due to the lack of mathematical work done in this area. It is always recommended to begin with the direct solver with no additional arguments before selecting a different method. Finding the steady-state solution is not limited to the Lindblad form of the master equation. Any time-independent Liouvillian constructed from a Hamiltonian and collapse operators can be used as an input:: >>> rho_ss = steadystate(L) where ``L`` is the Louvillian. All of the additional arguments can also be used in this case. .. _steady-args: Additional Solver Arguments ============================= The following additional solver arguments are available for the steady-state solver: .. cssclass:: table-striped .. list-table:: :widths: 10 30 60 :header-rows: 1 * - Keyword - Default - Description * - weight - None - Set the weighting factor used in the ``'direct'`` method. * - use_precond - False - Generate a preconditioner when using the ``'gmres'`` and ``'lgmres'`` methods. * - use_rcm - False - Use a Reverse Cuthill-Mckee reordering to minimize the bandwidth of the modified Liouvillian used in the LU decomposition. * - use_wbm - False - Use a Weighted Bipartite Matching algorithm to attempt to make the modified Liouvillian more diagonally dominant, and thus for favorable for preconditioning. * - power_tol - 1e-12 - Tolerance for the solution when using the 'power' method. * - power_maxiter - 10 - Maximum number of iterations of the power method. * - power_eps - 1e-15 - Small weight used in the "power" method. * - \*\*kwargs - {} - Options to pass through the linalg solvers. See the corresponding documentation from scipy for a full list. Further information can be found in the :func:`.steadystate` docstrings. .. _steady-example: Example: Harmonic Oscillator in Thermal Bath ============================================ A simple example of a system that reaches a steady state is a harmonic oscillator coupled to a thermal environment. Below we consider a harmonic oscillator, initially in the :math:`\left|10\right>` number state, and weakly coupled to a thermal environment characterized by an average particle expectation value of :math:`\left=2`. We calculate the evolution via master equation and Monte Carlo methods, and see that they converge to the steady-state solution. Here we choose to perform only a few Monte Carlo trajectories so we can distinguish this evolution from the master-equation solution. .. plot:: guide/scripts/ex_steady.py :include-source: qutip-5.1.1/doc/guide/guide-super.rst000066400000000000000000000107441474175217300175260ustar00rootroot00000000000000.. _super: ***************************************************** Superoperators, Pauli Basis and Channel Contraction ***************************************************** written by `Christopher Granade `, Institute for Quantum Computing In this guide, we will demonstrate the :func:`.tensor_contract` function, which contracts one or more pairs of indices of a Qobj. This functionality can be used to find rectangular superoperators that implement the partial trace channel :math:S(\rho) = \Tr_2(\rho)`, for instance. Using this functionality, we can quickly turn a system-environment representation of an open quantum process into a superoperator representation. .. _super-representation-plotting: Superoperator Representations and Plotting ========================================== We start off by first demonstrating plotting of superoperators, as this will be useful to us in visualizing the results of a contracted channel. In particular, we will use Hinton diagrams as implemented by :func:`~qutip.visualization.hinton`, which show the real parts of matrix elements as squares whose size and color both correspond to the magnitude of each element. To illustrate, we first plot a few density operators. .. plot:: :context: reset from qutip import hinton, identity, Qobj, to_super, sigmaz, tensor, tensor_contract from qutip.core.gates import cnot, hadamard_transform hinton(identity([2, 3]).unit()) hinton(Qobj([[1, 0.5], [0.5, 1]]).unit()) We show superoperators as matrices in the *Pauli basis*, such that any Hermicity-preserving map is represented by a real-valued matrix. This is especially convienent for use with Hinton diagrams, as the plot thus carries complete information about the channel. As an example, conjugation by :math:`\sigma_z` leaves :math:`\mathbb{1}` and :math:`\sigma_z` invariant, but flips the sign of :math:`\sigma_x` and :math:`\sigma_y`. This is indicated in Hinton diagrams by a negative-valued square for the sign change and a positive-valued square for a +1 sign. .. plot:: :context: close-figs hinton(to_super(sigmaz())) As a couple more examples, we also consider the supermatrix for a Hadamard transform and for :math:`\sigma_z \otimes H`. .. plot:: :context: close-figs hinton(to_super(hadamard_transform())) hinton(to_super(tensor(sigmaz(), hadamard_transform()))) .. _super-reduced-channels: Reduced Channels ================ As an example of tensor contraction, we now consider the map .. math:: S(\rho)=\Tr_2 (\scriptstyle \rm CNOT (\rho \otimes \ket{0}\bra{0}) \scriptstyle \rm CNOT^\dagger) We can think of the :math:`\scriptstyle \rm CNOT` here as a system-environment representation of an open quantum process, in which an environment register is prepared in a state :math:`\rho_{\text{anc}}`, then a unitary acts jointly on the system of interest and environment. Finally, the environment is traced out, leaving a *channel* on the system alone. In terms of `Wood diagrams `, this can be represented as the composition of a preparation