From 89e947ce7550cd5004c2d57d63353b3aad13b6cf Mon Sep 17 00:00:00 2001 From: Caleb Johnson Date: Fri, 6 Sep 2024 16:49:48 -0500 Subject: [PATCH] Initial commit to SQD public repository. Co-authored-by: Javier Robledo Moreno Co-authored-by: Iskandar Sitdikov Co-authored-by: Paul Schweigert Co-authored-by: Abdullah Ash Saki Co-authored-by: Stefano Barison --- .github/ISSUE_TEMPLATE/BUG_REPORT.yaml | 50 + .github/ISSUE_TEMPLATE/FEATURE_REQUEST.yaml | 14 + .github/dependabot.yml | 13 + .github/workflows/README.md | 37 + .github/workflows/citation.yml | 68 + .github/workflows/docs.yml | 54 + .github/workflows/lint.yml | 32 + .github/workflows/release.yml | 47 + .../workflows/test_development_versions.yml | 43 + .github/workflows/test_latest_versions.yml | 42 + .github/workflows/test_minimum_versions.yml | 39 + .gitignore | 131 ++ CODE_OF_CONDUCT.md | 3 + CONTRIBUTING.md | 26 + LICENSE.txt | 203 +++ README.md | 95 + SECURITY.md | 20 + docs/_static/.gitkeep | 0 docs/_templates/autosummary/class.rst | 32 + ...iskit_addon_sqd.configuration_recovery.rst | 10 + docs/apidocs/qiskit_addon_sqd.counts.rst | 10 + docs/apidocs/qiskit_addon_sqd.fermion.rst | 10 + docs/apidocs/qiskit_addon_sqd.qubit.rst | 10 + docs/apidocs/qiskit_addon_sqd.rst | 10 + docs/apidocs/qiskit_addon_sqd.subsampling.rst | 10 + docs/conf.py | 174 ++ ...ic_excitations_to_configuration_pool.ipynb | 195 ++ docs/how_tos/benchmark_pauli_projection.ipynb | 463 +++++ docs/how_tos/choose_subspace_dimension.ipynb | 364 ++++ docs/how_tos/index.rst | 10 + ...uli_operators_onto_hilbert_subspaces.ipynb | 157 ++ docs/how_tos/select_open_closed_shell.ipynb | 536 ++++++ ...use_oo_to_optimize_hamiltonian_basis.ipynb | 428 +++++ docs/images/lucj_ansatz_zig_zag_pattern.jpg | Bin 0 -> 542066 bytes docs/index.rst | 93 + docs/install.rst | 81 + docs/molecules/n2_fci.txt | 1611 +++++++++++++++++ .../01_getting_started_fermionic.ipynb | 531 ++++++ docs/tutorials/index.rst | 10 + pyproject.toml | 146 ++ qiskit_addon_sqd/__init__.py | 31 + qiskit_addon_sqd/configuration_recovery.py | 297 +++ qiskit_addon_sqd/counts.py | 158 ++ qiskit_addon_sqd/fermion.py | 452 +++++ qiskit_addon_sqd/qubit.py | 220 +++ qiskit_addon_sqd/subsampling.py | 153 ++ test/README.md | 95 + test/__init__.py | 10 + test/test_configuration_recovery.py | 19 + test/test_counts.py | 148 ++ test/test_fermion.py | 19 + test/test_qubit.py | 19 + test/test_subsampling.py | 275 +++ test/test_workflow.py | 19 + tox.ini | 67 + 55 files changed, 7790 insertions(+) create mode 100644 .github/ISSUE_TEMPLATE/BUG_REPORT.yaml create mode 100644 .github/ISSUE_TEMPLATE/FEATURE_REQUEST.yaml create mode 100644 .github/dependabot.yml create mode 100644 .github/workflows/README.md create mode 100644 .github/workflows/citation.yml create mode 100644 .github/workflows/docs.yml create mode 100644 .github/workflows/lint.yml create mode 100644 .github/workflows/release.yml create mode 100644 .github/workflows/test_development_versions.yml create mode 100644 .github/workflows/test_latest_versions.yml create mode 100644 .github/workflows/test_minimum_versions.yml create mode 100644 .gitignore create mode 100644 CODE_OF_CONDUCT.md create mode 100644 CONTRIBUTING.md create mode 100644 LICENSE.txt create mode 100644 README.md create mode 100644 SECURITY.md create mode 100644 docs/_static/.gitkeep create mode 100644 docs/_templates/autosummary/class.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.configuration_recovery.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.counts.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.fermion.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.qubit.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.rst create mode 100644 docs/apidocs/qiskit_addon_sqd.subsampling.rst create mode 100644 docs/conf.py create mode 100644 docs/how_tos/add_fermionic_excitations_to_configuration_pool.ipynb create mode 100644 docs/how_tos/benchmark_pauli_projection.ipynb create mode 100644 docs/how_tos/choose_subspace_dimension.ipynb create mode 100644 docs/how_tos/index.rst create mode 100644 docs/how_tos/project_pauli_operators_onto_hilbert_subspaces.ipynb create mode 100644 docs/how_tos/select_open_closed_shell.ipynb create mode 100644 docs/how_tos/use_oo_to_optimize_hamiltonian_basis.ipynb create mode 100644 docs/images/lucj_ansatz_zig_zag_pattern.jpg create mode 100644 docs/index.rst create mode 100644 docs/install.rst create mode 100644 docs/molecules/n2_fci.txt create mode 100644 docs/tutorials/01_getting_started_fermionic.ipynb create mode 100644 docs/tutorials/index.rst create mode 100644 pyproject.toml create mode 100644 qiskit_addon_sqd/__init__.py create mode 100644 qiskit_addon_sqd/configuration_recovery.py create mode 100644 qiskit_addon_sqd/counts.py create mode 100644 qiskit_addon_sqd/fermion.py create mode 100644 qiskit_addon_sqd/qubit.py create mode 100644 qiskit_addon_sqd/subsampling.py create mode 100644 test/README.md create mode 100644 test/__init__.py create mode 100644 test/test_configuration_recovery.py create mode 100644 test/test_counts.py create mode 100644 test/test_fermion.py create mode 100644 test/test_qubit.py create mode 100644 test/test_subsampling.py create mode 100644 test/test_workflow.py create mode 100644 tox.ini diff --git a/.github/ISSUE_TEMPLATE/BUG_REPORT.yaml b/.github/ISSUE_TEMPLATE/BUG_REPORT.yaml new file mode 100644 index 0000000..6bbe0ad --- /dev/null +++ b/.github/ISSUE_TEMPLATE/BUG_REPORT.yaml @@ -0,0 +1,50 @@ +name: 🐛 Bug report +description: Create a report to help us improve 🤔. +labels: ["bug"] + +body: + - type: markdown + attributes: + value: Thank you for reporting a bug! Before you do so, please ensure that you have tested on the latest released version of the code. If it does, please also use the search to see if there are any other related issues or pull requests. + + - type: textarea + attributes: + label: Environment + description: Please give the actual version number (_e.g._ 0.1.0) if you are using a release version, or the first 7-8 characters of the commit hash if you have installed from `git`. If anything else is relevant, you can add it to the list. + # The trailing spaces on the following lines are to make filling the form + # in easier. The type is 'textarea' rather than three separate 'input's + # to make the resulting issue body less noisy with headings. + value: | + - **qiskit-addon-sqd version**: + - **Python version**: + - **Operating system**: + validations: + required: true + + - type: textarea + attributes: + label: What is happening and why is it wrong? + description: A short description of what is going wrong, in words. + validations: + required: true + + - type: textarea + attributes: + label: How can we reproduce the issue? + description: Give some steps that show the bug. A [minimal working example](https://stackoverflow.com/help/minimal-reproducible-example) of code with output is best. If you are copying in code, please remember to enclose it in triple backticks (` ``` [multiline code goes here] ``` `) so that it [displays correctly](https://docs.github.com/en/github/writing-on-github/getting-started-with-writing-and-formatting-on-github/basic-writing-and-formatting-syntax). + validations: + required: true + + - type: textarea + attributes: + label: Traceback + description: If your code provided an error traceback, please paste it below, enclosed in triple backticks (` ``` [multiline code goes here] ``` `) so that it [displays correctly](https://docs.github.com/en/github/writing-on-github/getting-started-with-writing-and-formatting-on-github/basic-writing-and-formatting-syntax). + validations: + required: false + + - type: textarea + attributes: + label: Any suggestions? + description: Not required, but if you have suggestions for how a contributor should fix this, or any problems we should be aware of, let us know. + validations: + required: false diff --git a/.github/ISSUE_TEMPLATE/FEATURE_REQUEST.yaml b/.github/ISSUE_TEMPLATE/FEATURE_REQUEST.yaml new file mode 100644 index 0000000..4b66a76 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/FEATURE_REQUEST.yaml @@ -0,0 +1,14 @@ +name: 🚀 Feature request +description: Suggest an idea for this project 💡! +labels: ["type: feature request"] + +body: + - type: markdown + attributes: + value: Please make sure to browse the opened and closed issues to make sure that this idea has not previously been discussed. + + - type: textarea + attributes: + label: What should we add? + validations: + required: true diff --git a/.github/dependabot.yml b/.github/dependabot.yml new file mode 100644 index 0000000..7141543 --- /dev/null +++ b/.github/dependabot.yml @@ -0,0 +1,13 @@ +version: 2 +updates: + - package-ecosystem: "github-actions" + directory: "/" + labels: ["dependencies"] + schedule: + interval: "weekly" + - package-ecosystem: "pip" + directory: "/" + labels: ["dependencies"] + versioning-strategy: increase + schedule: + interval: "monthly" diff --git a/.github/workflows/README.md b/.github/workflows/README.md new file mode 100644 index 0000000..f0a38a9 --- /dev/null +++ b/.github/workflows/README.md @@ -0,0 +1,37 @@ +# GitHub Actions workflows + +This directory contains a number of workflows for use with [GitHub Actions](https://docs.github.com/actions). They specify what standards should be expected for development of this software, including pull requests. These workflows are designed to work out of the box for any research software prototype, especially those based on [Qiskit](https://qiskit.org/). + +## Lint check (`lint.yml`) + +This workflow checks that the code is formatted properly and follows the style guide by installing tox and running the [lint environment](/tests/#lint-environment) (`tox -e lint`). + +## Latest version tests (`test_latest_versions.yml`) + +This workflow installs the latest version of tox and runs [the current repository's tests](/tests/#test-py-environments) under each supported Python version on Linux and under a single Python version on macOS and Windows. This is the primary testing workflow. It runs for all code changes and additionally once per day, to ensure tests continue to pass as new versions of dependencies are released. + +## Development version tests (`test_development_versions.yml`) + +This workflow installs tox and modifies `pyproject.toml` to use the _development_ versions of certain Qiskit packages, using [extremal-python-dependencies](https://github.com/IBM/extremal-python-dependencies). For all other packages, the latest version is installed. This workflow runs on two versions of Python: the minimum supported version and the maximum supported version. Its purpose is to identify as soon as possible (i.e., before a Qiskit release) when changes in Qiskit will break the current repository. This workflow runs for all code changes, as well as on a timer once per day. + +## Minimum version tests (`test_minimum_versions.yml`) + +This workflow first installs the minimum supported tox version (the `minversion` specified in [`tox.ini`](/tox.ini)) and then installs the _minimum_ compatible version of each package listed in `pyproject.toml`, using [extremal-python-dependencies](https://github.com/IBM/extremal-python-dependencies). The purpose of this workflow is to make sure the minimum version specifiers in these files are accurate, i.e., that the tests actually pass with these versions. This workflow uses a single Python version, typically the oldest supported version, as the minimum supported versions of each package may not be compatible with the most recent Python release. + +Under the hood, this workflow uses a regular expression to change each `>=` and `~=` specifier in the dependencies to instead be `==`, as pip [does not support](https://github.com/pypa/pip/issues/8085) resolving the minimum versions of packages directly. Unfortunately, this means that the workflow will only install the minimum version of a package if it is _explicitly_ listed in one of the requirements files with a minimum version. For instance, if the only listed dependency is `qiskit>=1.0`, this workflow will install `qiskit==1.0` along with the latest version of each transitive dependency, such as `rustworkx`. + +## Code coverage (`coverage.yml`) + +This workflow tests the [coverage environment](/tests/#coverage-environment) on a single version of Python by installing tox and running `tox -e coverage`. + +## Documentation (`docs.yml`) + +This workflow ensures that the [Sphinx](https://www.sphinx-doc.org/) documentation builds successfully. It also publishes the resulting build to [GitHub Pages](https://pages.github.com/) if it is from the appropriate branch (e.g., `main`). + +## Citation preview (`citation.yml`) + +This workflow is only triggered when the `CITATION.bib` file is changed. It ensures that the file contains only ASCII characters ([escaped codes](https://en.wikibooks.org/wiki/LaTeX/Special_Characters#Escaped_codes) are preferred, as then the `bib` file will work even when `inputenc` is not used). It also compiles a sample LaTeX document which includes the citation in its bibliography and uploads the resulting PDF as an artifact so it can be previewed (e.g., before merging a pull request). + +## Release (`release.yml`) + +This workflow is triggered by a maintainer pushing a tag that represents a release. It publishes the release to github.com and to [PyPI](https://pypi.org/). diff --git a/.github/workflows/citation.yml b/.github/workflows/citation.yml new file mode 100644 index 0000000..6a018f0 --- /dev/null +++ b/.github/workflows/citation.yml @@ -0,0 +1,68 @@ +name: Citation preview + +on: + push: + branches: [ main ] + paths: ['CITATION.bib', '.github/workflows/citation.yml'] + pull_request: + branches: [ main ] + paths: ['CITATION.bib', '.github/workflows/citation.yml'] + +jobs: + build-preview: + runs-on: ubuntu-latest + timeout-minutes: 30 + steps: + - uses: actions/checkout@v4 + - name: Check for non-ASCII characters + run: | + # Fail immediately if there are any non-ASCII characters in + # the BibTeX source. We prefer "escaped codes" rather than + # UTF-8 characters in order to ensure the bibliography will + # display correctly even in documents that do not contain + # \usepackage[utf8]{inputenc}. + if [ -f "CITATION.bib" ]; then + python3 -c 'open("CITATION.bib", encoding="ascii").read()' + fi + - name: Install LaTeX + run: | + if [ -f "CITATION.bib" ]; then + sudo apt-get update + sudo apt-get install -y texlive-latex-base texlive-publishers + fi + - name: Run LaTeX + run: | + if [ -f "CITATION.bib" ]; then + arr=(${GITHUB_REPOSITORY//\// }) + export REPO=${arr[1]} + cat <<- EOF > citation-preview.tex + \documentclass[preprint,aps,physrev,notitlepage]{revtex4-2} + \usepackage{hyperref} + \begin{document} + \title{\texttt{$REPO} BibTeX test} + \maketitle + \noindent + \texttt{$REPO} + \cite{$REPO} + \bibliography{CITATION} + \end{document} + EOF + pdflatex citation-preview + fi + - name: Run BibTeX + run: | + if [ -f "CITATION.bib" ]; then + bibtex citation-preview + fi + - name: Re-run LaTeX + run: | + if [ -f "CITATION.bib" ]; then + pdflatex citation-preview + pdflatex citation-preview + fi + - name: Upload PDF + if: always() + uses: actions/upload-artifact@v4 + with: + name: citation-preview.pdf + path: citation-preview.pdf diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml new file mode 100644 index 0000000..2a5e77a --- /dev/null +++ b/.github/workflows/docs.yml @@ -0,0 +1,54 @@ +name: Build Sphinx docs + +on: + workflow_dispatch: + push: + tags: + - "[0-9]+.[0-9]+.[0-9]+*" + branches: + - main + - 'stable/**' + pull_request: + branches: + - main + - 'stable/**' + +jobs: + build_and_deploy_docs: + runs-on: ubuntu-latest + timeout-minutes: 20 + steps: + - uses: actions/checkout@v4 + with: + fetch-depth: 0 + - uses: actions/setup-python@v5 + with: + python-version: '3.10' + - name: Install dependencies + run: | + python -m pip install --upgrade pip + pip install tox + sudo apt-get update + sudo apt-get install -y pandoc + - name: Build docs + shell: bash + run: | + tox -edocs + - name: Prepare docs artifact + if: always() + shell: bash + run: | + mkdir artifact + cp -a docs/_build/html artifact/addon_sqd_html_docs + - name: Upload docs artifact + if: always() + uses: actions/upload-artifact@v4 + with: + name: addon_sqd_html_docs + path: ./artifact + - name: Deploy docs + if: ${{ github.ref == 'refs/heads/stable/0.3' }} + uses: peaceiris/actions-gh-pages@v4 + with: + github_token: ${{ secrets.GITHUB_TOKEN }} + publish_dir: ./docs/_build/html/ diff --git a/.github/workflows/lint.yml b/.github/workflows/lint.yml new file mode 100644 index 0000000..a7acd45 --- /dev/null +++ b/.github/workflows/lint.yml @@ -0,0 +1,32 @@ +name: Lint check + +on: + push: + branches: + - main + - 'stable/**' + pull_request: + branches: + - main + - 'stable/**' + +jobs: + lint: + runs-on: ubuntu-latest + timeout-minutes: 30 + steps: + - uses: actions/checkout@v4 + with: + fetch-depth: 0 + - name: Set up Python 3.10 + uses: actions/setup-python@v5 + with: + python-version: '3.10' + - name: Install tox + run: | + python -m pip install --upgrade pip + pip install tox + - name: Run lint check + shell: bash + run: | + tox -elint diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml new file mode 100644 index 0000000..664def4 --- /dev/null +++ b/.github/workflows/release.yml @@ -0,0 +1,47 @@ +name: Publish release + +on: + push: + tags: + - "[0-9]+.[0-9]+.[0-9]+*" + +jobs: + + github: + name: github + runs-on: ubuntu-latest + steps: + - name: Checkout tag + uses: actions/checkout@v4 + with: + ref: ${{ github.ref_name }} + - name: Publish release + uses: ghalactic/github-release-from-tag@v5 + if: github.ref_type == 'tag' + with: + token: ${{ secrets.GITHUB_TOKEN }} + generateReleaseNotes: "true" + + pypi: + name: pypi + runs-on: ubuntu-latest + needs: github + environment: + name: pypi + url: https://pypi.org/p/qiskit-addon-sqd + permissions: + id-token: write + steps: + - name: Checkout tag + uses: actions/checkout@v4 + with: + ref: ${{ github.ref_name }} + - name: Install `build` tool + run: | + python -m pip install --upgrade pip + pip install build + - name: Build distribution + run: | + python -m build + - name: Publish release to PyPI + uses: pypa/gh-action-pypi-publish@release/v1 diff --git a/.github/workflows/test_development_versions.yml b/.github/workflows/test_development_versions.yml new file mode 100644 index 0000000..9b4b6b4 --- /dev/null +++ b/.github/workflows/test_development_versions.yml @@ -0,0 +1,43 @@ +name: Development version tests + +on: + push: + branches: + - main + - 'stable/**' + pull_request: + branches: + - main + - 'stable/**' + schedule: + - cron: '0 1 * * *' + +jobs: + tests: + runs-on: ubuntu-latest + timeout-minutes: 30 + strategy: + max-parallel: 4 + matrix: + python-version: '3.10' + steps: + - uses: actions/checkout@v4 + - name: Set up Python ${{ matrix.python-version }} + uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Install dependencies (development versions) + shell: bash + run: | + python -m pip install --upgrade pip tox + python -m pip install extremal-python-dependencies==0.0.3 + extremal-python-dependencies pin-dependencies \ + "qiskit @ git+https://github.com/Qiskit/qiskit.git" \ + "pyscf @ git+https://github.com/pyscf/pyscf.git" \ + --inplace + - name: Test using tox environment + shell: bash + run: | + toxpyversion=$(echo ${{ matrix.python-version }} | sed -E 's/^([0-9]+)\.([0-9]+).*$/\1\2/') + tox -epy${toxpyversion} + tox -epy${toxpyversion}-notebook diff --git a/.github/workflows/test_latest_versions.yml b/.github/workflows/test_latest_versions.yml new file mode 100644 index 0000000..022454f --- /dev/null +++ b/.github/workflows/test_latest_versions.yml @@ -0,0 +1,42 @@ +name: Latest version tests + +on: + push: + branches: + - main + - 'stable/**' + pull_request: + branches: + - main + - 'stable/**' + schedule: + - cron: '0 1 * * *' + +jobs: + tests: + runs-on: ${{ matrix.os }} + timeout-minutes: 30 + strategy: + max-parallel: 4 + matrix: + os: [ubuntu-latest] + python-version: ["3.10", "3.11", "3.12"] + include: + - os: macos-latest + python-version: "3.12" + steps: + - uses: actions/checkout@v4 + - name: Set up Python ${{ matrix.python-version }} + uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Install dependencies + run: | + python -m pip install --upgrade pip + pip install tox + - name: Test using tox environment + shell: bash + run: | + toxpyversion=$(echo ${{ matrix.python-version }} | sed -E 's/^([0-9]+)\.([0-9]+).*$/\1\2/') + tox -epy${toxpyversion} + tox -epy${toxpyversion}-notebook diff --git a/.github/workflows/test_minimum_versions.yml b/.github/workflows/test_minimum_versions.yml new file mode 100644 index 0000000..9fe0dd2 --- /dev/null +++ b/.github/workflows/test_minimum_versions.yml @@ -0,0 +1,39 @@ +name: Minimum version tests + +on: + push: + branches: + - main + - 'stable/**' + pull_request: + branches: + - main + - 'stable/**' + +jobs: + tests: + runs-on: ubuntu-latest + timeout-minutes: 30 + strategy: + max-parallel: 4 + matrix: + python-version: '3.12' + steps: + - uses: actions/checkout@v4 + - name: Set up Python ${{ matrix.python-version }} + uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Install dependencies (minimum versions) + shell: bash + run: | + python -m pip install --upgrade pip + python -m pip install extremal-python-dependencies==0.0.3 + pip install "tox==$(extremal-python-dependencies get-tox-minversion)" + extremal-python-dependencies pin-dependencies-to-minimum --inplace + - name: Test using tox environment + shell: bash + run: | + toxpyversion=$(echo ${{ matrix.python-version }} | sed -E 's/^([0-9]+)\.([0-9]+).*$/\1\2/') + tox -epy${toxpyversion} + tox -epy${toxpyversion}-notebook diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..05d0012 --- /dev/null +++ b/.gitignore @@ -0,0 +1,131 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +pip-wheel-metadata/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ +docs/stubs/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ +.DS_Store/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ diff --git a/CODE_OF_CONDUCT.md b/CODE_OF_CONDUCT.md new file mode 100644 index 0000000..b1ca960 --- /dev/null +++ b/CODE_OF_CONDUCT.md @@ -0,0 +1,3 @@ +# Code of Conduct + +All members of this project agree to adhere to Qiskit's [code of conduct](https://github.com/Qiskit/qiskit/blob/main/CODE_OF_CONDUCT.md). diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md new file mode 100644 index 0000000..3d3b4c4 --- /dev/null +++ b/CONTRIBUTING.md @@ -0,0 +1,26 @@ +# Developer guide + +Development of the `qiskit-addon-sqd` package takes place [on GitHub](https://github.com/Qiskit/qiskit-addon-sqd). +The [Contributing to Qiskit](https://github.com/Qiskit/qiskit/blob/main/CONTRIBUTING.md) guide may serve as a +useful starting point, as this package builds on [Qiskit]. + +This package is written in [Python] and uses [tox] as a testing framework. A description of the available +`tox` test environments is located at [`test/README.md`](test/README.md). These environments are used in the +CI workflows, which are described at [`.github/workflows/README.md`](.github/workflows/README.md). + +Project configuration, including information about dependencies, is stored in [`pyproject.toml`](pyproject.toml). + +We use [Sphinx] for documentation and [reno] for release notes. +We use [Google style docstrings](https://sphinxcontrib-napoleon.readthedocs.io/en/latest/example_google.html), +except we omit the type of each argument, as type information is redundant with Python +[type hints](https://docs.python.org/3/library/typing.html). + +We require 100% coverage in all new code. +In rare cases where it is not possible to test a code block, we mark it with ``# pragma: no cover`` so that +the ``coverage`` tests will pass. + +[Qiskit]: https://www.ibm.com/quantum/qiskit +[Python]: https://www.python.org/ +[tox]: https://github.com/tox-dev/tox +[Sphinx]: https://www.sphinx-doc.org/ +[reno]: https://docs.openstack.org/reno/ diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..4c370ab --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,203 @@ + Copyright 2024 IBM and its contributors + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright 2017 IBM and its contributors. + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/README.md b/README.md new file mode 100644 index 0000000..7d1bc2d --- /dev/null +++ b/README.md @@ -0,0 +1,95 @@ +# Qiskit addon: sample-based quantum diagonalization (SQD) + +### Table of contents + +* [About](#about) +* [Documentation](#documentation) +* [Installation](#installation) +* [Computational requirements](#computational-requirements) +* [Deprecation Policy](#deprecation-policy) +* [Contributing](#contributing) +* [License](#license) +* [References](#references) + +---------------------------------------------------------------------------------------------------- + +### About + +Qiskit addons are a collection of modular tools for building utility-scale workloads powered by Qiskit. + +This package contains the Qiskit addon for sample-based quantum diagonalization (SQD) -- a technique for finding eigenvalues and eigenvectors of quantum operators, such as a quantum system Hamiltonian, using quantum and distributed classical computing together. + +Classical distributed computing is used to process samples obtained from a quantum processor, and to project and diagonalize a target Hamiltonian in a subspace spanned by them. This allows SQD to be robust to samples corrupted by quantum noise and deal with large Hamiltonians, such as chemistry Hamiltonians with millions of interaction terms, beyond the reach of any exact diagonalization methods. + +The SQD tool can target Hamiltonians expressed as linear combination of Pauli operators, or second-quantized fermionic operators. The input samples are obtained by quantum circuits defined by the user, which are believed to be good representations of eigenstates (e.g. the ground state) of a target operator. The convergence rate of SQD as a function of the number of samples improves with the sparseness of the target eigenstate. + +The projection and diagonalization steps are performed by a classical solver. We provide here two generic solvers, one for fermionic systems and another for qubit systems. Other solvers that might be more efficient for specific systems can be interfaced by the users. + +---------------------------------------------------------------------------------------------------- + +### Documentation + +All documentation is available at https://qiskit.github.io/qiskit-addon-sqd/. + +---------------------------------------------------------------------------------------------------- + +### Installation + +We encourage installing this package via `pip`, when possible: + +```bash +pip install 'qiskit-addon-sqd' +``` + +For more installation information refer to these [installation instructions](docs/install.rst). + +---------------------------------------------------------------------------------------------------- + +### Computational requirements + +The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this [tutorial](docs/tutorials/01_getting_started_fermionic.ipynb), those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**. + +The [`qiskit_addon_sqd.fermion.solve_fermion()`](qiskit_addon_sqd/fermion.py) function is multithreaded and capable of handling systems with ~25 spacial orbitals and ~10 electrons with subspace dimensions of ~$10^7$, using ~10-30 cores. + +##### Choosing subspace dimensions + +The choice of the subspace dimension affects the accuracy and runtime of the eigenstate solver. The larger the subspace the more accurate the calculation, at the cost of increasing the runtime and memory requirements. It is not known *a priori* the optimal subspace size, thus a convergence study with the subspace dimension may be performed, as described in this [example](docs/how_tos/choose_subspace_dimension.ipynb). + +##### The subspace dimension is set indirectly + +In this package, the user controls the number of bitstrings (see the `samples_per_batch` argument in [`qiskit_addon_sqd.subsampling.postselect_and_subsample()`](qiskit_addon_sqd/subsampling.py)) contained in each subspace. The value of this argument determines an upper bound to the subspace dimension in the case of quantum chemistry applications. See this [example](docs/how_tos/select_open_closed_shell.ipynb) for more details. + +---------------------------------------------------------------------------------------------------- + +### Deprecation Policy + +We follow [semantic versioning](https://semver.org/) and are guided by the principles in +[Qiskit's deprecation policy](https://github.com/Qiskit/qiskit/blob/main/DEPRECATION.md). +We may occasionally make breaking changes in order to improve the user experience. +When possible, we will keep old interfaces and mark them as deprecated, as long as they can co-exist with the +new ones. +Each