map, evolution under the system-environment unitary, and then a measurement map. .. figure:: figures/sprep-wood-diagram.png :align: center :width: 2.5in The two tensor wires on the left indicate where we must take a tensor contraction to obtain the measurement map. Numbering the tensor wires from 0 to 3, this corresponds to a :func:`.tensor_contract` argument of ``(1, 3)``. .. plot:: :context: :nofigs: tensor_contract(to_super(identity([2, 2])), (1, 3)) Meanwhile, the :func:`.super_tensor` function implements the swap on the right, such that we can quickly find the preparation map. .. plot:: :context: :nofigs: q = tensor(identity(2), basis(2)) s_prep = sprepost(q, q.dag()) For a :math:`\scriptstyle \rm CNOT` system-environment model, the composition of these maps should give us a completely dephasing channel. The channel on both qubits is just the superunitary :math:`\scriptstyle \rm CNOT` channel: .. plot:: :context: close-figs hinton(to_super(cnot())) We now complete by multiplying the superunitary :math:`\scriptstyle \rm CNOT` by the preparation channel above, then applying the partial trace channel by contracting the second and fourth index indices. As expected, this gives us a dephasing map. .. plot:: :context: close-figs hinton(tensor_contract(to_super(cnot()), (1, 3)) * s_prep) .. plot:: :context: reset :include-source: false :nofigs: # reset the context at the end qutip-5.1.1/doc/guide/guide-tensor.rst000066400000000000000000000303551474175217300177020ustar00rootroot00000000000000.. _tensor: ****************************************** Using Tensor Products and Partial Traces ****************************************** .. _tensor-products: Tensor products =============== To describe the states of multipartite quantum systems - such as two coupled qubits, a qubit coupled to an oscillator, etc. - we need to expand the Hilbert space by taking the tensor product of the state vectors for each of the system components. Similarly, the operators acting on the state vectors in the combined Hilbert space (describing the coupled system) are formed by taking the tensor product of the individual operators. In QuTiP the function :func:`~qutip.core.tensor.tensor` is used to accomplish this task. This function takes as argument a collection:: >>> tensor(op1, op2, op3) # doctest: +SKIP or a ``list``:: >>> tensor([op1, op2, op3]) # doctest: +SKIP of state vectors *or* operators and returns a composite quantum object for the combined Hilbert space. The function accepts an arbitrary number of states or operators as argument. The type returned quantum object is the same as that of the input(s). For example, the state vector describing two qubits in their ground states is formed by taking the tensor product of the two single-qubit ground state vectors: .. testcode:: [tensor] print(tensor(basis(2, 0), basis(2, 0))) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket Qobj data = [[1.] [0.] [0.] [0.]] or equivalently using the ``list`` format: .. testcode:: [tensor] print(tensor([basis(2, 0), basis(2, 0)])) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket Qobj data = [[1.] [0.] [0.] [0.]] This is straightforward to generalize to more qubits by adding more component state vectors in the argument list to the :func:`~qutip.core.tensor.tensor` function, as illustrated in the following example: .. testcode:: [tensor] print(tensor((basis(2, 0) + basis(2, 1)).unit(), (basis(2, 0) + basis(2, 1)).unit(), basis(2, 0))) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2, 2], [1, 1, 1]], shape = (8, 1), type = ket Qobj data = [[0.5] [0. ] [0.5] [0. ] [0.5] [0. ] [0.5] [0. ]] This state is slightly more complicated, describing two qubits in a superposition between the up and down states, while the third qubit is in its ground state. To construct operators that act on an extended Hilbert space of a combined system, we similarly pass a list of operators for each component system to the :func:`~qutip.core.tensor.tensor` function. For example, to form the operator that represents the simultaneous action of the :math:`\sigma_x` operator on two qubits: .. testcode:: [tensor] print(tensor(sigmax(), sigmax())) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True Qobj data = [[0. 0. 0. 1.] [0. 0. 1. 0.] [0. 1. 0. 0.] [1. 0. 0. 0.]] To create operators in a combined Hilbert space that only act on a single component, we take the tensor product of the operator acting on the subspace of interest, with the identity operators corresponding to the components that are to be unchanged. For example, the operator that represents :math:`\sigma_z` on the first qubit in a two-qubit system, while leaving the second qubit unaffected: .. testcode:: [tensor] print(tensor(sigmaz(), identity(2))) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True Qobj data = [[ 1. 0. 0. 0.] [ 0. 1. 0. 0.] [ 0. 0. -1. 0.] [ 0. 0. 0. -1.]] .. _tensor-product-example: Example: Constructing composite Hamiltonians ============================================ The :func:`~qutip.core.tensor.tensor` function is extensively used when constructing Hamiltonians for composite systems. Here we'll look at some simple examples. .. _tensor-product-example-2qubits: Two coupled qubits ------------------ First, let's consider a system of two coupled qubits. Assume that both the qubits have equal energy splitting, and that the qubits are coupled through a :math:`\sigma_x\otimes\sigma_x` interaction with strength g = 0.05 (in units where the bare qubit energy splitting is unity). The Hamiltonian describing this system is: .. testcode:: [tensor] H = tensor(sigmaz(), identity(2)) + tensor(identity(2), sigmaz()) + 0.05 * tensor(sigmax(), sigmax()) print(H) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True Qobj data = [[ 2. 