substantial improvement, breaking change, or deprecation will be documented in the release notes. + +---------------------------------------------------------------------------------------------------- + +### Contributing + +The developer guide is located at [CONTRIBUTING.md](https://github.com/Qiskit/qiskit-addon-sqd/blob/main/CONTRIBUTING.md>) +in the root of this project's repository. +By participating, you are expected to uphold Qiskit's [code of conduct](https://github.com/Qiskit/qiskit/blob/main/CODE_OF_CONDUCT.md). + +We use [GitHub issues](https://github.com/Qiskit/qiskit-addon-sqd/issues/new/choose) for tracking requests and bugs. + +---------------------------------------------------------------------------------------------------- + +### License + +[Apache License 2.0](LICENSE.txt) + +---------------------------------------------------------------------------------------------------- + +### References + +[1] Javier Robledo-Moreno, et al., [Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer](https://arxiv.org/abs/2405.05068), arXiv:2405.05068 [quant-ph]. + +[2] Keita Kanno, et al., [Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers](https://arxiv.org/abs/2302.11320), arXiv:2302.11320 [quant-ph]. diff --git a/SECURITY.md b/SECURITY.md new file mode 100644 index 0000000..6d50cc2 --- /dev/null +++ b/SECURITY.md @@ -0,0 +1,20 @@ +# Security Policy + +## Supported Versions + +The package supports one minor version release at a time, both for bug and security fixes. +For example, if the most recent release is 0.2.1, then the 0.2.x release series is currently supported. + +## Reporting a Vulnerability + +To report vulnerabilities, you can privately report a potential security issue +via the GitHub security vulnerabilities feature. This can be done here: + +https://github.com/Qiskit/qiskit-addon-sqd/security/advisories + +Please do **not** open a public issue about a potential security vulnerability. + +You can find more details on the security vulnerability feature in the GitHub +documentation here: + +https://docs.github.com/en/code-security/security-advisories/guidance-on-reporting-and-writing/privately-reporting-a-security-vulnerability diff --git a/docs/_static/.gitkeep b/docs/_static/.gitkeep new file mode 100644 index 0000000..e69de29 diff --git a/docs/_templates/autosummary/class.rst b/docs/_templates/autosummary/class.rst new file mode 100644 index 0000000..a2481c8 --- /dev/null +++ b/docs/_templates/autosummary/class.rst @@ -0,0 +1,32 @@ +{# + We show all the class's methods and attributes on the same page. By default, we document + all methods, including those defined by parent classes. +-#} + +{{ objname | escape | underline }} + +.. currentmodule:: {{ module }} + +.. autoclass:: {{ objname }} + :no-members: + :no-inherited-members: + :show-inheritance: + +{% block attributes_summary %} + {% if attributes %} + .. rubric:: Attributes + {% for item in attributes %} + .. autoattribute:: {{ item }} + {%- endfor %} + {% endif %} +{% endblock -%} + +{% block methods_summary %} + {% set wanted_methods = (methods | reject('==', '__init__') | list) %} + {% if wanted_methods %} + .. rubric:: Methods + {% for item in wanted_methods %} + .. automethod:: {{ item }} + {%- endfor %} + {% endif %} +{% endblock %} diff --git a/docs/apidocs/qiskit_addon_sqd.configuration_recovery.rst b/docs/apidocs/qiskit_addon_sqd.configuration_recovery.rst new file mode 100644 index 0000000..7724266 --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.configuration_recovery.rst @@ -0,0 +1,10 @@ +====================== +Configuration Recovery +====================== + +.. _qiskit_addon_sqd-configuration_recovery: + +.. automodule:: qiskit_addon_sqd.configuration_recovery + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/apidocs/qiskit_addon_sqd.counts.rst b/docs/apidocs/qiskit_addon_sqd.counts.rst new file mode 100644 index 0000000..9d80a54 --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.counts.rst @@ -0,0 +1,10 @@ +====== +Counts +====== + +.. _qiskit_addon_sqd-counts: + +.. automodule:: qiskit_addon_sqd.counts + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/apidocs/qiskit_addon_sqd.fermion.rst b/docs/apidocs/qiskit_addon_sqd.fermion.rst new file mode 100644 index 0000000..2470c78 --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.fermion.rst @@ -0,0 +1,10 @@ +======= +Fermion +======= + +.. _qiskit_addon_sqd-fermion: + +.. automodule:: qiskit_addon_sqd.fermion + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/apidocs/qiskit_addon_sqd.qubit.rst b/docs/apidocs/qiskit_addon_sqd.qubit.rst new file mode 100644 index 0000000..7eec7fa --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.qubit.rst @@ -0,0 +1,10 @@ +===== +Qubit +===== + +.. _qiskit_addon_sqd-qubit: + +.. automodule:: qiskit_addon_sqd.qubit + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/apidocs/qiskit_addon_sqd.rst b/docs/apidocs/qiskit_addon_sqd.rst new file mode 100644 index 0000000..94e67a0 --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.rst @@ -0,0 +1,10 @@ +==================================== +Sample-based Quantum Diagonalization +==================================== + +.. _qiskit_addon_sqd: + +.. automodule:: qiskit_addon_sqd + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/apidocs/qiskit_addon_sqd.subsampling.rst b/docs/apidocs/qiskit_addon_sqd.subsampling.rst new file mode 100644 index 0000000..f043d8a --- /dev/null +++ b/docs/apidocs/qiskit_addon_sqd.subsampling.rst @@ -0,0 +1,10 @@ +=========== +Subsampling +=========== + +.. _qiskit_addon_sqd-subsampling: + +.. automodule:: qiskit_addon_sqd.subsampling + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/conf.py b/docs/conf.py new file mode 100644 index 0000000..421ba88 --- /dev/null +++ b/docs/conf.py @@ -0,0 +1,174 @@ +# This code is part of a Qiskit project. +# +# (C) Copyright IBM 2024. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +import inspect +import os +import re +import sys +from importlib.metadata import version as metadata_version + +# The following line is required for autodoc to be able to find and import the code whose API should +# be documented. +sys.path.insert(0, os.path.abspath("..")) + +project = "Sample-based Quantum Diagonalization" +project_copyright = "2024, Qiskit addons team" +description = "Classically post-process noisy samples drawn from a quantum processor to produce more accurate energy estimations" +author = "Qiskit addons team" +language = "en" +release = metadata_version("qiskit-addon-sqd") + +html_theme = "qiskit-ecosystem" + +# This allows including custom CSS and HTML templates. +html_theme_options = { + "dark_logo": "images/qiskit-dark-logo.svg", + "light_logo": "images/qiskit-light-logo.svg", + "sidebar_qiskit_ecosystem_member": False, +} +html_static_path = ["_static"] +templates_path = ["_templates"] + +# Sphinx should ignore these patterns when building. +exclude_patterns = [ + "_build", + "_ecosystem_build", + "_qiskit_build", + "_pytorch_build", + "**.ipynb_checkpoints", + "jupyter_execute", +] + +extensions = [ + "sphinx.ext.napoleon", + "sphinx.ext.autodoc", + "sphinx.ext.autosummary", + "sphinx.ext.mathjax", + "sphinx.ext.linkcode", + "sphinx.ext.intersphinx", + "matplotlib.sphinxext.plot_directive", + "sphinx_copybutton", + "reno.sphinxext", + "nbsphinx", + "qiskit_sphinx_theme", +] + +html_last_updated_fmt = "%Y/%m/%d" +html_title = f"{project} {release}" + +# This allows RST files to put `|version|` in their file and +# have it updated with the release set in conf.py. +rst_prolog = f""" +.. |version| replace:: {release} +""" + +# Options for autodoc. These reflect the values from Terra. +autosummary_generate = True +autosummary_generate_overwrite = False +autoclass_content = "both" +autodoc_typehints = "description" +autodoc_typehints_description_target = "documented_params" +autodoc_member_order = "bysource" +autodoc_default_options = { + "inherited-members": None, +} + + +# This adds numbers to the captions for figures, tables, +# and code blocks. +numfig = True +numfig_format = {"table": "Table %s"} + +# Settings for Jupyter notebooks. +nbsphinx_execute = "never" + +add_module_names = False + +modindex_common_prefix = ["qiskit_addon_sqd."] + +intersphinx_mapping = { + "python": ("https://docs.python.org/3", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "qiskit": ("https://docs.quantum.ibm.com/api/qiskit/", None), + "rustworkx": ("https://www.rustworkx.org/", None), +} + +plot_working_directory = "." +plot_html_show_source_link = False + +# ---------------------------------------------------------------------------------- +# Source code links +# ---------------------------------------------------------------------------------- + + +def determine_github_branch() -> str: + """Determine the GitHub branch name to use for source code links. + + We need to decide whether to use `stable/` vs. `main` for dev builds. + Refer to https://docs.github.com/en/actions/learn-github-actions/variables + for how we determine this with GitHub Actions. + """ + # If CI env vars not set, default to `main`. This is relevant for local builds. + if "GITHUB_REF_NAME" not in os.environ: + return "main" + + # PR workflows set the branch they're merging into. + if base_ref := os.environ.get("GITHUB_BASE_REF"): + return base_ref + + ref_name = os.environ["GITHUB_REF_NAME"] + + # Check if the ref_name is a tag like `1.0.0` or `1.0.0rc1`. If so, we need + # to transform it to a Git branch like `stable/1.0`. + version_without_patch = re.match(r"(\d+\.\d+)", ref_name) + return f"stable/{version_without_patch.group()}" if version_without_patch else ref_name + + +GITHUB_BRANCH = determine_github_branch() + + +def linkcode_resolve(domain, info): + if domain != "py": + return None + + module_name = info["module"] + module = sys.modules.get(module_name) + if module is None or "qiskit_addon_sqd" not in module_name: + return None + + obj = module + for part in info["fullname"].split("."): + try: + obj = getattr(obj, part) + except AttributeError: + return None + is_valid_code_object = ( + inspect.isclass(obj) or inspect.ismethod(obj) or inspect.isfunction(obj) + ) + if not is_valid_code_object: + return None + try: + full_file_name = inspect.getsourcefile(obj) + except TypeError: + return None + if full_file_name is None or "/qiskit_addon_sqd/" not in full_file_name: + return None + file_name = full_file_name.split("/qiskit_addon_sqd/")[-1] + + try: + source, lineno = inspect.getsourcelines(obj) + except (OSError, TypeError): + linespec = "" + else: + ending_lineno = lineno + len(source) - 1 + linespec = f"#L{lineno}-L{ending_lineno}" + return f"https://github.com/Qiskit/qiskit-addon-sqd/tree/{GITHUB_BRANCH}/qiskit_addon_sqd/{file_name}{linespec}" diff --git a/docs/how_tos/add_fermionic_excitations_to_configuration_pool.ipynb b/docs/how_tos/add_fermionic_excitations_to_configuration_pool.ipynb new file mode 100644 index 0000000..a24ecc9 --- /dev/null +++ b/docs/how_tos/add_fermionic_excitations_to_configuration_pool.ipynb @@ -0,0 +1,195 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", + "metadata": {}, + "source": [ + "# Add fermionic transitions to the pool of configurations\n", + "\n", + "Here we demonstrate the functionalities to augment the pool of electronic\n", + "configurations obtained by the action of transition operators on each electronic \n", + "configuration.\n", + "\n", + "We demonstrate how to add single-electron hops of the type:\n", + "$$\n", + "c^\\dagger_{p\\sigma} c_{q\\sigma} |\\textbf{x} \\rangle\n", + "$$\n", + "for $p, q = 1, ..., N_\\textrm{orb}$ and $\\sigma \\in \\{ \\uparrow, \\downarrow\\}$,\n", + "and for all $|\\textbf{x} \\rangle$ in the batch of electronic configurations." + ] + }, + { + "cell_type": "markdown", + "id": "0a7e9fcd", + "metadata": {}, + "source": [ + "Let's begin by generating a batch of random electronic configurations" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e9506e0b-ed64-48bb-a97a-ef851b604af1", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "n_qubits = 8\n", + "n_orb = n_qubits // 2\n", + "\n", + "rand_seed = 22\n", + "np.random.seed(rand_seed)\n", + "\n", + "\n", + "# Generate some random bitstrings for testing\n", + "def random_bitstrings(n_samples, n_qubits):\n", + " return np.round(np.random.rand(n_samples, n_qubits)).astype(\"int\").astype(\"bool\")\n", + "\n", + "\n", + "bitstring_matrix = random_bitstrings(100, n_qubits)" + ] + }, + { + "cell_type": "markdown", + "id": "4155599f", + "metadata": {}, + "source": [ + "The excitation operators are specified inside a numpy array whose length is\n", + "equal to the number of fermionic nodes (or qubits). Each element of the array\n", + "must be a string that can take values:\n", + "\n", + "- ``'I'``: Identity\n", + "- ``'+'``: Creation operator\n", + "- ``'-'``: Annihilation operator\n", + "\n", + "Let's generate all possible single-electron transitions (amongst same spin \n", + "species)." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "389284f3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[['I' 'I' 'I' 'I' 'I' 'I' 'I' 'I']\n", + " ['+' '-' 'I' 'I' 'I' 'I' 'I' 'I']\n", + " ['-' '+' 'I' 'I' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' '+' '-' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' '-' '+' 'I' 'I']\n", + " ['+' 'I' '-' 'I' 'I' 'I' 'I' 'I']\n", + " ['-' 'I' '+' 'I' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' '+' 'I' '-' 'I']\n", + " ['I' 'I' 'I' 'I' '-' 'I' '+' 'I']\n", + " ['+' 'I' 'I' '-' 'I' 'I' 'I' 'I']\n", + " ['-' 'I' 'I' '+' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' '+' 'I' 'I' '-']\n", + " ['I' 'I' 'I' 'I' '-' 'I' 'I' '+']\n", + " ['I' '+' '-' 'I' 'I' 'I' 'I' 'I']\n", + " ['I' '-' '+' 'I' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' 'I' '+' '-' 'I']\n", + " ['I' 'I' 'I' 'I' 'I' '-' '+' 'I']\n", + " ['I' '+' 'I' '-' 'I' 'I' 'I' 'I']\n", + " ['I' '-' 'I' '+' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' 'I' '+' 'I' '-']\n", + " ['I' 'I' 'I' 'I' 'I' '-' 'I' '+']\n", + " ['I' 'I' '+' '-' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' '-' '+' 'I' 'I' 'I' 'I']\n", + " ['I' 'I' 'I' 'I' 'I' 'I' '+' '-']\n", + " ['I' 'I' 'I' 'I' 'I' 'I' '-' '+']]\n" + ] + } + ], + "source": [ + "transitions_single = np.array(\n", + " [[\"I\" for i in range(2 * n_orb)] for j in range(4 * (n_orb**2 - n_orb) // 2 + 1)]\n", + ")\n", + "count = 1\n", + "for i in range(n_orb):\n", + " for j in range(i + 1, n_orb):\n", + " # spin up\n", + " transitions_single[count, i] = \"+\"\n", + " transitions_single[count, j] = \"-\"\n", + " count += 1\n", + " transitions_single[count, i] = \"-\"\n", + " transitions_single[count, j] = \"+\"\n", + " count += 1\n", + "\n", + " # spin down\n", + " transitions_single[count, i + n_orb] = \"+\"\n", + " transitions_single[count, j + n_orb] = \"-\"\n", + " count += 1\n", + " transitions_single[count, i + n_orb] = \"-\"\n", + " transitions_single[count, j + n_orb] = \"+\"\n", + " count += 1\n", + "\n", + "print(transitions_single)" + ] + }, + { + "cell_type": "markdown", + "id": "c15c5b3f", + "metadata": {}, + "source": [ + "Let's now apply the transition operators to the configurations in ``bitstring_matrix``" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6a44f358", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(723, 8)\n", + "[[False False False ... False False True]\n", + " [False True False ... True False False]\n", + " [ True True True ... True False True]\n", + " ...\n", + " [ True False True ... False False True]\n", + " [ True True True ... True False True]\n", + " [False False False ... False False True]]\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.fermion import enlarge_batch_from_transitions\n", + "\n", + "bitstring_matrix_aug = enlarge_batch_from_transitions(bitstring_matrix, transitions_single)\n", + "\n", + "print(bitstring_matrix_aug.shape)\n", + "print(bitstring_matrix_aug)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/how_tos/benchmark_pauli_projection.ipynb b/docs/how_tos/benchmark_pauli_projection.ipynb new file mode 100644 index 0000000..1752539 --- /dev/null +++ b/docs/how_tos/benchmark_pauli_projection.ipynb @@ -0,0 +1,463 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "55900f6c-2fb6-4d2c-8745-29bad8b66d9f", + "metadata": {}, + "source": [ + "# Benchmark Pauli operator projection" + ] + }, + { + "cell_type": "markdown", + "id": "b5caa5b4", + "metadata": {}, + "source": [ + "### Pauli string action on a computational basis state\n", + "\n", + "The action of a Pauli string on a computational basis state is rather trivial, and just a single computational basis state itself. This is a direct consequence of the structure of Pauli matrices, which only have a single nonzero element on each of their rows. Consequently, their action on a qubit is:\n", + "\n", + "-------------------------------------------\n", + "\n", + "$$\n", + "\\sigma_x |0 \\rangle = |1 \\rangle\n", + "$$\n", + "\n", + "$$\n", + "\\sigma_x |1 \\rangle = |0 \\rangle\n", + "$$\n", + "\n", + "-------------------------------------------\n", + "\n", + "$$\n", + "\\sigma_y |0 \\rangle = i|1 \\rangle\n", + "$$\n", + "\n", + "$$\n", + "\\sigma_y |1 \\rangle = -i|0 \\rangle\n", + "$$\n", + "\n", + "-------------------------------------------\n", + "\n", + "$$\n", + "\\sigma_z |0 \\rangle = |0 \\rangle\n", + "$$\n", + "\n", + "$$\n", + "\\sigma_z |1 \\rangle = -|1 \\rangle\n", + "$$\n", + "\n", + "-------------------------------------------\n", + "\n", + "$$\n", + "I |0 \\rangle = |0 \\rangle\n", + "$$\n", + "\n", + "$$\n", + "I |1 \\rangle = |1 \\rangle\n", + "$$\n", + "\n", + "-------------------------------------------\n", + "\n", + "Each bit on the bitstring labeling the computational basis will be labeled by $x \\in \\{0, 1 \\}$. In order to keep the implementation at light as possible, we will\n", + "represent the bitstrings with `bool` variables: $0\\rightarrow \\textrm{False}$ and\n", + "$1\\rightarrow \\textrm{True}$.\n", + "\n", + "To represent the action of each Pauli operator in a computational basis state\n", + "we will assign three variables to it: `diag`, `sign`, `imag`. \n", + "- `diag` labels whether the operator is diagonal:\n", + " - $\\textrm{diag}(I) = \\textrm{True}$\n", + " - $\\textrm{diag}(\\sigma_x) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_y) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_z) = \\textrm{True}$\n", + "- `sign` Identifies if there is a sign change in the matrix element connected \n", + "to either 0 or 1:\n", + " - $\\textrm{diag}(I) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_x) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_y) = \\textrm{True}$\n", + " - $\\textrm{diag}(\\sigma_z) = \\textrm{True}$\n", + "- `imag` Identifies if there is a complex component to the matrix element:\n", + " - $\\textrm{diag}(I) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_x) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_y) = \\textrm{False}$\n", + " - $\\textrm{diag}(\\sigma_z) = \\textrm{True}$\n", + "\n", + "Let's label an arbitrary Pauli operator as $\\sigma \\in \\{ I, \\sigma_x, \\sigma_y\n", + "\\sigma_z\\}$. The action of the Pauli operator on a computational basis state \n", + "can then be represented by the logic operation:\n", + "$$\n", + "\\sigma |x \\rangle = |x == \\textrm{diag}(\\sigma) \\rangle (-1)^{x\\textrm{ and sign}(\\sigma)}\n", + "(i)^{\\textrm{imag}(\\sigma)}.\n", + "$$\n", + "The same is straightforwardly generalized to arbitrary number of qubits." + ] + }, + { + "cell_type": "markdown", + "id": "a8fd7e11", + "metadata": {}, + "source": [ + "Let's check that this works:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "dcb15308", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-------------------\n", + "I\n", + "|False> --> |False> ME:(1+0j)\n", + "|True> --> |True> ME:(1+0j)\n", + "-------------------\n", + "SX\n", + "|False> --> |True> ME:(1+0j)\n", + "|True> --> |False> ME:(1+0j)\n", + "-------------------\n", + "SZ\n", + "|False> --> |False> ME:(1+0j)\n", + "|True> --> |True> ME:(-1+0j)\n", + "-------------------\n", + "SY\n", + "|False> --> |True> ME:1j\n", + "|True> --> |False> ME:(-0-1j)\n" + ] + } + ], + "source": [ + "import time\n", + "\n", + "import numpy as np\n", + "from qiskit_addon_sqd.qubit import matrix_elements_from_pauli_string, sort_and_remove_duplicates\n", + "\n", + "\n", + "def connected_element_and_amplitude_bool(x, diag, sign, imag):\n", + " \"\"\"\n", + " Finds the connected element to computational basis state |x> under\n", + " the action of the Pauli operator represented by (diag, sign, imag).\n", + "\n", + " Args:\n", + " x: Value of the bit, either True or False.\n", + " diag: Whether the Pauli operator is diagonal (I, Z)\n", + " sigma: Whether the Pauli operator's rows differ in sign (Y, Z)\n", + " imag: Whether the Pauli operator is purely imaginary (Y)\n", + "\n", + " Returns:\n", + " A length-2 tuple:\n", + " - The connected element to x, either False or True\n", + " - The matrix element\n", + " \"\"\"\n", + " return x == diag, (-1) ** (x and sign) * (1j) ** (imag)\n", + "\n", + "\n", + "sigma_indices = [0, 1, 2, 3]\n", + "sigma_string = [\"I\", \"SX\", \"SZ\", \"SY\"]\n", + "sigma_diag = [True, False, True, False]\n", + "sigma_sign = [False, False, True, True]\n", + "sigma_imag = [False, False, False, True]\n", + "qubit_values = [False, True]\n", + "\n", + "for xi in sigma_indices:\n", + " print(\"-------------------\")\n", + " print(sigma_string[xi])\n", + " for x in qubit_values:\n", + " x_p, matrix_element = connected_element_and_amplitude_bool(\n", + " x, sigma_diag[xi], sigma_sign[xi], sigma_imag[xi]\n", + " )\n", + " print(\"|\" + str(x) + \"> --> |\" + str(x_p) + \"> ME:\" + str(matrix_element))" + ] + }, + { + "cell_type": "markdown", + "id": "f40a3463", + "metadata": {}, + "source": [ + "Let's generate some large number of bitstrings (50 M) for a 40-qubit system" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "74c16c91-cc5c-46ce-aff8-17d0e71ac50f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total number of unique bitstrings: 49998839\n" + ] + } + ], + "source": [ + "rand_seed = 22\n", + "np.random.seed(rand_seed)\n", + "\n", + "# Generate some random bitstrings for testing\n", + "\n", + "\n", + "def random_bitstrings(n_samples, n_qubits):\n", + " return np.round(np.random.rand(n_samples, n_qubits)).astype(\"int\").astype(\"bool\")\n", + "\n", + "\n", + "n_qubits = 40\n", + "bts_matrix = random_bitstrings(50_000_000, n_qubits)\n", + "\n", + "# We need to sort the bitstrings and just keep the unique ones\n", + "# NOTE: It is essential for the projection code to have the bitstrings sorted!\n", + "bts_matrix = sort_and_remove_duplicates(bts_matrix).astype(\"bool\")\n", + "\n", + "# Final subspace dimension after getting rid of duplicated bitstrings\n", + "d = bts_matrix.shape[0]\n", + "\n", + "print(\"Total number of unique bitstrings: \" + str(d))" + ] + }, + { + "cell_type": "markdown", + "id": "184bf287", + "metadata": {}, + "source": [ + "### Let's time the projection time for a Pauli String\n", + "\n", + "The Pauli string under consideration is $\\sigma_z \\otimes ... \\otimes \\sigma_z$.\n", + "\n", + "Different subspace dimensions are considered by just slicing the matrix of bitstrings. We time the subspace projection for the different subspace sizes." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8fe182bc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0 took 0.31216s\n", + "Iteration 1 took 0.510622s\n", + "Iteration 2 took 0.775817s\n", + "Iteration 3 took 1.047106s\n", + "Iteration 4 took 1.354705s\n", + "Iteration 5 took 1.583962s\n", + "Iteration 6 took 1.846798s\n", + "Iteration 7 took 2.072656s\n", + "Iteration 8 took 2.313123s\n", + "Iteration 9 took 2.539087s\n", + "Iteration 10 took 2.831971s\n", + "Iteration 11 took 3.149036s\n", + "Iteration 12 took 3.36273s\n", + "Iteration 13 took 3.661241s\n", + "Iteration 14 took 3.998323s\n", + "Iteration 15 took 4.310177s\n", + "Iteration 16 took 4.654591s\n", + "Iteration 17 took 4.686089s\n", + "Iteration 18 took 5.002513s\n", + "Iteration 19 took 5.188594s\n" + ] + } + ], + "source": [ + "pauli_str = [\"Z\" for i in range(n_qubits)]\n", + "\n", + "# Different subspace sizes to test\n", + "d_list = np.linspace(d / 1000, d, 20).astype(\"int\")\n", + "\n", + "# To store the walltime\n", + "time_array = np.zeros(20)\n", + "\n", + "for i in range(20):\n", + " int_bts_matrix = bts_matrix[: d_list[i], :]\n", + " time_1 = time.time()\n", + " _ = matrix_elements_from_pauli_string(int_bts_matrix, pauli_str)\n", + " time_array[i] = time.time() - time_1\n", + " print(f\"Iteration {i} took {round(time_array[i], 6)}s\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9abb110f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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zFdbGtGnTxqH4HFXRZ6qqz1pp7AsXLkS3bt3KPfbGz0FV51SpVNiyZQs2b96MX375BevXr8c333yDIUOG4Ndff62wvKOq8zP7+eef4+TJk1i6dGmZJCg/Px9paWlo0qQJ1Go1mjdvDrPZjCtXrqBJkybW44qLi3Ht2jW0aNGiVl5Hbfys1GTS6up+D5DnYI0duRSZTIZ58+bh4sWL+PDDD63bAwMDyx1VWFozUB31OeN/ZGQksrKyMHToUAwbNqzMw56/+sePH4/169cjLy8P33zzDSIiItCnT58yx/Xp0wdvvPEG9u3bhy+//BJHjx7F119/XeX5KytXWnty4z2o6P23WCxlmr1TU1MBwKaJUaFQYOTIkfj4449x5swZTJ06FZ9//jlOnz5tU7a0JqpUQUEBLl26ZD1XUlISrl27hsTERDz55JO46667MGzYsDIDcCIjIwEAR44cqfB9KK1plMvl5d6rYcOG2TSH3ig8PByXLl2yaTYHSuYhq2ulr0+j0VQYe3XmmvPy8sLQoUPxzjvv4NixY3jjjTewadOmCrsQhIeHAyj/NZ84cQKNGzeGr6+vw3Hc6Ny5czAajYiJiUGrVq2sD6Ak6WvVqhV+/fVXALAmuvv27bM5x759+2CxWCpMhAEgODgYKpWqzOcQKPsaHf1ZAcp+vk+fPg2LxVLp/HRVfX9V93uA3B8TO3I5gwYNQq9evfDee+9Zh/xHRkbixIkTyMzMtB73xx9/VDkyrzKlv1jKSxhr2/jx43HhwgV88sknZfbp9foyzVLlmTBhAgwGA5YtW4b169eXmeMvOzu7TO1G6S+rypph7CkXHh4OmUyGLVu22Bz38ccfV3je6xNzIQQ+/PBDyOVyDB06FABw7do1m+O9vLzQpUuXcuP973//a9NfaPHixTCZTBgxYgSAf2p7rn8dxcXFZeLr3r07WrVqhffee6/MfS8t26RJEwwaNAhLly7FpUuXyryu6z+D5bnjjjtgMpmwePFi6zaz2VwvKxxER0cjMjIS//d//1cmsQSqjr08WVlZZbZV9blq3rw5unXrhmXLltm8z0eOHMGvv/6KO+64w+E4ynPfffdhzZo1ZR5AyX1Ys2aNtR/ikCFDEBQUZHNfgJLPklqtxp133lnhdWQyGYYPH47vv/8e586ds24/fvw4NmzYYHOsRqNB48aNHfpZKZ16qVTpZ6X0812eir6/qvs9QJ6DTbHkkp599lmMGzcOiYmJmDZtGiZPnox33nkHw4cPx5QpU3DlyhUsWbIEnTp1qrJzdUWio6MBAE888QSGDx8OmUyG++67rzZfhtWDDz6Ib7/9FtOmTcPmzZsRExMDs9mMEydO4Ntvv8WGDRvKTMNwo+7du6NNmzZ46aWXYDAYbJphAWDZsmX4+OOPcc899yAyMhL5+fn45JNPoNFoKv1Fak85rVaLcePGYdGiRZAkCZGRkfj5558r7Gvm4+OD9evXIzY2Fr1798a6devwyy+/4MUXX0RwcDCAkoEoWVlZGDJkCEJCQpCeno5FixahW7du1ukbShUXF2Po0KEYP348Tp48iY8//hi33HIL7r77bgBAv379EBgYiNjYWDzxxBOQJAlffPFFmV9wXl5eWLx4MUaOHIlu3bohPj4ezZs3x4kTJ3D06FHrL+mPPvoIt9xyCzp37oxHHnkErVu3xuXLl7Fz505kZGTgjz/+qPD9HDlyJGJiYvDCCy8gLS0NHTt2xOrVq8v0basLXl5e+PTTTzFixAh06tQJ8fHxaNmyJS5cuIDNmzdDo9Hgp59+cuicc+fOxZYtW3DnnXciPDwcV65cwccff4yQkBDrwJ3yLFy4ECNGjEDfvn0xZcoU63QnWq221pbya9++Pdq3b1/uvlatWmH06NHW5yqVCq+99hpmzpyJcePGYfjw4di6dSuWL1+ON954w2aQR3leffVVrF+/Hv3798eMGTNgMpmwaNEidOrUCYcOHbI59uGHH8b8+fPx8MMPo0ePHtiyZYu1xro8Z8+exd13343bb78dO3fuxPLly3H//feja9euFZbp1q0bZDIZ3nrrLeTm5kKpVGLIkCFYsWJFtb4HyIM4YSQukRDin6ksyhuWbzabRWRkpIiMjLROh7F8+XLRunVroVAoRLdu3cSGDRsqnO5k4cKFZc6JG6YaMJlM4vHHHxfBwcFCkiSbKQtuPLZ0WoIbp3yIjY0Vvr6+Za41cOBA0alTJ5ttxcXF4q233hKdOnUSSqVSBAYGiujoaPHqq6+K3NzcSt+rUi+99JIAINq0aVNm3/79+8XEiRNFWFiYUCqVokmTJuKuu+4S+/btq/Sc9pbLzMwUY8eOFWq1WgQGBoqpU6eKI0eOlDvdia+vrzhz5oy47bbbhFqtFk2bNhWzZ88WZrPZetzKlSvFbbfdJpo0aSIUCoUICwsTU6dOFZcuXbIeU/oZSU5OFo8++qgIDAwUfn5+4oEHHrCZRkMIIbZv3y769OkjVCqVaNGihXjuuefEhg0byp0SYtu2beLWW28V/v7+wtfXV3Tp0kUsWrTI5pgzZ86Ihx56SDRr1kzI5XLRsmVLcdddd4mVK1dW+n4KIcS1a9fEgw8+KDQajdBqteLBBx8UBw4csHu6kxun6qjoc106Dc13331ns/3AgQNizJgxolGjRkKpVIrw8HAxfvx48fvvv5e59o2f6dL3vHQKld9//12MGjVKtGjRQigUCtGiRQsxceJEkZqaWia+G6f4+O2330RMTIxQqVRCo9GIkSNHimPHjtkcY28cjijvPSz13//+V7Rr104oFAoRGRkp3n33XZupYSqTnJwsoqOjhUKhEK1btxZLliwp9x7qdDoxZcoUodVqhb+/vxg/fry4cuVKhd8rx44dE/fee6/w9/cXgYGB4rHHHhN6vd7mnDdOdyKEEJ988olo3bq1dcqVzZs3V/t7gDyHJEQNe5MTEdWRxMRExMfHY+/evVXWaBI5w5w5c/Dqq6/WeGAWUW1hHzsiIiIiD8HEjoiIiMhDMLEjIiIi8hDsY0dERETkIVhjR0REROQhmNgREREReQi3nqDYYrHg4sWL8Pf3r9floYiIiIjqixAC+fn5aNGiBby8Kq+Tc+vE7uLFi1Uunk5ERETkCc6fP4+QkJBKj3HrxK50Ie7z589Do9E4ORoiIiKi2peXl4fQ0FBr3lMZt07sSptfNRoNEzsiIiLyaPZ0O+PgCSIiIiIPwcSOiIiIyEMwsSMiIiLyEEzsiIiIiDwEEzsiIiIiD8HEjoiIiMhDMLEjIiIi8hBuPY8dERERkTMIIZCtM6LQYIKv0huBarlLLG/KxI6IiIjITrl6I1alZGDZjjSkZ+ms28OD1IjtF4Gx0SHQquROi08SQginXb2G8vLyoNVqkZuby5UniIiIqE4lp2Zi+vIU6IvNAIDrE6jSujqVQobFk6IxMCq41q7rSL7DPnZEREREVUhOzUR8wh7ojWYI2CZ1+Pu5AKA3mhGfsAfJqZn1HySY2BERERFVKldvxPTlKSXJWxXtnEKUJHjTl6cgV2+sj/BsMLEjIiIiqsSqlAzoi81VJnWlhAD0xWas3p9Rt4GVg4kdERERUQWEEFi2I61aZRO3p6G+hzIwsSMiIiKqQLbOiPQsXZk+dVURANKzdMjR1W9zLBM7IiIiogoUGkw1Kl9Qw/KOYmJHREREVAFfZc2m/PWrYXlHcYJiIiIionIcPJ+DRb+nVqusBCAsSI0Adf1OVszEjoiIiOg6e9Oy8MHvp7D11FUAJUladYZAxMVE1PsyY0zsiIiIqMETQmDHmWv44PdT2H02CwAg85Jwz80t8VCfcNz3ya6SyYntyPC8JMBHLsOY7iF1HHVZTOyIiIjIIwghkK0zotBggq/SG4FqeZU1ZkIIJKVmYtHvp7D/XA4AQC6TcG90KGYMikRokBoAsHhSNOIT9gBS5ZMUl15uyaRop6wZy8SOiIiI3Fqu3ohVKRlYtiMN6Vk66/bwIDVi+0VgbHRImSTLYhHYePwyPtx0Gocv5AIAlN5emNgrDFMHtkZzrcrm+IFRwUiI71X1WrFyGZZMisaAWlwr1hGSqO+Z82qRI4viEhERkedJTs2sOtlSyLB4UjQGRgXDbBFYd+QSPtx0Gif+yi/ZL5dhUp8wPDKgNZr4+1R