0. 0. 0.05] [ 0. 0. 0.05 0. ] [ 0. 0.05 0. 0. ] [ 0.05 0. 0. -2. ]] .. _tensor-product-example-3qubits: Three coupled qubits -------------------- The two-qubit example is easily generalized to three coupled qubits: .. testcode:: [tensor] H = (tensor(sigmaz(), identity(2), identity(2)) + tensor(identity(2), sigmaz(), identity(2)) + tensor(identity(2), identity(2), sigmaz()) + 0.5 * tensor(sigmax(), sigmax(), identity(2)) + 0.25 * tensor(identity(2), sigmax(), sigmax())) print(H) **Output**: .. testoutput:: [tensor] :options: +NORMALIZE_WHITESPACE Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True Qobj data = [[ 3. 0. 0. 0.25 0. 0. 0.5 0. ] [ 0. 1. 0.25 0. 0. 0. 0. 0.5 ] [ 0. 0.25 1. 0. 0.5 0. 0. 0. ] [ 0.25 0. 0. -1. 0. 0.5 0. 0. ] [ 0. 0. 0.5 0. 1. 0. 0. 0.25] [ 0. 0. 0. 0.5 0. -1. 0.25 0. ] [ 0.5 0. 0. 0. 0. 0.25 -1. 0. ] [ 0. 0.5 0. 0. 0.25 0. 0. -3. ]] .. _tensor-product-example-jcmodel: A two-level system coupled to a cavity: The Jaynes-Cummings model ------------------------------------------------------------------- The simplest possible quantum mechanical description for light-matter interaction is encapsulated in the Jaynes-Cummings model, which describes the coupling between a two-level atom and a single-mode electromagnetic field (a cavity mode). Denoting the energy splitting of the atom and cavity ``omega_a`` and ``omega_c``, respectively, and the atom-cavity interaction strength ``g``, the Jaynes-Cummings Hamiltonian can be constructed as: .. plot:: :context: reset N = 6 omega_a = 1.0 omega_c = 1.25 g = 0.75 a = tensor(identity(2), destroy(N)) sm = tensor(destroy(2), identity(N)) sz = tensor(sigmaz(), identity(N)) H = 0.5 * omega_a * sz + omega_c * a.dag() * a + g * (a.dag() * sm + a * sm.dag()) hinton(H, fig=plt.figure(figsize=(12, 12))) Here ``N`` is the number of Fock states included in the cavity mode. .. _tensor-ptrace: Partial trace ============= The partial trace is an operation that reduces the dimension of a Hilbert space by eliminating some degrees of freedom by averaging (tracing). In this sense it is therefore the converse of the tensor product. It is useful when one is interested in only a part of a coupled quantum system. For open quantum systems, this typically involves tracing over the environment leaving only the system of interest. In QuTiP the class method :meth:`~qutip.core.qobj.Qobj.ptrace` is used to take partial traces. :meth:`~qutip.core.qobj.Qobj.ptrace` acts on the :class:`~qutip.core.qobj.Qobj` instance for which it is called, and it takes one argument ``sel``, which is a ``list`` of integers that mark the component systems that should be **kept**. All other components are traced out. For example, the density matrix describing a single qubit obtained from a coupled two-qubit system is obtained via: .. doctest:: [tensor] :options: +NORMALIZE_WHITESPACE >>> psi = tensor(basis(2, 0), basis(2, 1)) >>> psi.ptrace(0) Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[1. 0.] [0. 0.]] >>> psi.ptrace(1) Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0. 0.] [0. 1.]] Note that the partial trace always results in a density matrix (mixed state), regardless of whether the composite system is a pure state (described by a state vector) or a mixed state (described by a density matrix): .. doctest:: [tensor] :options: +NORMALIZE_WHITESPACE >>> psi = tensor((basis(2, 0) + basis(2, 1)).unit(), basis(2, 0)) >>> psi Quantum object: dims = [[2, 2], [1, 1]], shape = (4, 1), type = ket Qobj data = [[0.70710678] [0. ] [0.70710678] [0. ]] >>> psi.ptrace(0) Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0.5 0.5] [0.5 0.5]] >>> rho = tensor(ket2dm((basis(2, 0) + basis(2, 1)).unit()), fock_dm(2, 0)) >>> rho Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True Qobj data = [[0.5 0. 0.5 0. ] [0. 0. 0. 0. ] [0.5 0. 0.5 0. ] [0. 0. 0. 0. ]] >>> rho.ptrace(0) Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True Qobj data = [[0.5 0.5] [0.5 0.5]] Superoperators and Tensor Manipulations ======================================= As described in :ref:`states-super`, *superoperators* are operators that act on Liouville space, the vectorspace of linear operators. Superoperators can be represented using the isomorphism :math:`\mathrm{vec} : \mathcal{L}(\mathcal{H}) \to \mathcal{H} \otimes \mathcal{H}` [Hav03]_, [Wat13]_. To represent superoperators acting on :math:`\mathcal{L}(\mathcal{H}_1 \otimes \mathcal{H}_2)` thus takes some tensor rearrangement to get the desired ordering :math:`\mathcal{H}_1 \otimes \mathcal{H}_2 \otimes \mathcal{H}_1 \otimes \mathcal{H}_2`. In particular, this means that :func:`.tensor` does not act as one might expect on the results of :func:`.to_super`: .. doctest:: [tensor] >>> A = qeye([2]) >>> B = qeye([3]) >>> to_super(tensor(A, B)).dims [[[2, 3], [2, 3]], [[2, 3], [2, 3]]] >>> tensor(to_super(A), to_super(B)).dims [[[2], [2], [3], [3]], [[2], [2], [3], [3]]] In the former case, the result correctly has four copies of the compound index with dims ``[2, 3]``. In the latter case, however, each of the Hilbert space indices is listed independently and in the wrong order. The :func:`.super_tensor` function performs the needed rearrangement, providing the most direct analog to :func:`.tensor` on the underlying Hilbert space. In particular, for any two ``type="oper"`` Qobjs ``A`` and ``B``, ``to_super(tensor(A, B)) == super_tensor(to_super(A), to_super(B))`` and ``operator_to_vector(tensor(A, B)) == super_tensor(operator_to_vector(A), operator_to_vector(B))``. Returning to the previous example: .. doctest:: [tensor] >>> super_tensor(to_super(A), to_super(B)).dims [[[2, 3], [2, 3]], [[2, 3], [2, 3]]] The :func:`.composite` function automatically switches between :func:`.tensor` and :func:`.super_tensor` based on the ``type`` of its arguments, such that ``composite(A, B)`` returns an appropriate Qobj to represent the composition of two systems. .. doctest:: [tensor] >>> composite(A, B).dims [[2, 3], [2, 3]] >>> composite(to_super(A), to_super(B)).dims [[[2, 3], [2, 3]], [[2, 3], [2, 3]]] QuTiP also allows more general tensor manipulations that are useful for converting between superoperator representations [WBC11]_. In particular, the :func:`~qutip.core.tensor.tensor_contract` function allows for contracting one or more pairs of indices. This can be used to find superoperators that represent partial trace maps. Using this functionality, we can construct some quite exotic maps, such as a map from :math:`3 \times 3` operators to :math:`2 \times 2` operators: .. doctest:: [tensor] >>> tensor_contract(composite(to_super(A), to_super(B)), (1, 3), (4, 6)).dims [[[2], [2]], [[3], [3]]] .. TODO: remake from notebook to tutorials .. _channel contraction tutorial: github/qutip/qutip-notebooks/blob/master/examples/superop-contract.ipynb qutip-5.1.1/doc/guide/guide-visualization.rst000066400000000000000000000373151474175217300212740ustar00rootroot00000000000000.. _visual: .. plot:: :include-source: False import numpy as np from qutip import * import pylab as plt from warnings import warn plt.close("all") ********************************************* Visualization of quantum states and processes ********************************************* Visualization is often an important complement to a simulation of a quantum mechanical system. The first method of visualization that come to mind might be to plot the expectation values of a few selected operators. But on top of that, it can often be instructive to visualize for example the state vectors or density matices that describe the state of the system, or how the state is transformed as a function of time (see process tomography below). In this section we demonstrate how QuTiP and matplotlib can be used to perform a few types of visualizations that often can provide additional understanding of quantum system. .. _visual-fock: Fock-basis probability distribution =================================== In quantum mechanics probability distributions plays an important role, and as in statistics, the expectation values computed from a probability distribution does not reveal the full story. For example, consider an quantum harmonic oscillator mode with Hamiltonian :math:`H = \hbar\omega a^\dagger a`, which is in a state described by its density matrix :math:`\rho`, and which on average is occupied by two photons, :math:`\mathrm{Tr}[\rho a^\dagger a] = 2`. Given this information we cannot say whether the oscillator is in a Fock state, a thermal state, a coherent state, etc. By visualizing the photon distribution in the Fock state basis important clues about the underlying state can be obtained. One convenient way to visualize a probability distribution is to use histograms. Consider the following histogram visualization of the number-basis probability distribution, which can be obtained from the diagonal of the density matrix, for a few possible oscillator states with on average occupation of two photons. First we generate the density matrices for the coherent, thermal and fock states. .. plot:: :context: reset N = 20 rho_coherent = coherent_dm(N, np.sqrt(2)) rho_thermal = thermal_dm(N, 2) rho_fock = fock_dm(N, 2) Next, we plot histograms of the diagonals of the density matrices: .. plot:: :context: fig, axes = plt.subplots(1, 3, figsize=(12,3)) bar0 = axes[0].bar(np.arange(0, N)-.5, rho_coherent.diag()) lbl0 = axes[0].set_title("Coherent state") lim0 = axes[0].set_xlim([-.5, N]) bar1 = axes[1].bar(np.arange(0, N)-.5, rho_thermal.diag()) lbl1 = axes[1].set_title("Thermal state") lim1 = axes[1].set_xlim([-.5, N]) bar2 = axes[2].bar(np.arange(0, N)-.5, rho_fock.diag()) lbl2 = axes[2].set_title("Fock state") lim2 = axes[2].set_xlim([-.5, N]) plt.show() All these states correspond to an average of two photons, but by visualizing the photon distribution in Fock basis the differences between these states are easily appreciated. One frequently need to visualize the Fock-distribution in the way described above, so QuTiP provides a convenience function for doing this, see :func:`qutip.visualization.plot_fock_distribution`, and the following example: .. plot:: :context: close-figs fig, axes = plt.subplots(1, 3, figsize=(12,3)) fig, axes[0] = plot_fock_distribution(rho_coherent, fig=fig, ax=axes[0]); axes[0].set_title('Coherent state') fig, axes[1] = plot_fock_distribution(rho_thermal, fig=fig, ax=axes[1]); axes[1].set_title('Thermal state') fig, axes[2] = plot_fock_distribution(rho_fock, fig=fig, ax=axes[2]); axes[2].set_title('Fock state') fig.tight_layout() plt.show() .. _visual-dist: Quasi-probability distributions =============================== The probability distribution in the number (Fock) basis only describes the occupation probabilities for a discrete set of states. A more complete phase-space probability-distribution-like function for harmonic modes are the Wigner and Husumi Q-functions, which are full descriptions of the quantum state (equivalent to the density matrix). These are called quasi-distribution functions