6vVy9Eav3ZyBxe9kkMi6mJInU+NRuTZ0j+Q4TOyIiInJLyamZiE/YU+UarpJUkuQ93L8Vfj9+BWcyCwGUTEXyUN9wTLmlFRr5KR26thACOTojCgwm+Cm9EWBHs291OZLvOHUeuzlz5kCSJJtH+/btnRkSERERuYFcvRHTl6dUmdTh7/0WAfx3y1mcySyExscbTw1ri+3PD8Fzt7d3OKkDAEmSEOirQGiQGoG+inof/VoRp/ex69SpE3777Tfrc29vp4dERERELm5VSgb0xWaHpyEZ2r4J3ruvG/xrubnUVTg9i/L29kazZs2cHQYRERG5CSEElu1Ic7icBOD0lYJ6Xw2iPjl9SbFTp06hRYsWaN26NR544AGcO3euwmMNBgPy8vJsHkRERNSwZOuMSM/SOVxbJwCkZ+mQozPWRVguwamJXe/evZGYmIj169dj8eLFOHv2LPr374/8/Pxyj583bx60Wq31ERoaWs8RExERkbMVGkw1Kl9Qw/KuzKVGxebk5CA8PBzvvPMOpkyZUma/wWCAwWCwPs/Ly0NoaChHxRIRETUgWYXF6P7axmqXP/DyrQj0VdRiRHXLkVGxLtXIHBAQgKioKJw+fbrc/UqlEkql4yNXiIiIyHMEquUID1LjnIPNsRKAsCA1AtSeOXACcIE+dtcrKCjAmTNn0Lx5c2eHQkRERC5KkiSM6NzM4T52ABAXE+EyU5PUBacmds888wySk5ORlpaGHTt24J577oFMJsPEiROdGRYRERG5sI3HLuNzB0fFekklK1CM6R5SN0G5CKc2xWZkZGDixIm4du0agoODccstt2DXrl0IDnbO+mpERETkuoQQWJL8JxZsOAEhgA7N/XHyr3y7Vp4AgCWTosusGetpnJrYff311868PBEREbmJIqMZs1YfxpoDFwAAk/qEYfbITthx5lrVa8XKZVgyKRoDojy/4silBk8QERER3ehKfhEe/TwFB8/nQOYlYc7IjniwbwQAYGBUMHbOGorV+zOQuD0N6Vk6a7mwIDXiYiIwNjoEGg9daeJGLjXdiaMcGf5LRERE7ufIhVw88vk+XMotglYlx8cPdEdMm8blHiuEQI7OiAKDCX5KbwSo5R4xUMJtpzshIiIiKrX28CU8/e1BFBktaB3si89ie6JVY98Kj5ckCYG+Creao662MbEjIiIilyKEwAe/n8a7v6UCAAZEBWPRxJs9fuBDbWBiR0RERC5DX2zGMyv/wC+HLgEAptzSCrNGtIe3zKWm3nVZTOyIiIjIJVzK1eORz/fhyIU8yGUSXh99Eyb0DHN2WG6FiR0RERE53cHzOXj08324km9AkK8Cix/ojt6tGzk7LLfDxI6IiIic6oeDF/DsykMoNlnQrqk/Po3tgdAgtbPDcktM7IiIiKhOCCGQrTOi0GCCr9IbgTdMP2KxCLy98SQ+2nwGADCsQxO8d9/N8FMyPakuvnNERERUq3L1RqxKycCyHbYTBocHqRHbr2TCYG8vCU99cxAbj10GAEwfFIlnbmsHmZf7zzvnTJygmIiIqAGpqhatppJTM6tc4stH7oVGfkpkZOuhkHlh/tjOGNM9pNZi8DScoJiIiIhs2FOLVtN54pJTMxGfsAcCtgldqdJteqMFGdl6aHzkSJzcE93DAmt0XfoHEzsiIiIPd2Mt2vXOZenw2s/H8H+/nsTiSdEYGBVcrWvk6o2YvjylJKmzsy3QaLYgMtivWtej8nG2PyIiIg9WWoumN5rLrUkr3aY3mhGfsAfJqZnVus6qlAzoi812J3UAUGQ0Y/X+jGpdj8rHxI6IiMhDOVKLJkRJgjd9eQpy9UaHriOEwLIdadWKMXF7Gty4u7/LYVMsERGRh7LWotl5vBAlS3qt3p+B+JhWNvuMZguyC4txrbAYWaX/LzAgq7AYF3L0Nv327CUApGfpkKMzItBX4XB5KouJHRERkQeqbi2aAPD2ryex4/RVZOuM1iTO0Vo8RxQYTEzsagkTOyIiIg+UrTNWqxYNAAoMZmw8fqXMdi8JCFQrEORb8mjkp0AjXyVUchn+u/XPasfKCYlrD99JIiIiD1RoMNWo/NO3RqFNEz8E+SrQ2E+BIF8ltCp5uRMICyGw4ehfOJels7vZFyiZ1y4sSI0Adc2mWaF/MLEjIiLyQL41rAV7sE+43c2jkiQhtl8EXvv5mMPXiYuJqNUJkhs6joolIiLyQIFqOcKD1HA0ZZJQMmmxo7VoY6NDoFLIYG+O5iUBKoWMK07UMiZ2REREHqi0Fq06E4lUpxZNq5Jj8aRoSECVyV3p/iWTomu82gXZYmJHRETkgSwWgfSsQofK1LQWbWBUMBLie0Ell5UkeDfsL92mksuQGN8LA6q5ygVVjH3siIiIPIzRbMFzKw9hzYELAP5OsKTKJymurVq0gVHB2DlrKFbvz0Didtt1acOC1IiLKVmXVuPDmrq6IAk3nu45Ly8PWq0Wubm50Gg0zg6HiIjI6QoNJkz/cj+2pGZC5iXhrbFdEOyvtFkr9vpf/KW1aiqFDEsmRddqLZoQAjk6IwoMJvgpvRGglnOgRDU4ku+wxo6IiMhDXC0wYHLiXhzKyIVKLsPHk7pjcLsmAOCUWjRJkhDoq+Dkw/WINXZEREQe4HyWDg9+thtp13QIVMvxv7ieuDkssMxxrEVzP6yxIyIiakCOXsxFXMJeZOYb0DJAhc+n9EJksF+5x7IWzbMxsSMiInJjO05fxaNfpKDAYEL7Zv5YNrkXmmp8nB0WOQkTOyIiIjf186GLePqbP1BstqB3qyD896EenBeugWNiR0RE5IYSt5/Fqz8fgxDAiJua4d0J3eAjlzk7LHIyJnZERERuRAiBhRtO4uOkMwBK1nSdc3cnyLw4AIKY2BEREbkNk9mCWasP47uUDADAv2+NwmND2nBUK1kxsSMiInID+mIzZq7Yj00nrsBLAt68pzPu6xXm7LDIxTCxIyIicnHZhcWYvGwvDpzLgdLbCx/e3x23dmzq7LDIBTGxIyIicjIhBLJ1RhQaTPBVeiPwukmDM7J1eOh/e/BnZiG0Kjk+i+2BHhFBTo6YXBUTOyIiIifJ1RuxKiUDy3bYLvMVHqRGbL8IdAnRYuaK/bicZ0BzrQ8+n9wLbZv6OzFicnVM7IiIiJwgOTUT05enQF9sLrPvXJYOr/18DKVrfrZt4ofPp/RCc62qfoMkt8PEjoiIqJ4lp2YiPmEPBIDyFmy/cdu/hrVlUkd28XJ2AERERA1Jrt6I6ctTSpK68rK6G0gS8MzKQ8jVG+s8NnJ/TOyIiIjq0aqUDOiLzXYldUBJ8qcvNmP1/oy6DYw8AhM7IiKieiKEwLIdadUqm7g9DcLebJAaLCZ2RERE9SRbZ0R6lq7cfnWVEQDSs3TI0bE5lirHxI6IiKieFBpMNSpfUMPy5PmY2BEREdUTX2XNJqPwq2F58nxM7IiIiOpJoFqOsCC1w+UklExaHKCW135Q5FGY2BEREdUTg8kCjap6tW5xMRHWZcaIKsLEjoiIqB5cytVj3JKdOHIhD0BJLZw9vCRApZBhTPeQuguOPAYTOyIiojqWkp6FkYu24/CFXASq5Xjh9vaQpJLJhytTun/JpGhoVWyGpaqxFyYREVEd+nbvefzn+yMoNlvQvpk/PnmoB0KD1OjQQmOzVuz1U6CU5nsquQxLJkVjQFRwvcdN7omJHRERUR0wmS14Y+1xJGxPAwAM79QU74zvZh0ZOzAqGDtnDcXq/RlI3J6G9CydtWxYkBpxMREYGx0CjQ9r6sh+knDjaazz8vKg1WqRm5sLjUbj7HCIiIgAADm6Yjy24gC2nb4KAHhqWFs8MaQtvLzKb3sVQiBHZ0SBwQQ/pTcC1HIOlCArR/Id1tgRERHVotTL+Xjk831Iv6aDWiHD2+O6YkTn5pWWkSQJgb4KBPoq6ilK8lRM7IiIiGrJxmOX8dTXB1BYbEZIoAqfPNQDHZqzRYnqDxM7IiKiGhJC4KPNp/H2xlQIAfRpHYSPH4hGEGvgqJ4xsSMiIqoBXbEJz648hF8OXQIAPNgnHK+M7Ai5jDOKUf1jYkdERFRNF3L0eGTZPhy7lAdvLwlzR92E+3uHOTssasCY2BEREd1ACIFsnRGFBhN8ld4ILGeU6t60LEz7IgXXCovRyFeBxZOi0atVkJMiJirBxI6IiOhvuXojVqVkYNkO23nlwoPUiO1XMq+cViXHV3vO4ZUfjsBoFujYXIP/PhSNkEC1EyMnKsF57IiIiAAkp2ZWvRKEQoa+kY3w+/ErAIA7OzfHwnFdoFawnoTqjiP5jsv07Jw/fz4kScJTTz3l7FCIiKiBSU7NRHzCHuiNZgjYJnX4+7kAoCs2W5O6Z26Lwof338ykjlyKSyR2e/fuxdKlS9GlSxdnh0JERA1Mrt6I6ctTSpI3O9uwlN5eeLBvBFeHIJfj9MSuoKAADzzwAD755BMEBgY6OxwiImpgVqVkQF9stjupA4BikwWr92fUXVBE1eT0xG7mzJm48847MWzYMGeHQkREDYwQAst2pFWrbOL2NLhxN3XyUE7tGPD1119j//792Lt3r13HGwwGGAwG6/O8vLy6Co2IiBqAbJ3RZvSrvQSA9CwdcnRGru9KLsVpNXbnz5/Hk08+iS+//BI+Pj52lZk3bx60Wq31ERoaWsdREhGRJys0mGpUvqCG5Ylqm9OmO/n+++9xzz33QCaTWbeZzWZIkgQvLy8YDAabfUD5NXahoaGc7oSIiKolq7AY3V/bWO3yB16+lTV2VOccme7EaU2xQ4cOxeHDh222xcfHo3379nj++efLJHUAoFQqoVQq6ytEIiLycIFqOcKD1DiXpSszxUllJABhQWoEqOV1FRpRtTgtsfP398dNN91ks83X1xeNGjUqs52IiKguSJKE2H4RmPvzMYfLxsVwuhNyPZxVkYiIGjSZg8mZlwT4yGUY0z2kjiIiqj6XSuySkpKcHQIRETUQQgi8//spvPfbKQB/LxsmVT5JcWkOuGRSNLQqNsOS63H6PHZERET1zWi24PlVh6xJ3czBkUiI7wmVXAYJ/6wNW6p0m0ouQ2J8LwyICq7niIns41I1dkRERHWt0GDCjC/3Izk1E14SMHfUTZjUJxwAsHPWUKzen4HE7Wk289uFBakRFxOBsdEh0Piwpo5cl9OmO6kNjgz/JSIiupJfhMmJe3HkQh585F74cGJ3DOvYtMxxQgjk6IwoMJjgp/RGgFrOgRLkNG4x3QkREVF9On2lAHEJe5CRrUeQrwL/i+uJbqEB5R4rSRICfRWco47cDhM7IiLyeHvTsvDwsn3I1RsR3kiNZfG9ENHY19lhEdU6JnZEROTR1h2+hCe/OYhikwVdQwPwv9geaOTHye7JMzGxIyIij/W/bWfx2i/HIAQwrEMTLJrYHSpF2ZWNiDwFEzsiIvI4FovAm2uP49NtZwEAk/qEYc7ITvCWcZYv8mxM7IiIyKMUGc3493d/4JdDlwAAz93eDtMHRnJUKzUITOyIiMhj5OqMeOSLfdhzNgtymYQF93bBPTdz6S9qOJjYERGRWxBCIFtnRKHBBF+lNwJvmFsuI1uHuIS9OH2lAP5Kbyx5MBoxbRo7MWKi+sfEjoiIXFqu3ohVKRlYtsN2NYjwIDVi+5WsBpGRrUN8wl5cyTegmcYHCfE90aE5J66nhocrTxARkctKTs3E9OUp0BebAQDX/8IqratTeJcMiDCYLGjX1B+Jk3uiuVZVv4ES1SGuPEFERG4vOTUT8Ql7IGCb0JUq3WYwWQAAHZr54+upfaFVcS1Xarg47puIiFxOrt6I6ctTSpI6O9uVrm+mJWqomNgREZHLWZWSAX2x2e6kDgD0xWas3p9Rd0ERuQEmdkRE5FKEEFi2I61aZRO3p8GNu44T1RgTOyIicinZOiPSs3Tl9qurjEBJc2yOzlgXYRG5BSZ2RETkUgoNphqVL6hheSJ3xsSOiIhciq+yZhM2+NWwPJE7Y2JHREQuJVAtR3iQGo6u7CqhZNLiADWnO6GGi4kdERG5FEmScEfn5g73sQOAuJgIm2XGiBoa1lcTEZFL+fnQRSTuOOtQGS8J8JHLMKZ7SB1FReQemNgREZFLMJktmL/uBD7dVpLUdWjmj5OX86ucpLi0gm7JpGiuOkENHptiiYjI6a7kF+GBT3dbk7qpA1vjp8dvQUJ8L6jkMkhAmT53pdtUchkS43thQFRwPUdN5HpYY0dERE6Vkp6FGV/ux+U8A/yU3lh4bxeM6NwcADAwKhg7Zw3F6v0ZSNyeZrNsWFiQGnExERgbHQKND2vqiABAEm48RXdeXh60Wi1yc3Oh0WicHQ4RETlACIHPd6bjtZ+PwWQRaNPED0smRaNNE78Kj8/RGVFgMMFP6Y0AtZwDJahBcCTfYY0dERHVO12xCS+uPozvD14EANzZuTkW3Nul0jnsJElCoK8Cgb6K+gqTyO0wsSMionqVdrUQ05an4MRf+ZB5SZg1oj2m3NKKtW9EtYCJHRER1Zvfjl3Gv749iPwiExr7KfDh/d3Rp3UjZ4dF5DGY2BERUZ0zWwTe+y0VizadBgBEhwfio/u7o5nWx8mREXkWJnZERFSnsguL8cTXB7D11FUAQFy/CLx4RwcovDnjFlFtY2JHRETVIoRAts6IQoMJvkpvBJYzSvVwRi6mLU/BhRw9fORemD+mC0bf3NJJERN5PiZ2RETkkFy9EatSMrBsh+28cuFBasT2K5lXTquS45u95/DyD0dRbLIgvJEaSyZFo0NzTk1FVJc4jx0REdktOTUT05enQF9sBgBc/wuktK7ORyFD74hAJKWWNL0O69AEb4/vxuW+iKqJ89gREVGtS07NRHzCnpK1W8vZX7pNX2y2JnXP3BaFGYPawMuLU5kQ1Qf2XCUioirl6o2YvjylJKmzs51H6e2FB/tGMKkjqkdM7IiIqEqrUjKgLzbbndQBQLHJgtX7M+ouKCIqg4kdERFVSgiBZTvSqlU2cXsa3LgrN5HbYWJHRESVytYZkZ6lK7dfXWUEgPQsHXJ0xroIi4jKwcSOiIgqVWgw1ah8QQ3LE5H97BoV++OPPzp84ltvvRUqlcrhckRE5Fp8lTWbQMGvhuWJyH52/bSNHj3aoZNKkoRTp06hdevW1YmJiIhciK7YBLVCBt3fc9fZSwIQFqRGgJrz1xHVF7v/jPrrr7/QpEkTu4719/evdkBEROQa8ouM+DjpDD7bdhbFJku1zhEXE1FmmTEiqjt2JXaxsbEONatOmjSJK0EQEbkpk9mCr/eex7sbU3GtsBgA0CM8AEcu5sFgstg15YmXBPjIZRjTPaSOoyWi63FJMSIiAlAyrUnSyUy8ufY4Tl0pAAC0buyLWXd0wLAOTbDl1NV/Vp6o5DeHJJU0wybG98KAqOB6iZ3Ik9XrkmJ5eXnYtGkT2rVrhw4dOtT0dERE5ATHL+XhzbXHsfVUyVJggWo5nhoWhft7h0EuK5lAYWBUMBLie1W5VqxKLsOSSdFM6oicwOEau/Hjx2PAgAF47LHHoNfr0bVrV6SllUxA+fXXX2Ps2LF1FWsZrLEjIrIlhEC2zohCgwm+Sm8EquWV9nG7kleEt39NxXcp52ERgELmhbiYCMwc3AZaVfmDHnL1Rqzen4HE7WlIz9JZt4cHqREXE4Gx0SHQ+HDABFFtqdMauy1btuCll14CAKxZswZCCOTk5GDZsmV4/fXX6zWxIyKiErl6I1alZGDZjrLJVmy/kmTr+kRNX2zGJ1v/xJLkM9bRrnd2bo7nb2+PsEbqSq+lVckRH9MKcf0ikKMzosBggp/SGwFVJJFEVPccrrFTqVRITU1FaGgoHnroIbRo0QLz58/HuXPn0LFjRxQUFNRVrGWwxo6ICEhOzay6eVQhw+JJ0ejfpjHWHLiAhRtO4q+8IgBAt9AAvHxXB0SHB9Vv4ERklzqtsQsNDcXOnTsRFBSE9evX4+uvvwYAZGdnw8fHp3oRExFRtSSnZv4zoKGc/aXb9EYz4hP2IDRIjfRrJTV6LQNUeH5Ee4zs0pw1bUQewuHE7qmnnsIDDzwAPz8/hIeHY9CgQQBKmmg7d+5c2/EREVEFcvVGTF+eUuUoVfy9XwBIv6aDn0KGx4a2RVy/CPjIZfURKhHVE4cTuxkzZqB37944d+4cbr31Vnh5lYyWat26NV5//fVaD5CIiMq3KiUD+mJzuTV1lZk2KBLTBkbWSUxE5Fycx46IyA0JITBoYRLOZekcSuxKl/lKenYQm1+J3IQj+Y6XPSd8+umnUVhYaHcAs2bNQlZWlt3HExGRY7J1RqQ7mNQBfzfHZumQozPWRVhE5GR2JXbvv/8+dDpd1Qf+7aOPPkJOTk51YyIioioUGkw1Kl9Qw/JE5Jrs6mMnhEBUVJTd1faO1O4REZHjfJU1WzjIr4blicg12fWTnZCQ4PCJmzZt6nAZIiKyT6BajvAgdbX72AWouTIEkSeyK7GLjY2t6ziIiMgBkiRhQs9QLNhw0uGycTERHDhB5KFYF09E5IbOXi3EN/vOO1TGSwJ85DKM6R5SR1ERkbMxsSMicjM7Tl/F9C/3I1dvRJBajhy9scpJiksr6JZMirZZM5aIPItdo2LryuLFi9GlSxdoNBpoNBr07dsX69atc2ZIREQu7Ytd6Xjwf3uQqzeiW2gA1j81AAnxvaCSyyDhn7VhS5VuU8llSIzvhQFRwfUfNBHVG6fW2IWEhGD+/Plo27YthBBYtmwZRo0ahQMHDqBTp07ODI2IyKUYzRbM/ekYvtiVDgAY3a0F5o/tAh+5DE00Ptg5ayhW789A4vY0pGf9Mz1VWJAacTERGBsdAo0Pa+qIPF21V544ffo0zpw5gwEDBkClUkEIUSudcYOCgrBw4UJMmTKlymO58gQRNQS5OiNmrEjB9tPXIEnAs8PbYfrAyHK/c4UQyNEZUWAwwU/pjQC1nAMliNycI/mOwzV2165dw4QJE7Bp0yZIkoRTp06hdevWmDJlCgIDA/H2229XK2iz2YzvvvsOhYWF6Nu3b7XOQUTkaU5fKcAjn+/D2auFUCtkeG9CN9zWqVmFx0uShEBfBQJ9FfUYJRG5Cof72P3rX/+Ct7c3zp07B7Vabd0+YcIErF+/3uEADh8+DD8/PyiVSkybNg1r1qxBx44dyz3WYDAgLy/P5kFE5Km2pGbino+34+zVQrQMUGHltH6VJnVERA7X2P3666/YsGEDQkJsh8u3bdsW6enpDgfQrl07HDx4ELm5uVi5ciViY2ORnJxcbnI3b948vPrqqw5fg4jInQghkLgjDa/9fAwWAfQID8SSB6PR2E/p7NCIyMU5XGNXWFhoU1NXKisrC0ql4186CoUCbdq0QXR0NObNm4euXbvi/fffL/fYWbNmITc31/o4f96xOZyIiFxdscmCF9ccwas/lSR1Y7uH4MtHejOpIyK7OJzY9e/fH59//rn1uSRJsFgsWLBgAQYPHlzjgCwWCwwGQ7n7lEqldWqU0gcRkafILizGg5/txld7zkGSgBfvaI//G9cFSm+Zs0MjIjfhcFPsggULMHToUOzbtw/FxcV47rnncPToUWRlZWH79u0OnWvWrFkYMWIEwsLCkJ+fjxUrViApKQkbNmxwNCwiIrd26nI+pizbh3NZOvgpvfHBxG4Y0p5rbhORYxxO7G666Sakpqbiww8/hL+/PwoKCjBmzBjMnDkTzZs3d+hcV65cwUMPPYRLly5Bq9WiS5cu2LBhA2699VZHwyIicllCCGTrjCg0mOCr9EbgDVOQbD5xBY9/dQAFBhNCg1T4LLYnopr6OzFiInJX1Z7HzhVwHjsicmW5eiNWpWRg2Q7bSYPDg9SI7ReBsd1b4tt9GXhz3XEIAfRqFYQlk6IRxKlKiOg6juQ71UrsioqKcOjQIVy5cgUWi8Vm39133+3o6aqNiR0Ruark1ExMX54CfbEZAHD9F21pXZ2XlwSzpWTPfT1DMXfUTVB4O3WlRyJyQXU6QfH69evx0EMP4erVq2X2SZIEs9ns6CmJiDxKcmom4hP2QMA2oStVuq00qbu/VxjeuOcmrhBBRDXm8J+Gjz/+OMaNG4dLly7BYrHYPJjUEVFDl6s3YvrylJKkzo72EAnA9wcvIK/IVNehEVED4HBid/nyZTz99NNo2pSjtYiIbrQqJQP6YrNdSR1QUnunLzZj9f6MOo2LiBoGhxO7e++9F0lJSXUQChGRexNCYNmOtGqVTdyeBjcey0ZELsLhPnYffvghxo0bh61bt6Jz586Qy+U2+5944olaC46IyJ1k64w2o1/tJQCkZ+mQozMikCNiiagGHE7svvrqK/z666/w8fFBUlKSTWdfSZKY2BFRg1VoqFk/uQKDiYkdEdWIw4ndSy+9hFdffRUvvPACvLw4LJ+IqJSv0uGvVBt+NSxPRORwZlZcXIwJEyYwqSMiukGgWo6wIJXD5SSUTFocoJZXeSwRUWUczs5iY2PxzTff1EUsRERu7XyWHsUmS9UHliMuJoLz2BFRjTlc7282m7FgwQJs2LABXbp0KTN44p133qm14IiI3MXGY5fx9LcHkf/3fHQSyp+c+EZeEuAjl2FM95A6jY+IGgaHE7vDhw/j5ptvBgAcOXLEZh//2iSihsZktmDhryexNPlPAED3sAA82Dcc//72DwCVT1Jc+pW5ZFI0tCo2wxJRzTmc2G3evLku4iAicjtX8orw2FcHsOdsFgBgckwrvDCiPRTeXgjyVVa5VqxKLsOSSdEYEBVcv4ETkcfiECwiomrYeeYaHv/qAK4WGOCn9MaCe7vgjs7NrfsHRgVj56yhWL0/A4nb02zmtwsLUiMuJgJjo0Og8WFNHRHVHknYMdX5mDFjkJiYCI1GgzFjxlR67OrVq2stuKrk5eVBq9UiNzcXGo2m3q5LRA2XxSKwdMufWLjhBCwCaNfUH4sndUfrYL8KywghkKMzosBggp/SGwFqObuuEJHdHMl37Kqx02q11i8hjUbDLyQiapBydUb8+7uD+O34FQDAmO4t8cbozlApZJWWkyQJgb4KTj5MRHXOrho7V8UaOyKqL0cu5GL6lyk4n6WHwtsLr97dCff1DOUfukRU5xzJdxyex27IkCHIyckp96JDhgxx9HRERC5NCIEVu89hzOIdOJ+lR2iQCqun98PEXmFM6ojI5Tg8eCIpKQnFxcVlthcVFWHr1q21EhQRkSvQFZvwnzVHsPrABQDAsA5N8fa4rtByhQgiclF2J3aHDh2y/vvYsWP466+/rM/NZjPWr1+Pli1b1m50RER1QAiBbJ0RhQYTfJXeCCxnMMOZzALMWL4fJy/nw0sCnru9PR7t3xpeXqylIyLXZXdi161bN0iSBEmSym1yValUWLRoUa0GR0RUm3L1RqxKycCyHbbTj4QHqRHbr2T6Ea1Kjl8OXcLzqw6hwGBCYz8lPrz/ZvRp3ciJkRMR2cfuwRPp6ekQQqB169bYs2cPgoP/mVBToVCgSZMmkMkqHxlW2zh4gojslZyaWfWEwQoZbmnTGL8euwwA6NUqCB9OvBlNND71GywR0XVqfboTAAgPDwcAWCzVW+CaiMhZklMzEZ+wBwLlr99auk1XbLYmddMGRuKZ26LgLXN4jBkRkdPwG4uIPFqu3ojpy1NKkjo7J3dSenth+qBIJnVE5Hb4rUVEHm1VSgb0xWa7kzoAKDZZsHp/Rt0FRURUR5jYEZHHEkJg2Y60apVN3J4GN56/nYgaKCZ2ROSxsnVGpGfpyu1XVxkBID1LhxydsS7CIiKqM0zsiMhjFRpMNSpfUMPyRET1za5RsYGBgXYvnZOVlVWjgIiIaouv0uHFdWz41bA8EVF9s+tb67333qvjMIiIap+vQoYAlRw5eseaVCUAYUFqBHDpMCJyM3YldrGxsXUdBxFRrUo6eQVzfzrmcFJXKi4mwu6WCiIiV2FXYpeXl2f3CbkCBBE50/ksHeb+fAwb/55oOMhXgYIiE4wWi11TnnhJgI9chjHdQ+o4UiKi2mdXYhcQEFDlX65CCEiSBLPZXCuBERE5Ql9sxuLkM1iSfAbFJgu8vSTE9YvAE8Pa4sC5HMQn7AGkyicpLv2aWzIpGloVm2GJyP3Yldht3ry5ruMgIqoWIQQ2HP0Lr/18HBdy9ACAmDaNMGdkJ7Rt6g8AGBgVjIT4XlWvFSuXYcmkaAyICgYRkTuShBvPwOnIorhE5HlOX8nHnB+PYdvpqwCAFlofvHxXR9x+U7NyWxly9Uas3p+BxO1pSM/SWbeHB6kRFxOBsdEh0Piwpo6IXIsj+U61EzudTodz586huLjYZnuXLl2qc7pqYWJH5DmEEMjWGVFoMMFX6Y1AtbzCLiD5RUZ88PspJGxPg8kioPD2wrQBrTF9UBuoFDK7rpWjM6LAYIKf0hsBlVyLiMjZHMl3HJ6kKTMzE/Hx8Vi3bl25+9nHjogckas3YlVKBpbtKFuLFtuvpBattL+bEALfH7yAN9eeQGa+AQAwrENTvHJXR4Q1Utt9TUmSEOirQKCvonZfDBGRkzmc2D311FPIycnB7t27MWjQIKxZswaXL1/G66+/jrfffrsuYiQiD5WcmmnT7+1657J0eO3nY/i/X09i8aRoNPJVYM6PR7EvPRsA0KqxL14Z2RGD2zWp77CJiFyWw4ndpk2b8MMPP6BHjx7w8vJCeHg4br31Vmg0GsybNw933nlnXcRJRB4mOTUT8Ql7IIBy13It3aYvNiPuf3us29QKGR4b0gZTbmkFpXfVza5ERA2Jw4ldYWEhmjQp+Qs5MDAQmZmZiIqKQufOnbF///5aD5CIPE+u3ojpy1NKkroqevlev/v2m5ph9siOaK5V1WV4RERuy8vRAu3atcPJkycBAF27dsXSpUtx4cIFLFmyBM2bN6/1AInI86xKyYC+2GzXhMGlJAC9WwUxqSMiqoTDNXZPPvkkLl26BACYPXs2br/9dnz55ZdQKBRITEys7fiIyMMIIbBsR1q1yiZuT0NcPy71RURUEbsTu7Nnz6JVq1aYNGmSdVt0dDTS09Nx4sQJhIWFoXHjxnUSJBF5jmyd0Wb0q70EgPQsHXJ0Ro5mJSKqgN2JXWRkJMLDwzF48GAMGTIEgwYNQkhICNRqNbp3716XMRKRByk0mGpUvsBgYmJHRFQBuxO7TZs2ISkpCUlJSfjqq69QXFyM1q1bY8iQIRg8eDAGDx6Mpk2b1mWsROQBfJUO9wCx4VfD8kREnszub8hBgwZh0KBBAICioiLs2LHDmugtW7YMRqMR7du3x9GjR+sqViLyAIFqOZr4K3Hl7wmG7SUBCAtSI0DNJb+IiCpSrT99fXx8MGTIENxyyy0YPHgw1q1bh6VLl+LEiRO1HR8ReZCswmK8/ssxh5O6UnExHDhBRFQZhxK74uJi7Nq1C5s3b0ZSUhJ2796N0NBQDBgwAB9++CEGDhxYV3ESkRsTQmDV/gt445djyNYZAQDeXhLMFlHu5MQ38pIAH7kMY7qH1G2gRERuzu7EbsiQIdi9ezdatWqFgQMHYurUqVixYgXnriOiSp29WoiX1hzGjjPXAADtm/njzTGdkV9kQnzC3ytKVJLdlVbQLZkUbV0zloiIymd3Yrd161Y0b97cOiJ24MCBaNSoUV3GRkRurNhkwX+3nMEHm06j2GSB0tsLTw2LwsP9W0EuK5kbPSG+l81asdfnd6UNriq5DEsmRWNAVHD9vgAiIjckCWHf3O+FhYXYunUrkpKSsHnzZhw8eBBRUVEYOHCgNdELDq7fL968vDxotVrk5uZCo9HU67WJqGL70rLw4prDSL1cAADo37YxXh99E8Ib+ZY5NldvxOr9GUjcnmYzv114kBpxMREYGx0CjQ9r6oio4XIk37E7sbtRfn4+tm3bZu1v98cff6Bt27Y4cuRItYKuDiZ2RK4lV2/EgvUn8OXucwCARr4KvHxXR4zq1qLKQQ9CCOTojCgwmOCn9EaAWs6BEkREcCzfqfaEUL6+vggKCkJQUBACAwPh7e2N48ePV/d0ROSChBDI1hlRaDDBV+mNwAqSLSEE1h7+C3N+OorMv0e8ju8Rghfv6IAAtX2TCUuShEBfBScfJiKqAbsTO4vFgn379lmbYrdv347CwkK0bNkSgwcPxkcffYTBgwfXZaxEVE9y9UasSsnAsh1lm0dj+5U0j5YOZMjI1uGVH45i04krAIDWwb54857O6NOafXCJiOqb3U2xGo0GhYWFaNasmXWliUGDBiEyMrKuY6wQm2KJal9yambVAxoUMnx4/834M7MQ72xMha7YDLlMwoxBbTBjcCSU3rJ6j5uIyFPVSVPswoULMXjwYERFRdU4QCJyTcmpmYhP2AMBlDu/XOk2fbEZkxP3Wbf3igjCm2NuQpsm/vURJhERVcDuxG7q1Kl1GQcROVmu3ojpy1NKkroq6vGv3z37ro6I7RcBLy8OdCAicjaupk1EAIBVKRnQF5vtWgmilPT3f5jUERG5Bi9nB0BEzieEwLIdadUqm7g9DdWcNYmIiGoZEzsiQrbOiPQsnUO1dUBJk