because unlike real probability distribution functions they can for example be negative. In addition to being more complete descriptions of a state (compared to only the occupation probabilities plotted above), these distributions are also great for demonstrating if a quantum state is quantum mechanical, since for example a negative Wigner function is a definite indicator that a state is distinctly nonclassical. Wigner function --------------- In QuTiP, the Wigner function for a harmonic mode can be calculated with the function :func:`qutip.wigner.wigner`. It takes a ket or a density matrix as input, together with arrays that define the ranges of the phase-space coordinates (in the x-y plane). In the following example the Wigner functions are calculated and plotted for the same three states as in the previous section. .. plot:: :context: close-figs xvec = np.linspace(-5,5,200) W_coherent = wigner(rho_coherent, xvec, xvec) W_thermal = wigner(rho_thermal, xvec, xvec) W_fock = wigner(rho_fock, xvec, xvec) # plot the results fig, axes = plt.subplots(1, 3, figsize=(12,3)) cont0 = axes[0].contourf(xvec, xvec, W_coherent, 100) lbl0 = axes[0].set_title("Coherent state") cont1 = axes[1].contourf(xvec, xvec, W_thermal, 100) lbl1 = axes[1].set_title("Thermal state") cont0 = axes[2].contourf(xvec, xvec, W_fock, 100) lbl2 = axes[2].set_title("Fock state") plt.show() .. _visual-cmap: Custom Color Maps ~~~~~~~~~~~~~~~~~ The main objective when plotting a Wigner function is to demonstrate that the underlying state is nonclassical, as indicated by negative values in the Wigner function. Therefore, making these negative values stand out in a figure is helpful for both analysis and publication purposes. Unfortunately, all of the color schemes used in Matplotlib (or any other plotting software) are linear colormaps where small negative values tend to be near the same color as the zero values, and are thus hidden. To fix this dilemma, QuTiP includes a nonlinear colormap function :func:`qutip.matplotlib_utilities.wigner_cmap` that colors all negative values differently than positive or zero values. Below is a demonstration of how to use this function in your Wigner figures: .. plot:: :context: close-figs import matplotlib as mpl from matplotlib import cm psi = (basis(10, 0) + basis(10, 3) + basis(10, 9)).unit() xvec = np.linspace(-5, 5, 500) W = wigner(psi, xvec, xvec) wmap = wigner_cmap(W) # Generate Wigner colormap nrm = mpl.colors.Normalize(-W.max(), W.max()) fig, axes = plt.subplots(1, 2, figsize=(10, 4)) plt1 = axes[0].contourf(xvec, xvec, W, 100, cmap=cm.RdBu, norm=nrm) axes[0].set_title("Standard Colormap"); cb1 = fig.colorbar(plt1, ax=axes[0]) plt2 = axes[1].contourf(xvec, xvec, W, 100, cmap=wmap) # Apply Wigner colormap axes[1].set_title("Wigner Colormap"); cb2 = fig.colorbar(plt2, ax=axes[1]) fig.tight_layout() plt.show() Husimi Q-function ----------------- The Husimi Q function is, like the Wigner function, a quasiprobability distribution for harmonic modes. It is defined as .. math:: Q(\alpha) = \frac{1}{\pi}\left<\alpha|\rho|\alpha\right> where :math:`\left|\alpha\right>` is a coherent state and :math:`\alpha = x + iy`. In QuTiP, the Husimi Q function can be computed given a state ket or density matrix using the function :func:`.qfunc`, as demonstrated below. .. plot:: :context: close-figs Q_coherent = qfunc(rho_coherent, xvec, xvec) Q_thermal = qfunc(rho_thermal, xvec, xvec) Q_fock = qfunc(rho_fock, xvec, xvec) fig, axes = plt.subplots(1, 3, figsize=(12,3)) cont0 = axes[0].contourf(xvec, xvec, Q_coherent, 100) lbl0 = axes[0].set_title("Coherent state") cont1 = axes[1].contourf(xvec, xvec, Q_thermal, 100) lbl1 = axes[1].set_title("Thermal state") cont0 = axes[2].contourf(xvec, xvec, Q_fock, 100) lbl2 = axes[2].set_title("Fock state") plt.show() If you need to calculate the Q function for many states with the same phase-space coordinates, it is more efficient to use the :obj:`.QFunc` class. This stores various intermediary results to achieve an order-of-magnitude improvement compared to calling :obj:`.qfunc` in a loop. .. code-block:: python xs = np.linspace(-1, 1, 101) qfunc_calculator = qutip.QFunc(xs, xs) q_state1 = qfunc_calculator(qutip.rand_dm(5)) q_state2 = qfunc_calculator(qutip.rand_ket(100)) .. _visual-oper: Visualizing operators ===================== Sometimes, it may also be useful to directly visualizing the underlying matrix representation of an operator. The density matrix, for example, is an operator whose elements can give insights about the state it represents, but one might also be interesting in plotting the matrix of an Hamiltonian to inspect the structure and relative importance of various elements. QuTiP offers a few functions for quickly visualizing matrix data in the form of histograms, :func:`qutip.visualization.matrix_histogram` and as Hinton diagram of weighted squares, :func:`qutip.visualization.hinton`. These functions takes a :class:`.Qobj` as first argument, and optional arguments to, for example, set the axis labels and figure title (see the function's documentation for details). For example, to illustrate the use of :func:`qutip.visualization.matrix_histogram`, let's visualize of the Jaynes-Cummings Hamiltonian: .. plot:: :context: close-figs N = 5 a = tensor(destroy(N), qeye(2)) b = tensor(qeye(N), destroy(2)) sx = tensor(qeye(N), sigmax()) H = a.dag() * a + sx - 0.5 * (a * b.dag() + a.dag() * b) # visualize H lbls_list = [[str(d) for d in range(N)], ["u", "d"]] xlabels = [] for inds in tomography._index_permutations([len(lbls) for lbls in