2x6lg45f6//SkREzsXEjohQaDDVqHxBDcsTEVHtcGpiN2/ePPTs2RP+/v5o0qQJRo8ejZMnTzozJKIGyVdZs+62fjUsT0REtcOpiV1ycjJmzpyJXbt2YePGjTAajbjttttQWFjozLCIGhy1wgsBKsfXY5VQMmlxgJpruRIRuQKn/pm9fv16m+eJiYlo0qQJUlJSMGDAACdFRdSwbD5xBa/+dBQ5+ur1k4uLieCarkRELsKl2k9yc3MBAEFBQeXuNxgMMBgM1ud5eXn1EheRJ0q/VojXfj6G346XLAXWyE+B/CITjGZLlfPYAYCXBPjIZRjTPaSOIyUiInu5zOAJi8WCp556CjExMbjpppvKPWbevHnQarXWR2hoaD1HSeT+9MVmvP3rSdz67hb8dvwKvL0kPDqgNZKeGYRPHuoBCUBVFXCl+5dMirauGUtERM5n91qxdW369OlYt24dtm3bhpCQ8msAyquxCw0N5VqxRHYQQmDt4b/wxi/HcDG3CADQv21jzB7Z0WYpMHvXil0yKRoDooLrKXoioobLkbViXSKxe+yxx/DDDz9gy5YtaNWqld3lHHmhRA1Z6uV8zPnxKHacuQYAaBmgwst3dcTwTk3L7R+Xqzdi9f4MJG5PQ3qWzro9PEiNuJgIjI0OgcaHNXVERPXBbRI7IQQef/xxrFmzBklJSWjbtq1D5ZnYUUMjhEC2zohCgwm+Sm8EquWVDlzIKzLi/d9OIXFHGswWAYW3F6YPjMS0gZFQKWR2XS9HZ0SBwQQ/pTcCqrgeERHVPkfyHacOnpg5cyZWrFiBH374Af7+/vjrr78AAFqtFiqVypmhEbmUXL0Rq1IysGxH2Rq02H4lNWjX93WzWARWH7iA+etO4GpBSfeF2zo2xct3dURokNru60qShEBfBQJ9FbX3YoiIqM44tcauor/8ExISEBcXV2V51thRQ2Bvn7fFk6IxMCoYhzNy8cqPR3DgXA4AoHVjX8y+uxMGsj8cEZFbcpsaOxfo3kfk0pJTMxGfsAcCKHcd19JteqMZ8Ql7MKBtMJJPZUIIQK2Q4YmhbTE5phUU3i4zAJ6IiOqQS81jR0T/yNUbMX15SklSV8XfQEKUJHlJqZkAgFHdWmDWiA5opvWp8ziJiMh1MLEjclGrUjKgLzaXW1NXmbh+EZhzd6c6iYmIiFwb22eIXJAQAst2pDlcTkLJEmHs5kBE1DAxsSNyQdk6I9KzdA7X1gkA6Vk65Oiqt+4rERG5NyZ2RC6o0GCqUfmCGpYnIiL3xMSOyAX5KmvW/dWvhuWJiMg9MbEjckGBajnCg9RwdI0HCSWTFgeoudwXEVFDxMSOyAVJkoQ+kY0c7mMHAHExEVz2i4iogWJ7DZGLyS8y4rWfj+HbfRkOlfOSAB+5DGO6h9RRZERE5OpYY0fkQnb9eQ0j3t+Kb/dlQJKAETc1g5cEVFUBV7p/yaRomzVjiYioYWGNHZELKDKa8favJ/HptrMQAggJVOHtcV3Ru3Uj+9aKlcuwZFI0BnA9WCKiBo2JHZGTHbmQi399cxCnrhQAAO7rGYr/3NXROrJ1YFQwds4aitX7M5C4PQ3pWTpr2bAgNeJiIjA2OgQaH9bUERE1dJJw4ynq8/LyoNVqkZubC41G4+xwiBxiMluwOOkM3v/9FEwWgcZ+Srw1tjOGdmhaYRkhBHJ0RhQYTPBTeiNALedACSIiD+dIvsMaOyIn+DOzAE9/+wcOns8BUNKX7o17OiPIV1FpOUmSEOirQGAVxxERUcPExI6oHgkh8MWudLy59jiKjBb4+3hj7qhOGN2tJWveiIioxpjYEdWQEALZOiMKDSb4Kr0RWEHz6KVcPZ5beQhbT10FAMS0aYSF93ZFiwBVfYdMREQeiokdUTXl6o1YlZKBZTtsBzSEB6kR269kQINWJYcQAj/+cREvf38EeUUmKL29MGtEezzUNwJeXqylIyKi2sPBE0TVYNcUJAoZFt7bBWsP/4VfDl8CAHQN0eLt8d3Qpolf/QZMRERui4MniOpQcmom4hP2QADlLvlVuk1fbMbMFQcAAN5eEh4f0hYzB0fCW8Z5wYmIqG4wsSNyQK7eiOnLU0qSuirqukt3SwA+n9IL/SIb13F0RETU0LHqgMgBq1IyoC82V5nU3ejkX/l1ExAREdF1mNgR2UkIgWU70qpVNnF7Gty4OysREbkJJnZEdsrWGZGepSu3X11lBID0LB1ydMa6CIuIiMiKiR2RnQoNphqVL6hheSIioqowsSOyk6+yZmON/GpYnoiIqCpM7IjsFKiWo6lG6XA5CSWTFgeo5bUfFBER0XVYhUBkh8x8A+atO47LeYZqlY+LieBasEREVOeY2BFVwmS24Itd6Xjn11Tk/91HzttLgtki7BpE4SUBPnIZxnQPqdtAiYiIwMSOqEJ707Lw8vdHcOLvOei6hGgxd9RNyNUbEZ+wB0DlkxSXVtAtmRQNrYrNsEREVPeY2BHdoLTZdfX+CwCAALUczw1vjwk9QyHzKsnWEuJ7Vb1WrFyGJZOiMSAquB6jJyKihoyJHdHfTGYLlu9Kx9t/N7tKEnBfz1A8O7w9gnwVNscOjArGzllDsXp/BhK3pyE9S2fdFxakRlxMBMZGh0Djw5o6IiKqP5Jw4+nw8/LyoNVqkZubC41G4+xwyI1V1OzaLTSgyrJCCOTojCgwmOCn9EaAWs6BEkREVGscyXdYY0ceSQiBbJ0RhQYTfJXeCKwg2crMN2D+uhNYtT8DAKBVyfHc7e1wX88wa7NrVSRJQqCvAoE31OoRERHVNyZ25FFy9UasSsnAsh22zaPhQWrE9itpHtWq5P80u25MRX5R5c2uRERE7oJNseQxklMzqx7QoJDh6VujsGr/BRy/lAcA6NxSi7mjOuHmsMD6DZiIiMgObIqlBic5NRPxCXsggHLnlyvdpis24/VfjgMoaXZ9dng7TOxlf7MrERGRK2NiR24vV2/E9OUpJUmdnfXP3l4SfnwsBuGNfOs0NiIiovrEtWLJ7a1KyYC+2Gx3UgcAZovAphNX6i4oIiIiJ2BiR25NCIFlO9KqVTZxexrcuIspERFRGUzsyK1l64xIz9LZtW7r9QSA9CwdcnTGugiLiIjIKZjYkVsrNJhqVL6ghuWJiIhcCRM7cmu+ypqN//GrYXkiIiJXwsSO3FqgWo7QQJXD5SSUTFocoOZarkRE5DmY2JFbO3u1ELq/JyR2VFxMBNd0JSIij8J2KHJbm05cxpNfHUS+wWRdWcKeQRReEuAjl2FM95C6DI+IiKjescaO3I4QAh9tPo0py/Yh32BCz4hAvH/fzZAkoKoKuNL9SyZFQ6tiMywREXkW1tiRWyk0mPDsyj+w9vBfAIAHeodh9shOUHh7QauWV71WrFyGJZOiMSAquH4DJyIiqgdM7MhtnLumw6Nf7MOJv/Ihl0l49e6bcH/vMOv+gVHB2DlrKFbvz0Di9jSkZ+ms+8KC1IiLicDY6BBofFhTR0REnkkSbjz1fl5eHrRaLXJzc6HRaJwdDtWhracy8diKA8jVGxHsr8SSSd0RHR5U4fFCCOTojCgwmOCn9EaAWs6BEkRE5JYcyXdYY0cuTQiBT7eexbx1x2ERQNfQACydFI1mWp9Ky0mShEBfBQJ9FfUUKRERkfMxsSOXVWQ044VVh/D9wYsAgHHRIXht9E3wkcucHBkREZFrYmJHLulCjh5Tv9iHIxfyIPOS8MpdHfFQ33A2pxIREVWCiR25nF1/XsPML/fjWmExgnwV+Oj+7ugb2cjZYREREbk8JnbkMoQQ+GJXOub+dAwmi0CnFhosfTAaIYFqZ4dGRETkFpjYUb0QQiBbZ0ShwQRfpTcCbxilajCZ8fL3R/DtvgwAwKhuLTB/TBeoFOxPR0REZC8mdlSncvVGrErJwLIdtvPKhQepEduvZF65IqMZU79IwcHzOfCSgFkjOuDh/q3Yn46IiMhBnMeO6kxyamaVK0EovL3gI5chV2+EViXHook3c1UIIiKi63AeO3K65NRMxCfsgYBtQleqdJvBZIHBZEFIgApfPtIb4Y186zFKIiIiz+Ll7ADI8+TqjZi+PKUkqbOzPvhaYTEC1JxMmIiIqCaY2FGtW5WSAX2x2e6kDiiZjHj1/oy6C4qIiKgBcGpit2XLFowcORItWrSAJEn4/vvvnRkO1QIhBJbtSKtW2cTtaXDjLp9ERERO59TErrCwEF27dsVHH33kzDCoFmXrjEjP0pXbr64yAkB6lg45OmNdhEVERNQgOHXwxIgRIzBixAhnhkC1rNBgqlH5AoMJgb7sa0dERFQd7GNHtcpXWbO/FfxqWJ6IiKghc6vfogaDAQaDwfo8Ly/PidFQeQLVcoQGqnA+W+9QOQlAWJAaAWp53QRGRETUALhVjd28efOg1Wqtj9DQUGeHRDfYfy4H+dVsjo2LieBqE0RERDXgVondrFmzkJuba32cP3/e2SHR30xmC97/7RTGL92JHJ0REv5ZXaIqXhKgUsgwpntIXYZIRETk8dyqKVapVEKpVDo7DLrBuWs6/Ovbg0hJzwYAjO7WAsNvaoaZX+4HUPkkxaUVdEsmRUOrYjMsERFRTTg1sSsoKMDp06etz8+ePYuDBw8iKCgIYWFhToyM7CGEwJoDF/DKD0dRYDDBX+mN10bfhNE3twQAJMT3qnKtWJVchiWTork+LBERUS2QhBNnhE1KSsLgwYPLbI+NjUViYmKV5R1ZFJdqV67eiP98fwQ//XERANAzIhDvjO+G0CB1meNW789A4vY0pGfprNvDg9SIi4nA2OgQaHxYU0dERFQRR/IdpyZ2NcXEzjl2/3kNT3/7By7k6CHzkvCvYW0xfVAbyLwq7lUnhECOzogCgwl+Sm8EqOUcKEFERGQHR/Idt+pjR85lNFvw3m+p+DjpDIQAwhup8d6Ebrg5LLDKspIkIdBXwcmHiYiI6hATO7LL2auFePLrAziUkQsAGN8jBK+M7MQJhYmIiFwIfys3YEIIZOuMKDSY4Kv0RmA5zaNCCHyz9zxe/ekY9EYztCo55o3pjDs6N3dS1ERERFQRJnYNUK7eiFUpGVi2o+yAhth+JQMatCo5sguL8cLqQ9hw9DIAoG/rRnhnQlc016qcFToRERFVgoMnGpjk1MyqpyBRyPDY4DZYtjMNl/MMkMskPHNbOzzSvzW8KhkgQURERLWPgyeoXMmpmYhP2AMB24SuVOk2XbEZCzacBABEBvvi/ftuxk0ttfUVJhEREVUTE7sGIldvxPTlKSVJnZ11tN5eElY83AdNtT51GhsRERHVDrdaK5aqb1VKBvTFZruTOgAwWwTWHrlUd0ERERFRrWJi1wAIIbBsR1q1yiZuT4Mbd8MkIiJqUJjYNQDZOiPSs3Tl9qurjACQnqVDjs5YF2ERERFRLWNi1wAUGkw1Kl9Qw/JERERUP5jYNQC+NVwdgqtLEBERuQcmdg1AoFqOsCC1w+UklExaHKCW135QREREVOuY2DUAp68UoNhkrlbZuJiIMsuMERERkWtiG5sHs1gEEnak4a31J1BssgAoqYWzZxCFlwT4yGUY0z2kTmMkIiKi2sMaOw91MUePSZ/txms/H0OxyYJB7YLx/n3dIElAVRVwpfuXTIqGVsVmWCIiInfBGjsPI4TAj39cxH++P4L8IhNUchleurMDHugdBkmSEKBWVL1WrFyGJZOiMSAquN7jJyIioupjYudBcnTFeOn7I/jlUMlqEV1DA/Du+K5oHexnPWZgVDB2zhqK1fszkLg9DelZOuu+sCA14mIiMDY6BBof1tQRERG5G0m48bICeXl50Gq1yM3NhUajcXY4TrUlNRPPrvwDl/MMkHlJeHJoW8wYFAlvWcWt7UII5OiMKDCY4Kf0RoBazoESRERELsaRfIc1dm5OX2zG/HXHsWxnOgCgdbAv3h3fDV1DA6osK0kSAn0VCPRV1HGUREREVB+Y2LmxQxk5eOqbg/gzsxAAENs3HC+M6ACVQubkyIiIiMgZmNi5GCEEsnVGFBpM8FV6I7Cc5lGT2YKPNp/Bok2nYLIINPFXYuG4rhjIwQ5EREQNGhM7F5GrN2JVSgaW7bAd0BAepEZsv5IBDVqVHH9mFuDpb//AwfM5AIA7uzTHG6NvQoCazalEREQNHQdPuIDk1MyqpyBRyDAuOgTf7suA3miGv483Xh99E+7u2oIDHoiIiDwYB0+4keTUTMQn7IFA+StClG7TFZutAyT6RTbC/43rihYBqvoKk4iIiNwAEzsnytUbMX15SklSZ2e9qVwm4eP7uyOAI1mJiIjoBlxSzIlWpWRAX2y2O6kDAJNZYM3BC3UXFBEREbktJnZOIoTAsh1p1SqbuD0Nbtw1koiIiOoIEzsnydYZkZ6lK7dfXWUEgPQsHXJ0xroIi4iIiNwYEzsnKTSYalS+oIbliYiIyPMwsXMSX2XNxq341bA8EREReR4mdk6QV2REwrY/UZ3Z5ySUTFocoJbXdlhERETk5ljtU490xSYk7kjD0uQ/kauvfh+5uJgITkpMREREZTCxqwcGkxkrdp/DR5vP4GqBAQDQpokfpg9sjZd/OAq90b4pT7wkwEcuw5juIXUcMREREbkjJnZ1yGi2YFVKBj74/RQu5hYBAMKC1HhqWFuM6tYSMi8Jjf19EJ+wB5Aqn6S4tIJuyaRoaFVshiUiIqKymNhVQQiBbJ0RhQYTfJXeCFTLq2wGtVgEfjp0Ee9uTEXaNR0AoKlGiSeGtsX4HqGQy/7p2jgwKhgJ8b2qXitWLsOSSdEYEBVcmy+PiIiIPAgTuwrk6o1YlZKBZTvSkJ6ls24PD1Ijtl8ExkaHlKk5E0Lg12OX8c6vqTh5OR8AEOSrwIxBkZjUJxw+clm51xoYFYyds4Zi9f4MJG63vV5YkBpxMSXX0/iwpo6IiIgqJgk3XsIgLy8PWq0Wubm50Gg0tXbe5NTMqmvQFDIsnhSNgVHBEEJg66mrePvXk/gjIxcA4O/jjUf7t0b8La0cmppECIEcnREFBhP8lN4IsKOGkIiIiDyXI/kOa+xukJyaifiEPRBAuatClG7TG82IT9iDWXd0wMZjl7HnbBaAkibT+JgIPDqgNQLUCoevL0kSAn0VCPR1vCwRERE1bEzsrpOrN2L68pSSpK6KekwhSpK8N345DgBQyLzwQJ8wzBjUBsH+yjqPlYiIiOhGTOyusyolA/pis8Prt3YPC8CH93dHiwBVncRFREREZA+uPPE3IQSW7UhzuJwE4FpBMZprfWo9JiIiIiJHMLH7W7bOiPQsncO1dQJAepYOObrqryRBREREVBuY2P2t0GCqUfmCGpYnIiIiqikmdn/zdWBKkvI4MqUJERERUV1gYve3QLUc4UFqODpjnISSSYsD1Jw8mIiIiJyLid3fJElCbL+IapWNi4ngJMJERETkdEzsrjM2OgQqhQz25mheUskKFGO6h9RtYERERER2YGJ3Ha1KjsWToiEBVSZ3pfuXTIous2YsERERkTMwsbvBwKhgJMT3gkouK0nwbthfuk0llyExvhcGRAXXf5BERERE5eBQznIMjArGzllDsXp/BhK3pyE9S2fdFxakRlxMBMZGh0Djw5o6IiIich2SEFWtiuq68vLyoNVqkZubC41GUyfXEEIgR2dEgcEEP6U3AtRyDpQgIiKieuNIvsMauypIkoRAXwUCfRXODoWIiIioUuxjR0REROQhmNgREREReQgmdkREREQegokdERERkYdgYkdERETkIZjYEREREXkIJnZEREREHsKt57ErnVs5Ly/PyZEQERER1Y3SPMeeNSXcOrHLz88HAISGhjo5EiIiIqK6lZ+fD61WW+kxbr2kmMViwcWLF+Hv789lvhqwvLw8hIaG4vz583W2tBxVH++Pa+P9cW28P66tvu6PEAL5+flo0aIFvLwq70Xn1jV2Xl5eCAkJcXYY5CI0Gg2/+FwY749r4/1xbbw/rq0+7k9VNXWlOHiCiIiIyEMwsSMiIiLyEEzsyO0plUrMnj0bSqXS2aFQOXh/XBvvj2vj/XFtrnh/3HrwBBERERH9gzV2RERERB6CiR0RERGRh2BiR0REROQhmNiRW9iyZQtGjhyJFi1aQJIkfP/99zb7hRB45ZVX0Lx5c6hUKgwbNgynTp1yTrAN0Lx589CzZ0/4+/ujSZMmGD16NE6ePGlzTFFREWbOnIlGjRrBz88PY8eOxeXLl50UccOyePFidOnSxTrXVt++fbFu3Trrft4b1zJ//nxIkoSnnnrKuo33yHnmzJkDSZJsHu3bt7fud7V7w8SO3EJhYSG6du2Kjz76qNz9CxYswAcffIAlS5Zg9+7d8PX1xfDhw1FUVFTPkTZMycnJmDlzJnbt2oWNGzfCaDTitttuQ2FhofWYf/3rX/jpp5/w3XffITk5GRcvXsSYMWOcGHXDERISgvnz5yMlJQX79u3DkCFDMGrUKBw9ehQA740r2bt3L5YuXYouXbrYbOc9cq5OnTrh0qVL1se2bdus+1zu3ggiNwNArFmzxvrcYrGIZs2aiYULF1q35eTkCKVSKb766isnREhXrlwRAERycrIQouR+yOVy8d1331mPOX78uAAgdu7c6awwG7TAwEDx6aef8t64kPz8fNG2bVuxceNGMXDgQPHkk08KIfjz42yzZ88WXbt2LXefK94b1tiR2zt79iz++usvDBs2zLpNq9Wid+/e2LlzpxMja7hyc3MBAEFBQQCAlJQUGI1Gm3vUvn17hIWF8R7VM7PZjK+//hqFhYXo27cv740LmTlzJu68806bewHw58cVnDp1Ci1atEDr1q3xwAMP4Ny5cwBc89649VqxRADw119/AQCaNm1qs71p06bWfVR/LBYLnnrqKcTExOCmm24CUHKPFAoFAgICbI7lPao/hw8fRt++fVFUVAQ/Pz+sWbMGHTt2xMGDB3lvXMDXX3+N/fv3Y+/evWX28efHuXr37o3ExES0a9cOly5dwquvvor+/fvjyJEjLnlvmNgRUa2aOXMmjhw5YtMHhZyvXbt2OHjwIHJzc7Fy5UrExsYiOTnZ2WERgPPnz+PJJ5/Exo0b4ePj4+xw6AYjRoyw/rtLly7o3bs3wsPD8e2330KlUjkxsvKxKZbcXrNmzQCgzCiky5cvW/dR/Xjsscfw888/Y/PmzQgJCbFub9asGYqLi5GTk2NzPO9R/VEoFGjTpg2io6Mxb948dO3aFe+//z7vjQtISUnBlStX0L17d3h7e8Pb2xvJycn44IMP4O3tjaZNm/IeuZCAgABERUXh9OnTLvnzw8SO3F6rVq3QrFkz/P7779ZteXl52L17N/r27evEyBoOIQQee+wxrFmzBps2bUKrVq1s9kdHR0Mul9vco5MnT+LcuXO8R05isVhgMBh4b1zA0KFDcfjwYRw8eND66NGjBx544AHrv3mPXEdBQQHOnDmD5s2bu+TPD5tiyS0UFBTg9OnT1udnz57FwYMHERQUhLCwMDz11FN4/fXX0bZtW7Rq1Qovv/wyWrRogdGjRzsv6AZk5syZWLFiBX744Qf4+/tb+5ZotVqoVCpotVpMmTIFTz/9NIKCgqDRaPD444+jb9++6NOnj5Oj93yzZs3CiBEjEBYWhvz8fKxYsQJJSUnYsGED740L8Pf3t/ZHLeXr64tGjRpZt/MeOc8zzzyDkSNHIjw8HBcvXsTs2bMhk8kwceJE1/z5ccpYXCIHbd68WQAo84iNjRVClEx58vLLL4umTZsKpVIphg4dKk6ePOncoBuQ8u4NAJGQkGA9Rq/XixkzZojAwEChVqvFPffcIy5duuS8oBuQyZMni/DwcKFQKERwcLAYOnSo+PXXX637eW9cz/XTnQjBe+RMEyZMEM2bNxcKhUK0bNlSTJgwQZw+fdq639XujSSEEM5JKYmIiIioNrGPHREREZGHYGJHRERE5CGY2BERERF5CCZ2RERERB6CiR0RERGRh2BiR0REROQhmNgREREReQgmdkREREQegokdkQdKSkqCJEllFqb2RDe+1sTERAQEBDg1JnvExcXV25J3n332GW677bYanSMtLQ2SJOHgwYMAqn7f58yZg27dutXomo44duwYQkJCUFhYWG/XJHJFTOyIXExmZiamT5+OsLAwKJVKNGvWDMOHD8f27dudHZpbmDBhAlJTU50dRpXef/99JCYm1vl1ioqK8PLLL2P27Nk1Ok9oaCguXbpUZk3TijzzzDM2C6PXtY4dO6JPnz5455136u2aRK7I29kBEJGtsWPHori4GMuWLUPr1q1x+fJl/P7777h27ZqzQ3MLKpUKKpXK2WFUSavV1st1Vq5cCY1Gg5iYmBqdRyaToVmzZnYf7+fnBz8/vxpd01Hx8fF45JFHMGvWLHh789cbNUyssSNyITk5Odi6dSveeustDB48GOHh4ejVqxdmzZqFu+++G0DZJrHScpIkISkpyeZ827dvR5cuXeDj44M+ffrgyJEj1n3p6ekYOXIkAgMD4evri06dOmHt2rUA/mlm++WXXyosf+3aNUycOBEtW7aEWq1G586d8dVXX9lc32KxYMGCBWjTpg2USiXCwsLwxhtvWPefP38e48ePR0BAAIKCgjBq1CikpaVV+h6tXbsWUVFRUKlUGDx4cJnjK2oS/N///oewsDD4+flhxowZMJvNWLBgAZo1a4YmTZrYxFX6nj788MMIDg6GRqPBkCFD8Mcff5Q57xdffIGIiAhotVrcd999yM/Ptx6zcuVKdO7cGSqVCo0aNcKwYcOsTYU3NsUaDAY88cQTaNKkCXx8fHDLLbdg79691v2l9+T3339Hjx49oFar0a9fP5w8ebLS9+vrr7/GyJEjbbaVXvvNN99E06ZNERAQgLlz58JkMuHZZ59FUFAQQkJCkJCQYC1T3ueuMjc2xVosFsydOxchISFQKpXo1q0b1q9fX+b8q1evxuDBg6FWq9G1a1fs3LnTekxln1kAuPXWW5GVlYXk5GS7YiTyREzsiFxIaS3H999/D4PBUOPzPfvss3j77bexd+9eBAcHY+TIkTAajQCAmTNnwmAwYMuWLTh8+DDeeuutMjUslZUvKipCdHQ0fvnlFxw5cgSPPvooHnzwQezZs8daftasWZg/fz5efvllHDt2DCtWrEDTpk0BAEajEcOHD4e/vz+2bt2K7du3w8/PD7fffjuKi4vLfT3nz5/HmDFjMHLkSBw8eBAPP/wwXnjhhSrfhzNnzmDdunVYv349vvrqK3z22We48847kZGRgeTkZLz11lv4z3/+g927d1vLjBs3DleuXMG6deuQkpKC7t27Y+jQocjKyrI57/fff4+ff/4ZP//8M5KTkzF//nwAwKVLlzBx4kRMnjwZx48fR1JSEsaMGQMhRLkxPvfcc1i1ahWWLVuG/fv3o02bNhg+fLjN9QDgpZdewttvv419+/bB29sbkydPrvS1b9u2DT169CizfdOmTbh48SK2bNmCd955B7Nnz8Zdd92FwMBA7N69G9OmTcPUqVORkZFR5ftrj/fffx9vv/02/u///g+HDh3C8OHDcffdd+PUqVNlXt8zzzyDgwcPIioqChMnToTJZAJQ9WdWoVCgW7du2Lp1a63ETOSWBBG5lJUrV4rAwEDh4+Mj+vXrJ2bNmiX++OMP6/6zZ88KAOLAgQPWbdnZ2QKA2Lx5sxBCiM2bNwsA4uuvv7Yec+3aNaFSqcQ333wjhBCic+fOYs6cOeXGYE/58tx5553i3//+txBCiLy8PKFUKsUnn3xS7rFffPGFaNeunbBYLNZtBoNBqFQqsWHDhnLLzJo1S3Ts2NFm2/PPPy8AiOzsbCGEEAkJCUKr1Vr3z549W6jVapGXl2fdNnz4cBERESHMZrN1W7t27cS8efOEEEJs3bpVaDQaUVRUZHOtyMhIsXTp0grP++yzz4revXsLIYRISUkRAERaWlq5ryU2NlaMGjVKCCFEQUGBkMvl4ssvv7TuLy4uFi1atBALFiwQQvxzT3777TfrMb/88osAIPR6fbnXKP1cbNmypcy1w8PDy7z+/v37W5+bTCbh6+srvvrqKyFE2c9daTyVve9du3a1Pm/RooV44403bOLo2bOnmDFjhs35P/30U+v+o0ePCgDi+PHjQojKP7Ol7rnnHhEXF1fpMUSejDV2RC5m7NixuHjxIn788UfcfvvtSEpKQvfu3avV0b5v377WfwcFBaFdu3Y4fvw4AOCJJ57A66+/jpiYGMyePRuHDh1yqLzZbMZrr72Gzp07IygoCH5+ftiwYQPOnTsHADh+/DgMBgOGDh1abmx//PEHTp8+DX9/f2tNZVBQEIqKinDmzJlyyxw/fhy9e/euMMaKREREwN/f3/q8adOm6NixI7y8vGy2XblyxRpbQUEBGjVqZI3Nz88PZ8+etYntxvM2b97ceo6uXbti6NCh6Ny5M8aNG4dPPvkE2dnZ5cZ35swZGI1Gm35wcrkcvXr1sr7fpbp06WJzPQDWa95Ir9cDAHx8fMrs69SpU5nX37lzZ+tzmUyGRo0aVXhuR+Tl5eHixYtl+vnFxMQ49Prs+cyqVCrodLoax0zkrpjYEbkgHx8f3HrrrXj55ZexY8cOxMXFWUc1lv4yFtc16ZU2jzri4Ycfxp9//okHH3wQhw8fRo8ePbBo0SK7yy9cuBDvv/8+nn/+eWzevBkHDx7E8OHDrc2oVQ1gKCgoQHR0NA4ePGjzSE1Nxf333+/w66mMXC63eS5JUrnbLBaLNbbmzZuXie3kyZN49tlnKz1v6TlkMhk2btyIdevWoWPHjli0aBHatWuHs2fP1tprkSQJAKzXvFGjRo0gSVK5CaWj70l9qez12fOZzcrKQnBwcP0FTORimNgRuYGOHTtaO92X/tK6dOmSdX9FHdp37dpl/Xd2djZSU1PRoUMH67bQ0FBMmzYNq1evxr///W988skndpffvn07Ro0ahUmTJqFr165o3bq1zTQjbdu2hUqlqnDKi+7du+PUqVNo0qQJ2rRpY/OoaMRohw4dbPrw3RhjbenevTv++usveHt7l4mtcePGdp9HkiTExMTg1VdfxYEDB6BQKLBmzZoyx0VGRkKhUNhMaWM0GrF371507Nix2q9DoVCgY8eOOHbsWLXPURs0Gg1atGhRZsqe7du3O/z6qvrMHjlyBDfffHONYyZyV0zsiFzItWvXMGTIECxfvhyHDh3C2bNn8d1332HBggUYNWoUgJKasD59+mD+/Pk4fvw4kpOT8Z///Kfc882dOxe///47jhw5gri4ODRu3Ng6EvOpp57Chg0bcPbsWezfvx+bN2+2SfqqKt+2bVts3LgRO3bswPHjxzF16lRcvnzZWtbHxwfPP/88nnvuOXz++ec4c+YMdu3ahc8++wwA8MADD6Bx48YYNWoUtm7dirNnzyIpKQlPPPFEhR32p02bhlOnTuHZZ5/FyZMnsWLFijqZC27YsGHo27cvRo8ejV9//RVpaWnYsWMHXnrpJezbt8+uc+zevRtvvvkm9u3bh3PnzmH16tXIzMws8x4DgK+vL6ZPn45nn30W69evx7Fjx/DII49Ap9NhypQpNXotw4cPx7Zt22p0jtrw7LPP4q233sI333yDkydP4oUXXsDBgwfx5JNP2n2Oqj6zaWlpuHDhAoYNG1YXL4HILXCiHyIX4ufnh969e+Pdd9+19rsKDQ3FI488ghdffNF63P/+9z9MmTIF0dHRaNeuHRYsWFDuygLz58/Hk08+iVOnTqFbt2746aefoFAoAJT0kZs5cyYyMjKg0Whw++23491337W7/H/+8x/8+eefGD58ONRqNR599FGMHj0aubm51vIvv/wyvL298corr+DixYto3rw5pk2bBgBQq9XYsmULnn/+eYwZMwb5+flo2bIlhg4dCo1GU+77ExYWhlWrVuFf//oXFi1ahF69euHNN9+scmSooyRJwtq1a/HSSy8hPj4emZmZaNasGQYMGGAd1VsVjUaDLVu24L333kNeXh7Cw8Px9ttvY8SIEeUeP3/+fFgsFjz44IPIz89Hjx49sGHDBgQGBtbotUyZMgU9evRAbm5uvc2dV54nnngCubm5+Pe//40rV66gY8eO+PHHH9G2bVu7z1HVZ/arr77CbbfdhvDw8Lp4CURuQRKigrH3RNRgJSUlYfDgwcjOznaL5bmocuPGjUP37t0xa9YsZ4dSZ4qLi9G2bVusWLGixpMxE7kzNsUSEXm4hQsX1vsqEPXt3LlzePHFF5nUUYPHGjsiKoM1dkRE7omJHREREZGHYFMsERERkYdgYkdERETkIZjYEREREXkIJnZEREREHoKJHREREZGHYGJHRERE5CGY2BERERF5CCZ2RERERB6CiR0RERGRh/h/Upbmdpk9iqkAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Data for energies plot\n", + "x1 = d_list\n", + "y1 = time_array\n", + "\n", + "# Plot energies\n", + "plt.title(\"Runtime vs subspace dimension 40 qubits\")\n", + "plt.xlabel(\"Subspace dimension (millions)\")\n", + "plt.ylabel(\"Wall time [s]\")\n", + "plt.xticks([1e7, 2e7, 3e7, 4e7, 5e7], [str(i) for i in [10, 20, 30, 40, 50]])\n", + "plt.plot(x1, y1, marker=\".