lbls_list]): xlabels.append("".join([lbls_list[k][inds[k]] for k in range(len(lbls_list))])) fig, ax = matrix_histogram(H, xlabels, xlabels, limits=[-4,4]) ax.view_init(azim=-55, elev=45) plt.show() Similarly, we can use the function :func:`qutip.visualization.hinton`, which is used below to visualize the corresponding steadystate density matrix: .. plot:: :context: close-figs rho_ss = steadystate(H, [np.sqrt(0.1) * a, np.sqrt(0.4) * b.dag()]) hinton(rho_ss) plt.show() .. _visual-qpt: Quantum process tomography ========================== Quantum process tomography (QPT) is a useful technique for characterizing experimental implementations of quantum gates involving a small number of qubits. It can also be a useful theoretical tool that can give insight in how a process transforms states, and it can be used for example to study how noise or other imperfections deteriorate a gate. Whereas a fidelity or distance measure can give a single number that indicates how far from ideal a gate is, a quantum process tomography analysis can give detailed information about exactly what kind of errors various imperfections introduce. The idea is to construct a transformation matrix for a quantum process (for example a quantum gate) that describes how the density matrix of a system is transformed by the process. We can then decompose the transformation in some operator basis that represent well-defined and easily interpreted transformations of the input states. To see how this works (see e.g. [Moh08]_ for more details), consider a process that is described by quantum map :math:`\epsilon(\rho_{\rm in}) = \rho_{\rm out}`, which can be written .. math:: :label: qpt-quantum-map \epsilon(\rho_{\rm in}) = \rho_{\rm out} = \sum_{i}^{N^2} A_i \rho_{\rm in} A_i^\dagger, where :math:`N` is the number of states of the system (that is, :math:`\rho` is represented by an :math:`[N\times N]` matrix). Given an orthogonal operator basis of our choice :math:`\{B_i\}_i^{N^2}`, which satisfies :math:`{\rm Tr}[B_i^\dagger B_j] = N\delta_{ij}`, we can write the map as .. math:: :label: qpt-quantum-map-transformed \epsilon(\rho_{\rm in}) = \rho_{\rm out} = \sum_{mn} \chi_{mn} B_m \rho_{\rm in} B_n^\dagger. where :math:`\chi_{mn} = \sum_{ij} b_{im}b_{jn}^*` and :math:`A_i = \sum_{m} b_{im}B_{m}`. Here, matrix :math:`\chi` is the transformation matrix we are after, since it describes how much :math:`B_m \rho_{\rm in} B_n^\dagger` contributes to :math:`\rho_{\rm out}`. In a numerical simulation of a quantum process we usually do not have access to the quantum map in the form Eq. :eq:`qpt-quantum-map`. Instead, what we usually can do is to calculate the propagator :math:`U` for the density matrix in superoperator form, using for example the QuTiP function :func:`qutip.propagator.propagator`. We can then write .. math:: \epsilon(\tilde{\rho}_{\rm in}) = U \tilde{\rho}_{\rm in} = \tilde{\rho}_{\rm out} where :math:`\tilde{\rho}` is the vector representation of the density matrix :math:`\rho`. If we write Eq. :eq:`qpt-quantum-map-transformed` in superoperator form as well we obtain .. math:: \tilde{\rho}_{\rm out} = \sum_{mn} \chi_{mn} \tilde{B}_m \tilde{B}_n^\dagger \tilde{\rho}_{\rm in} = U \tilde{\rho}_{\rm in}. so we can identify .. math:: U = \sum_{mn} \chi_{mn} \tilde{B}_m \tilde{B}_n^\dagger. Now this is a linear equation systems for the :math:`N^2 \times N^2` elements in :math:`\chi`. We can solve it by writing :math:`\chi` and the superoperator propagator as :math:`[N^4]` vectors, and likewise write the superoperator product :math:`\tilde{B}_m\tilde{B}_n^\dagger` as a :math:`[N^4\times N^4]` matrix :math:`M`: .. math:: U_I = \sum_{J}^{N^4} M_{IJ} \chi_{J} with the solution .. math:: \chi = M^{-1}U. Note that to obtain :math:`\chi` with this method we have to construct a matrix :math:`M` with a size that is the square of the size of the superoperator for the system. Obviously, this scales very badly with increasing system size, but this method can still be a very useful for small systems (such as system comprised of a small number of coupled qubits). Implementation in QuTiP ----------------------- In QuTiP, the procedure described above is implemented in the function :func:`qutip.tomography.qpt`, which returns the :math:`\chi` matrix given a density matrix propagator. To illustrate how to use this function, let's consider the SWAP gate for two qubits. In QuTiP the function :func:`.swap` generates the unitary transformation for the state kets: .. plot:: :context: close-figs from qutip.core.gates import swap U_psi = swap() To be able to use this unitary transformation matrix as input to the function :func:`qutip.tomography.qpt`, we first need to convert it to a transformation matrix for the corresponding density matrix: .. plot:: :context: U_rho = spre(U_psi) * spost(U_psi.dag()) Next, we construct a list of operators that define the basis :math:`\{B_i\}` in the form of a list of operators for each composite system. At the same time, we also construct a list of corresponding labels that will be used when plotting the :math:`\chi` matrix. .. plot:: :context: op_basis = [[qeye(2), sigmax(), sigmay(), sigmaz()]] * 2 op_label = [["i", "x", "y", "z"]] * 2 We are now ready to compute :math:`\chi` using :func:`qutip.tomography.qpt`, and to plot it using :func:`qutip.tomography.qpt_plot_combined`. .. plot:: :context: chi = qpt(U_rho, op_basis) fig = qpt_plot_combined(chi, op_label, r'SWAP') plt.show() For a slightly more advanced example, where the density matrix propagator is calculated from the dynamics of a system defined by its Hamiltonian and collapse operators using the function :func:`.propagator`, see notebook "Time-dependent master equation: Landau-Zener transitions" on the tutorials section on the QuTiP web site. qutip-5.1.1/doc/guide/guide.rst000066400000000000000000000007371474175217300163730ustar00rootroot00000000000000.. _guide: ******************* Users Guide ******************* .. toctree:: :maxdepth: 2 guide-overview.rst guide-basics.rst guide-states.rst guide-tensor.rst guide-super.rst guide-dynamics.rst guide-environments.rst guide-heom.rst guide-steady.rst guide-piqs.rst guide-correlation.rst guide-bloch.rst guide-visualization.rst guide-saving.rst guide-random.rst guide-settings.rst guide-measurement.rst guide-control.rst qutip-5.1.1/doc/guide/heom/000077500000000000000000000000001474175217300154655ustar00rootroot00000000000000qutip-5.1.1/doc/guide/heom/bosonic.rst000066400000000000000000000360671474175217300176670ustar00rootroot00000000000000#################### Bosonic Environments #################### In this section we consider a simple two-level system coupled to a Drude-Lorentz bosonic bath. The system Hamiltonian, :math:`H_{sys}`, and the bath spectral density, :math:`J_D`, are .. math:: H_{sys} &= \frac{\epsilon \sigma_z}{2} + \frac{\Delta \sigma_x}{2} J_D(\omega) &= \frac{2\lambda \gamma \omega}{\gamma^2 + \omega^2}, We will demonstrate how to describe the bath using two different expansions of the spectral density correlation function (Matsubara's expansion and a PadĂŠ expansion), how to evolve the system in time, and how to calculate the steady state. First we will do this in the simplest way, using the built-in implementations of the two bath expansions, :class:`~qutip.solver.heom.DrudeLorentzBath` and :class:`~qutip.solver.heom.DrudeLorentzPadeBath`. We will do this both with a truncated expansion and show how to include an approximation to all of the remaining terms in the bath expansion. .. admonition:: Environment API We will also explain how to achieve the same results using the :class:`.DrudeLorentzEnvironment` that was introduced in the :ref:`section on environments `. The "bath" classes are part of an older API that is less powerful than the "environment" API, but often more convenient to use when one only uses the HEOM solver and does not need any of the new features. Afterwards, we will show how to calculate the correlation function expansion coefficients and to use those coefficients to construct your own bath description so that you can implement your own bosonic baths / environments. Finally, we will demonstrate how to simulate a system coupled to multiple independent baths, as occurs, for example, in certain photosynthesis processes. A tutorial notebook containing a complete example similar to this one is the `HEOM example notebook 1a `_. Describing the system and bath ------------------------------ First, let us construct the system Hamiltonian ``H_sys`` and the initial system state ``rho0``: .. plot:: :context: reset :nofigs: from qutip import basis, sigmax, sigmaz # The system Hamiltonian: eps = 0.5 # energy of the 2-level system Del = 1.0 # tunnelling term H_sys = 0.5 * eps * sigmaz() + 0.5 * Del * sigmax() # Initial state of the system: rho0 = basis(2,0) * basis(2,0).dag() Now let us describe the bath properties: .. plot:: :context: :nofigs: # Bath properties: gamma = 0.5 # cut off frequency lam = 0.1 # coupling strength T = 0.5 # temperature # System-bath coupling operator: Q = sigmaz() where :math:`\gamma` (``gamma``), :math:`\lambda` (``lam``) and the temperature :math:`T` are the parameters of a Drude-Lorentz bath, and ``Q`` is the coupling operator between the system and the bath. We may the pass these parameters to either :class:`~qutip.solver.heom.DrudeLorentzBath` or :class:`~qutip.solver.heom.DrudeLorentzPadeBath` to construct an expansion of the bath correlations: .. plot:: :context: :nofigs: from qutip.solver.heom import DrudeLorentzBath from qutip.solver.heom import DrudeLorentzPadeBath # Number of expansion terms to retain: Nk = 2 # Matsubara expansion: bath = DrudeLorentzBath(Q, lam, gamma, T, Nk) # PadĂŠ expansion: bath = DrudeLorentzPadeBath(Q, lam, gamma, T, Nk) Here, ``Nk`` is the number of terms to retain within the expansion of the bath. .. admonition:: Environment API Using the environment API, we first create an abstract :class:`.DrudeLorentzEnvironment` describing the bath, and then use its functions to create exponential expansions such as the Matsubara and Pade ones: .. plot:: :context: :nofigs: from qutip.core.environment import DrudeLorentzEnvironment env = DrudeLorentzEnvironment(T, lam, gamma) # Matsubara expansion: approx = env.approx_by_matsubara(Nk) # PadĂŠ expansion: approx = env.approx_by_pade(Nk) Note that the coupling operator ``Q`` is not part of the environment objects. .. _heom-bosonic-system-and-bath-dynamics: System and bath dynamics ------------------------ Now we are ready to construct a solver: .. plot:: :context: :nofigs: from qutip.solver.heom import HEOMSolver max_depth = 5 # maximum hierarchy depth to retain options = {"nsteps": 15_000} solver = HEOMSolver(H_sys, bath, max_depth=max_depth, options=options) and to calculate the system evolution as a function of time: .. code-block:: python tlist = [0, 10, 20] # times to evaluate the system state at result = solver.run(rho0, tlist) The ``max_depth`` parameter determines how many levels of the hierarchy to retain. As a first approximation, hierarchy depth may be thought of as similar to the order of Feynman Diagrams (both classify terms by increasing number of interactions). The ``result`` is a standard QuTiP results object with the attributes: - ``times``: The times at which the state was evaluated (i.e. ``tlist``). - ``states``: The system states at each time. - ``expect``: A list with the values of each expectation operator at each time. - ``e_data``: A dictionary with the values of each expectation operator at each time. - ``ado_states``: See below (a list of instances of :class:`~qutip.solver.heom.HierarchyADOsState`). If ``ado_return=True`` is passed to ``.run(...)