\", markersize=20)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8c486bc7", + "metadata": {}, + "source": [ + "Let's do the same for 60 qubits" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "359ed3f3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total number of unique bitstrings: 50000000\n" + ] + } + ], + "source": [ + "n_qubits = 60\n", + "bts_matrix = random_bitstrings(50_000_000, n_qubits)\n", + "\n", + "# We need to sort the bitstrings and just keep the unique ones\n", + "bts_matrix = sort_and_remove_duplicates(bts_matrix).astype(\"bool\")\n", + "\n", + "# Final subspace dimension after getting rid of duplicated bitstrings\n", + "d = bts_matrix.shape[0]\n", + "\n", + "print(\"Total number of unique bitstrings: \" + str(d))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "7bb0d8d8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration 0 took 0.331874s\n", + "Iteration 1 took 0.604671s\n", + "Iteration 2 took 0.91632s\n", + "Iteration 3 took 1.219938s\n", + "Iteration 4 took 1.598329s\n", + "Iteration 5 took 1.9079s\n", + "Iteration 6 took 2.188979s\n", + "Iteration 7 took 2.530264s\n", + "Iteration 8 took 2.827899s\n", + "Iteration 9 took 3.154194s\n", + "Iteration 10 took 3.514766s\n", + "Iteration 11 took 3.83003s\n", + "Iteration 12 took 4.185016s\n", + "Iteration 13 took 4.514196s\n", + "Iteration 14 took 4.948467s\n", + "Iteration 15 took 5.388114s\n", + "Iteration 16 took 5.596917s\n", + "Iteration 17 took 5.776064s\n", + "Iteration 18 took 6.082537s\n", + "Iteration 19 took 6.356327s\n" + ] + } + ], + "source": [ + "pauli_str = [\"Z\" for i in range(n_qubits)]\n", + "\n", + "# Different subspace sizes to test\n", + "d_list = np.linspace(d / 1000, d, 20).astype(\"int\")\n", + "\n", + "# It is better to do this once\n", + "row_array = np.arange(d)\n", + "\n", + "# To store the walltime\n", + "time_array = np.zeros(20)\n", + "\n", + "for i in range(20):\n", + " int_bts_matrix = bts_matrix[: d_list[i], :]\n", + " int_row_array = row_array[: d_list[i]]\n", + " time_1 = time.time()\n", + " _ = matrix_elements_from_pauli_string(int_bts_matrix, pauli_str)\n", + " time_array[i] = time.time() - time_1\n", + " print(f\"Iteration {i} took {round(time_array[i], 6)}s\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6b961c81", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Data for energies plot\n", + "x1 = d_list\n", + "y1 = time_array\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(6, 6))\n", + "\n", + "# Plot energies\n", + "axs.plot(x1, y1, marker=\".\", markersize=20)\n", + "axs.set_title(\"Runtime vs subspace dimension 60 qubits\")\n", + "axs.set_xlabel(\"Subspace dimension (millions)\")\n", + "plt.xticks([1e7, 2e7, 3e7, 4e7, 5e7], [str(i) for i in [10, 20, 30, 40, 50]])\n", + "axs.set_ylabel(\"Wall time [s]\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/how_tos/choose_subspace_dimension.ipynb b/docs/how_tos/choose_subspace_dimension.ipynb new file mode 100644 index 0000000..8bbfbc5 --- /dev/null +++ b/docs/how_tos/choose_subspace_dimension.ipynb @@ -0,0 +1,364 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", + "metadata": {}, + "source": [ + "# Bound the subspace dimension\n", + "\n", + "In this tutorial, we will show the effect of the subspace dimension in the [self-consistent configuration recovery technique](https://arxiv.org/abs/2405.05068).\n", + "\n", + "***A priori***, we do not know what is the correct subspace dimension to obtain a target level of accuracy. However, we do know that increasing the subspace dimension increases the accuracy of the method. Therefore, we can study the accuracy of the predictions as a function of the subspace dimension." + ] + }, + { + "cell_type": "markdown", + "id": "a6755afb-ca1e-4473-974b-ba89acc8abce", + "metadata": {}, + "source": [ + "### First we will specify the molecule and its properties\n", + "\n", + "In this example, we will approximate the ground state energy of an $\\textrm{N}_{2}$ molecule." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "677f54ac-b4ed-47e3-b5ba-5366d3a520f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsing ../molecules/n2_fci.txt\n" + ] + } + ], + "source": [ + "from pyscf import ao2mo, tools\n", + "\n", + "# Specify molecule properties\n", + "num_orbitals = 16\n", + "num_elec_a = num_elec_b = 5\n", + "open_shell = False\n", + "spin_sq = 0\n", + "\n", + "# Read in molecule from disk\n", + "mf_as = tools.fcidump.to_scf(\"../molecules/n2_fci.txt\")\n", + "hcore = mf_as.get_hcore()\n", + "eri = ao2mo.restore(1, mf_as._eri, num_orbitals)\n", + "nuclear_repulsion_energy = mf_as.mol.energy_nuc()" + ] + }, + { + "cell_type": "markdown", + "id": "c58e988c-a109-44cd-a975-9df43250c318", + "metadata": {}, + "source": [ + "### Generate a dummy counts dictionary to proxy samples taken from a QPU\n", + "\n", + "Here, we randomly generate bitstrings sampled from the uniform distribution. SQD can effectively estimate the ground state of $N_2$ using uniformly sampled bitstrings; however, that is not the case for more complex molecules." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e9506e0b-ed64-48bb-a97a-ef851b604af1", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_addon_sqd.counts import generate_counts_uniform\n", + "\n", + "# Create a seed to control randomness throughout this workflow\n", + "rand_seed = 42\n", + "\n", + "# Generate random samples\n", + "counts_dict = generate_counts_uniform(10_000, num_orbitals * 2, rand_seed=rand_seed)" + ] + }, + { + "cell_type": "markdown", + "id": "851bc98e-9c08-4e78-9472-36301abc11d8", + "metadata": {}, + "source": [ + "### Transform the counts dict into a bitstring matrix and probability array for post-processing\n", + "\n", + "In order to speed up the bitwise processing required in this workflow, we use Numpy arrays to hold representations of the bitstrings and sampling frequencies." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7a102a7f-aae6-4583-ab82-ae40fcb5496a", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qiskit_addon_sqd.counts import counts_to_arrays\n", + "\n", + "# Convert counts into bitstring and probability arrays\n", + "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)" + ] + }, + { + "cell_type": "markdown", + "id": "eb704101-0fe8-4d12-b572-b1d844e35a90", + "metadata": {}, + "source": [ + "### Iteratively refine the samples using SQD and approximate the ground state\n", + "\n", + "\n", + "Let's wrap the self-consisten configuration recovery loop into a function\n", + "\n", + "There are a few user-controlled options which are important for this technique:\n", + "- ``iterations``: Number of self-consistent configuration recovery iterations\n", + "- ``n_batches``: Number of batches of configurations used by the different calls to the eigenstate solver\n", + "- ``samples_per_batch``: Number of unique configurations to include in each batch\n", + "- ``max_davidson_cycles``: Maximum number of Davidson cycles to run during ground state approximation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b72c048e-fe8e-4fc2-b28b-03138249074e", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n", + "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n", + "from qiskit_addon_sqd.utils.fermion import (\n", + " bitstring_matrix_to_sorted_addresses,\n", + " flip_orbital_occupancies,\n", + " solve_fermion,\n", + ")\n", + "\n", + "\n", + "def configuration_recovery_loop(\n", + " hcore: np.ndarray,\n", + " eri: np.ndarray,\n", + " num_elec_a: int,\n", + " num_elec_b: int,\n", + " spin_sq: float,\n", + " iterations: int,\n", + " n_batches: int,\n", + " samples_per_batch: int,\n", + " max_davidson_cycles: int,\n", + ") -> tuple[np.ndarray, np.ndarray]:\n", + " \"\"\"Perform SQD.\"\"\"\n", + " # Self-consistent configuration recovery loop\n", + " e_hist = np.zeros((iterations, n_batches)) # energy history\n", + " s_hist = np.zeros((iterations, n_batches)) # spin history\n", + " d_hist = np.zeros((iterations, n_batches)) # subspace dimension history\n", + " occupancy_hist = np.zeros((iterations, 2 * num_orbitals))\n", + " occupancies_bitwise = None # orbital i corresponds to column i in bitstring matrix\n", + " for i in range(iterations):\n", + " print(f\"Starting configuration recovery iteration {i}\")\n", + " # On the first iteration, we have no orbital occupancy information from the\n", + " # solver, so we just post-select from the full bitstring set based on hamming weight.\n", + " if occupancies_bitwise is None:\n", + " bs_mat_tmp = bitstring_matrix_full\n", + " probs_arr_tmp = probs_arr_full\n", + "\n", + " # In following iterations, we use both the occupancy info and the target hamming\n", + " # weight to correct bitstrings.\n", + " else:\n", + " bs_mat_tmp, probs_arr_tmp = recover_configurations(\n", + " bitstring_matrix_full,\n", + " probs_arr_full,\n", + " occupancies_bitwise,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Throw out samples with incorrect hamming weight and create batches of subsamples.\n", + " batches = postselect_and_subsample(\n", + " bs_mat_tmp,\n", + " probs_arr_tmp,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " samples_per_batch,\n", + " n_batches,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n", + " int_e = np.zeros(n_batches)\n", + " int_s = np.zeros(n_batches)\n", + " int_d = np.zeros(n_batches)\n", + " int_occs = np.zeros((n_batches, 2 * num_orbitals))\n", + " cs = []\n", + " for j in range(n_batches):\n", + " addresses = bitstring_matrix_to_sorted_addresses(batches[j], open_shell=open_shell)\n", + " int_d[j] = len(addresses[0]) * len(addresses[1])\n", + " energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n", + " addresses,\n", + " hcore,\n", + " eri,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " spin_sq=spin_sq,\n", + " max_davidson=max_davidson_cycles,\n", + " )\n", + " energy_sci += nuclear_repulsion_energy\n", + " int_e[j] = energy_sci\n", + " int_s[j] = spin\n", + " int_occs[j, :num_orbitals] = avg_occs[0]\n", + " int_occs[j, num_orbitals:] = avg_occs[1]\n", + " cs.append(coeffs_sci)\n", + "\n", + " # Combine batch results\n", + " avg_occupancy = np.mean(int_occs, axis=0)\n", + " # The occupancies from the solver should be flipped to match the bits in the bitstring matrix.\n", + " occupancies_bitwise = flip_orbital_occupancies(avg_occupancy)\n", + "\n", + " # Track optimization history\n", + " e_hist[i, :] = int_e\n", + " s_hist[i, :] = int_s\n", + " d_hist[i, :] = int_d\n", + " occupancy_hist[i, :] = avg_occupancy\n", + "\n", + " return e_hist.flatten(), d_hist.flatten()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e0847f28", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting configuration recovery iteration 0\n", + "Starting configuration recovery iteration 1\n", + "Starting configuration recovery iteration 2\n", + "Starting configuration recovery iteration 3\n", + "Starting configuration recovery iteration 4\n", + "Starting configuration recovery iteration 0\n", + "Starting configuration recovery iteration 1\n", + "Starting configuration recovery iteration 2\n", + "Starting configuration recovery iteration 3\n", + "Starting configuration recovery iteration 4\n", + "Starting configuration recovery iteration 0\n", + "Starting configuration recovery iteration 1\n", + "Starting configuration recovery iteration 2\n", + "Starting configuration recovery iteration 3\n", + "Starting configuration recovery iteration 4\n", + "Starting configuration recovery iteration 0\n", + "Starting configuration recovery iteration 1\n", + "Starting configuration recovery iteration 2\n", + "Starting configuration recovery iteration 3\n", + "Starting configuration recovery iteration 4\n" + ] + } + ], + "source": [ + "list_samples_per_batch = [50, 200, 400, 600]\n", + "\n", + "# SQD options\n", + "iterations = 5\n", + "\n", + "# Eigenstate solver options\n", + "n_batches = 10\n", + "max_davidson_cycles = 200\n", + "\n", + "energies = []\n", + "subspace_dimensions = []\n", + "\n", + "for samples_per_batch in list_samples_per_batch:\n", + " e_hist, d_hist = configuration_recovery_loop(\n", + " hcore,\n", + " eri,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " spin_sq,\n", + " iterations,\n", + " n_batches,\n", + " samples_per_batch,\n", + " max_davidson_cycles,\n", + " )\n", + " energies.append(np.min(e_hist))\n", + "\n", + " index_min = np.argmin(e_hist)\n", + " subspace_dimensions.append(d_hist[index_min])" + ] + }, + { + "cell_type": "markdown", + "id": "9d78906b-4759-4506-9c69-85d4e67766b3", + "metadata": {}, + "source": [ + "### Visualize the results\n", + "\n", + "This plot shows that increasing the subspace dimension leads to more accurate results." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Data for energies plot\n", + "x1 = subspace_dimensions\n", + "n2_exact = -109.10288938\n", + "y1 = energies\n", + "\n", + "fig, axs = plt.subplots(1, 1, figsize=(12, 6))\n", + "\n", + "# Plot energies\n", + "axs.plot(x1, y1, marker=\".