`` the full set of auxilliary density operators (ADOs) that make up the hierarchy at each time will be returned as ``result.ado_states``. We will describe how to use these to determine other properties, such as system-bath currents, later in the :ref:`fermionic guide `. If one has a full set of ADOs from a previous call of ``.run(...)``, one may supply it as the initial state of the solver by calling ``.run(result.ado_states[-1], tlist, ado_init=True)``. As with other QuTiP solvers, if expectation operators or functions are supplied using ``.run(..., e_ops=[...])`` the expectation values are available in ``result.expect`` and ``result.e_data``. .. admonition:: Environment API When using the environment API, one needs to pass the coupling operator to the HEOM solver together with the approximated environment: .. plot:: :context: :nofigs: solver = HEOMSolver(H_sys, (approx, Q), max_depth=max_depth, options=options) Below we run the solver again, but use ``e_ops`` to store the expectation values of the population of the system states and the coherence: .. plot:: :context: # Define the operators that measure the populations of the two # system states: P11p = basis(2,0) * basis(2,0).dag() P22p = basis(2,1) * basis(2,1).dag() # Define the operator that measures the 0, 1 element of density matrix # (corresonding to coherence): P12p = basis(2,0) * basis(2,1).dag() # Run the solver: tlist = np.linspace(0, 20, 101) result = solver.run(rho0, tlist, e_ops={"11": P11p, "22": P22p, "12": P12p}) # Plot the results: fig, axes = plt.subplots(1, 1, sharex=True, figsize=(6, 6)) axes.plot(result.times, np.real(result.e_data["11"]), 'b', linewidth=2, label="P11") axes.plot(result.times, np.real(result.e_data["12"]), 'r', linewidth=2, label="P12") axes.set_xlabel(r't', fontsize=16) axes.legend(loc=0, fontsize=16) Steady state ------------ Using the same solver, we can also determine the steady state of the combined system and bath using: .. plot:: :context: :nofigs: steady_state, steady_ados = solver.steady_state() where ``steady_state`` is the steady state of the system and ``steady_ados`` is the steady state of the full hierarchy. The ADO states are described more fully in the section on :ref:`determining currents ` and in the API documentation for :class:`~qutip.solver.heom.HierarchyADOsState`. Matsubara Terminator -------------------- When constructing the Drude-Lorentz bath we have truncated the expansion at ``Nk = 2`` terms and ignore the remaining terms. However, since the coupling to these higher order terms is comparatively weak, we may consider the interaction with them to be Markovian, and construct an additional Lindbladian term that captures their interaction with the system and the lower order terms in the expansion. This additional term is called the ``terminator`` because it terminates the expansion. The :class:`~qutip.solver.heom.DrudeLorentzBath` and :class:`~qutip.solver.heom.DrudeLorentzPadeBath` both provide a means of calculating the terminator for a given expansion: .. plot:: :context: :nofigs: # Matsubara expansion: bath = DrudeLorentzBath(Q, lam, gamma, T, Nk) # PadĂŠ expansion: bath = DrudeLorentzPadeBath(Q, lam, gamma, T, Nk) # Add terminator to the system Liouvillian: delta, terminator = bath.terminator() HL = liouvillian(H_sys) + terminator # Construct solver: solver = HEOMSolver(HL, bath, max_depth=max_depth, options=options) This captures the Markovian effect of the remaining terms in the expansion without having to fully model many more terms. The terminator amplitude ``delta`` is an approximation to the strength of the effect of the remaining terms in the expansion (i.e. how strongly the terminator is coupled to the rest of the system). .. admonition:: Environment API Here, the terminator amplitude can be returned directly by the ``approx_by_matsubara`` and ``approx_by_pade`` methods used earlier. Based on it, the special function ``environment.system_terminator`` can then be used to construct the terminator Liouvillian: .. plot:: :context: :nofigs: from qutip.core.environment import system_terminator # Matsubara expansion: approx, delta = env.approx_by_matsubara(Nk, compute_delta=True) # PadĂŠ expansion: approx, delta = env.approx_by_pade(Nk, compute_delta=True) # Add terminator to the system Liouvillian: terminator = system_terminator(Q, delta) HL = liouvillian(H_sys) + terminator # Construct solver solver = HEOMSolver(HL, (approx, Q), max_depth=max_depth, options=options) Matsubara expansion coefficients -------------------------------- So far we have relied on the built-in :class:`~qutip.solver.heom.DrudeLorentzBath` to construct the Drude-Lorentz bath expansion for us. Now we will calculate the coefficients ourselves and construct a :class:`~qutip.solver.heom.BosonicBath` directly. A similar procedure can be used to apply :class:`~qutip.solver.heom.HEOMSolver` to any bosonic bath for which we can calculate the expansion coefficients. The Matsubara expansion of the Drude-Lorentz correlation function is detailed in the section on the :ref:`Drude-Lorentz Environment