\", markersize=20, label=\"Estimated\")\n", + "axs.set_xticks(x1)\n", + "axs.set_xticklabels(x1)\n", + "axs.axhline(y=n2_exact, color=\"red\", linestyle=\"--\", label=\"Exact\")\n", + "axs.set_title(\"Approximated Ground State Energy vs subspace dimension\")\n", + "axs.set_xlabel(\"Subspace dimension\")\n", + "axs.set_ylabel(\"Energy (Ha)\")\n", + "axs.legend()\n", + "\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/how_tos/index.rst b/docs/how_tos/index.rst new file mode 100644 index 0000000..e410c27 --- /dev/null +++ b/docs/how_tos/index.rst @@ -0,0 +1,10 @@ +############# +How-To Guides +############# + +This page summarizes the available how-to guides. + +.. nbgallery:: + :glob: + + * diff --git a/docs/how_tos/project_pauli_operators_onto_hilbert_subspaces.ipynb b/docs/how_tos/project_pauli_operators_onto_hilbert_subspaces.ipynb new file mode 100644 index 0000000..58193de --- /dev/null +++ b/docs/how_tos/project_pauli_operators_onto_hilbert_subspaces.ipynb @@ -0,0 +1,157 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "21a1d83f-183f-4da9-bb8c-71400120fd31", + "metadata": {}, + "source": [ + "# Project Pauli operators onto Hilbert subspaces" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "74c16c91-cc5c-46ce-aff8-17d0e71ac50f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qiskit_addon_sqd.qubit import matrix_elements_from_pauli_string, sort_and_remove_duplicates\n", + "\n", + "L = 22\n", + "\n", + "# Write all of the Pauli strings for the Heisenberg model\n", + "paulis = []\n", + "for i in range(L):\n", + " pstr = [\"I\" for i in range(L)]\n", + " # Sigma_x\n", + " pstr[i] = \"X\"\n", + " pstr[(i + 1) % L] = \"X\"\n", + " paulis.append(pstr)\n", + "\n", + " pstr = [\"I\" for i in range(L)]\n", + " # Sigma_y\n", + " pstr[i] = \"Y\"\n", + " pstr[(i + 1) % L] = \"Y\"\n", + " paulis.append(pstr)\n", + "\n", + " pstr = [\"I\" for i in range(L)]\n", + " # Sigma_z\n", + " pstr[i] = \"Z\"\n", + " pstr[(i + 1) % L] = \"Z\"\n", + " paulis.append(pstr)" + ] + }, + { + "cell_type": "markdown", + "id": "0540e60f", + "metadata": {}, + "source": [ + "Let's make some random bitstrings" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "56350454", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Subspace dimension: 4194276\n", + "Full Hilbert space dimension: 4194304\n" + ] + } + ], + "source": [ + "rand_seed = 22\n", + "np.random.seed(rand_seed)\n", + "\n", + "\n", + "def random_bitstrings(n_samples, n_qubits):\n", + " return np.round(np.random.rand(n_samples, n_qubits)).astype(\"int\").astype(\"bool\")\n", + "\n", + "\n", + "bts_matrix = random_bitstrings(50_000_000, L)\n", + "\n", + "# NOTE: It is essential for the projection code to have the bitstrings sorted!\n", + "bts_matrix = sort_and_remove_duplicates(bts_matrix)\n", + "\n", + "print(\"Subspace dimension: \" + str(bts_matrix.shape[0]))\n", + "print(\"Full Hilbert space dimension: \" + str(2**L))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "f31f5e40", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.sparse import coo_matrix\n", + "from scipy.sparse.linalg import eigsh\n", + "\n", + "d = bts_matrix.shape[0]\n", + "\n", + "# The first Pauli operator\n", + "matrix_elements, row_coords, col_coords = matrix_elements_from_pauli_string(bts_matrix, paulis[0])\n", + "\n", + "# The complex double precision is required to match exactly Netket's results\n", + "# We can relax it to complex64 most likely\n", + "ham = coo_matrix((matrix_elements, (row_coords, col_coords)), (d, d), dtype=\"complex128\")\n", + "\n", + "# The remaining Pauli operators\n", + "# It will be a good idea to make this operation in parallel\n", + "for i in range(len(paulis) - 1):\n", + " matrix_elements, row_coords, col_coords = matrix_elements_from_pauli_string(\n", + " bts_matrix, paulis[i + 1]\n", + " )\n", + " ham += coo_matrix((matrix_elements, (row_coords, col_coords)), (d, d))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "3ce6e519", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-39.14735935]\n" + ] + } + ], + "source": [ + "# And we finally diagonalize\n", + "E, V = eigsh(ham, k=1, which=\"SA\")\n", + "\n", + "print(E)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/how_tos/select_open_closed_shell.ipynb b/docs/how_tos/select_open_closed_shell.ipynb new file mode 100644 index 0000000..781d6af --- /dev/null +++ b/docs/how_tos/select_open_closed_shell.ipynb @@ -0,0 +1,536 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "72420c62-2716-4f64-ad5b-73394b481cc1", + "metadata": {}, + "source": [ + "# Understand open-shell vs closed-shell options and its effect in the subspace construction\n", + "\n", + "In this \"how-to\", we will show how to choose subpace dimensions in the `sqd` package to post-process quantum samples using the [self-consistent configuration recovery technique](https://arxiv.org/abs/2405.05068). \n", + "\n", + "More importantly, this \"how-to\" also highlights some differences in the behaviour in the susbapce construction when run in `open_shell = False` or `open_shell = True` modes:\n", + "\n", + "- `open_shell = False` only works when the number of spin-up and spin-down electrons is the same. \n", + "\n", + "- `open_shell = True` must be used when the number of spin-up and spin-down electrons is different. It can also be used when the number of spin-up and spin-down electrons is the same. However, in this last case, there is a difference in the sizes of the subspaces generated between `open_shell = False` and `open_shell = True`, as discussed in this notebook.\n", + "\n", + "**NOTE:** Some of the electronic-configuration (bitstring) manipulations in this package have as a goal to preserve the total spin symmetry $S^2$. Standard Selected Counfiguration Interaction (SCI) solvers cannot impose $S^2$ conservation exactly. Consequently, they do so approximately via a Lagrange multiplier. \n", + "\n", + "The choice of electronic configurations entering the eigenstate solver can also have a strong effect in the conservation of spin. For example, in a (2-electron,2-orbital) system, one may sample the configuration $|1001\\rangle$ (having a single spin-up excitation over the RHF state $|0101\\rangle$) which is a linear combination of the open-shell singlet and triplet states, respectively $(|1001\\rangle ± |0110\\rangle) /\\sqrt{2}$. If the configuration |0110⟩ is not sampled, one can construct neither eigenfunction of total spin, leading to spin contamination or redundancy (i.e. the configuration |1001⟩ is involved in a CI calculation, but has coefficient 0 in the CI vector). Consider that a single sample $|1001\\rangle$ is generated in the quantum computer, this is how the `sqd` package handles this situation:\n", + "\n", + "- `open_shell = False`: \n", + "\n", + " 1. The $1001$ bitstring is split in half, representing spin-up and spin-down configurations: $10$ (up) and $01$ (down).\n", + " \n", + " 2. The list of unique spin-polarized configurations is constructed: $\\mathcal{U} = [01, 10]$.\n", + "\n", + " 3. We then consider all possible combinations of $\\mathcal{U}$ elements to form the basis: $\\left \\{ |0101\\rangle, |0110\\rangle , |1001\\rangle , |1010\\rangle \\right \\}$, which contains the singlet and triplet states.\n", + "\n", + "\n", + "- `open_shell = True`: \n", + "\n", + " 1. Contrary to the `open_shell = False` case, we do not combine the halves of the bitstring to form the basis." + ] + }, + { + "cell_type": "markdown", + "id": "a6755afb-ca1e-4473-974b-ba89acc8abce", + "metadata": {}, + "source": [ + "## Closed-Shell\n", + "\n", + "This example shows how the bitstrings are manipulated in a (2-electron, 4-orbital) system." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "677f54ac-b4ed-47e3-b5ba-5366d3a520f9", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify molecule properties\n", + "num_orbitals = 4\n", + "num_elec_a = num_elec_b = 1\n", + "open_shell = False" + ] + }, + { + "cell_type": "markdown", + "id": "c58e988c-a109-44cd-a975-9df43250c318", + "metadata": {}, + "source": [ + "### Specify by hand a dictionary of measurement outcomes" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e9506e0b-ed64-48bb-a97a-ef851b604af1", + "metadata": {}, + "outputs": [], + "source": [ + "counts_dict = {\"00010010\": 1 / 2.0 - 0.01, \"01001000\": 1 / 2.0 - 0.01, \"00010001\": 0.02}" + ] + }, + { + "cell_type": "markdown", + "id": "851bc98e-9c08-4e78-9472-36301abc11d8", + "metadata": {}, + "source": [ + "### Transform the counts dict into a bitstring matrix and probability array for post-processing" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7a102a7f-aae6-4583-ab82-ae40fcb5496a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[False False False True False False True False]\n", + " [False True False False True False False False]\n", + " [False False False True False False False True]]\n", + "[0.49 0.49 0.02]\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.counts import counts_to_arrays\n", + "\n", + "# Convert counts into bitstring and probability arrays\n", + "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)\n", + "print(bitstring_matrix_full)\n", + "print(probs_arr_full)" + ] + }, + { + "cell_type": "markdown", + "id": "eb704101-0fe8-4d12-b572-b1d844e35a90", + "metadata": {}, + "source": [ + "### Subsample a single batch of size two:\n", + "\n", + "- ``n_batches = 1``: Number of batches of configurations used by the different calls to the eigenstate solver\n", + "- ``samples_per_batch = 2``: Number of unique configurations to include in each batch" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "fe60aee2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[False False False True False False True False]\n", + " [False True False False True False False False]]\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n", + "\n", + "n_batches = 1\n", + "samples_per_batch = 2\n", + "\n", + "# seed for random number generator\n", + "rand_seed = 48\n", + "\n", + "# Generate the batches\n", + "batches = postselect_and_subsample(\n", + " bitstring_matrix_full,\n", + " probs_arr_full,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " samples_per_batch,\n", + " n_batches,\n", + " rand_seed=rand_seed,\n", + ")\n", + "\n", + "print(batches[0])" + ] + }, + { + "cell_type": "markdown", + "id": "93a6d05a", + "metadata": {}, + "source": [ + "### Obtain decimal representation of the spin-up and spin-down bitstrings used by the eigenstate solver\n", + "\n", + "The fist element in the tuple corresponds to the decimal representation of the spin-up configurations, while the second element in the tuple corresponds to the decimal representation of the spin-down configurations" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ef90e039", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([1, 2, 4, 8], dtype=int64), array([1, 2, 4, 8], dtype=int64))\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.fermion import bitstring_matrix_to_sorted_addresses\n", + "\n", + "addresses = bitstring_matrix_to_sorted_addresses(batches[0], open_shell=open_shell)\n", + "print(addresses)" + ] + }, + { + "cell_type": "markdown", + "id": "70d7883c", + "metadata": {}, + "source": [ + "Note that while the number of samples per batch is 2, and the sampled bitstrings are: $00010010$ and $01001000$, four electronic configurations are generated per spin-species. In this case, the set of unique spin-polarized configurations is given by:\n", + "$$\n", + "\\mathcal{U} = \\{ 0001, 0010, 0100, 1000 \\}\n", + "$$\n", + "whose base-10 decimal representation is \n", + "$$\n", + "\\mathcal{U}_{10} = \\{ 1, 2, 4, 8 \\}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "03b32ed5", + "metadata": {}, + "source": [ + "### Basis of the subspace:\n", + "\n", + "The eigenstate solver takes all possible pairs of spin-up and spin-down bitstrings to construnct the basis $\\mathcal{B}$ of the subspace:\n", + " \n", + "- Element 1: $|00010001\\rangle$ \n", + "\n", + "- Element 2: $|00010010\\rangle$ \n", + "\n", + "- Element 3: $|00010100\\rangle$ \n", + "\n", + "- Element 4: $|00011000\\rangle$ \n", + "\n", + "- Element 5: $|00100001\\rangle$ \n", + "\n", + "- Element 6: $|00100010\\rangle$ \n", + "\n", + "- Element 7: $|00100100\\rangle$ \n", + "\n", + "- Element 8: $|00101000\\rangle$ \n", + " \n", + "- Element 9: $|01000001\\rangle$ \n", + "\n", + "- Element 10: $|01000010\\rangle$ \n", + "\n", + "- Element 11: $|01000100\\rangle$ \n", + "\n", + "- Element 12: $|01001000\\rangle$ \n", + "\n", + "- Element 13: $|10000001\\rangle$ \n", + "\n", + "- Element 14: $|10000010\\rangle$ \n", + "\n", + "- Element 15: $|10000100\\rangle$ \n", + "\n", + "- Element 16: $|10001000\\rangle$ \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "11c924ee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Basis elements of the subspace:\n", + "|00010001>\n", + "|00010010>\n", + "|00010100>\n", + "|00011000>\n", + "|00100001>\n", + "|00100010>\n", + "|00100100>\n", + "|00101000>\n", + "|01000001>\n", + "|01000010>\n", + "|01000100>\n", + "|01001000>\n", + "|10000001>\n", + "|10000010>\n", + "|10000100>\n", + "|10001000>\n" + ] + } + ], + "source": [ + "addresses_up = addresses[0]\n", + "addresses_dn = addresses[1]\n", + "\n", + "print(\"Basis elements of the subspace:\")\n", + "\n", + "for address_up in addresses_up:\n", + " for address_dn in addresses_dn:\n", + " format_name = \"{0:0\" + str(num_orbitals) + \"b}\"\n", + " print(\"|\" + format_name.format(address_up) + format_name.format(address_dn) + \">\")" + ] + }, + { + "cell_type": "markdown", + "id": "aa43a4fc", + "metadata": {}, + "source": [ + "**The subspace dimension is upper-bounded by**: $2 \\cdot$ (`samples_per_batch`)$^2$" + ] + }, + { + "cell_type": "markdown", + "id": "9412e52b", + "metadata": {}, + "source": [ + "## Open-Shell\n", + "\n", + "This example shows how the bitstrings are manipulated in a (2-electron, 4-orbital) system." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9b515b8a", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify molecule properties\n", + "num_orbitals = 4\n", + "num_elec_a = num_elec_b = 1\n", + "open_shell = True" + ] + }, + { + "cell_type": "markdown", + "id": "9ef78560", + "metadata": {}, + "source": [ + "### Specify by hand a dictionary of measurement outcomes" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "06b2185a", + "metadata": {}, + "outputs": [], + "source": [ + "counts_dict = {\"00010010\": 1 / 2.0 - 0.01, \"01001000\": 1 / 2.0 - 0.01, \"00010001\": 0.02}" + ] + }, + { + "cell_type": "markdown", + "id": "08b32957", + "metadata": {}, + "source": [ + "### Transform the counts dict into a bitstring matrix and probability array for post-processing" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "90561893", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[False False False True False False True False]\n", + " [False True False False True False False False]\n", + " [False False False True False False False True]]\n", + "[0.49 0.49 0.02]\n" + ] + } + ], + "source": [ + "# Convert counts into bitstring and probability arrays\n", + "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)\n", + "print(bitstring_matrix_full)\n", + "print(probs_arr_full)" + ] + }, + { + "cell_type": "markdown", + "id": "416bfb6c", + "metadata": {}, + "source": [ + "### Subsample a single batch of size two:\n", + "\n", + "- ``n_batches = 1``: Number of batches of configurations used by the different calls to the eigenstate solver\n", + "- ``samples_per_batch = 2``: Number of unique configurations to include in each batch" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "cf4fe11d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[False False False True False False True False]\n", + " [False True False False True False False False]]\n" + ] + } + ], + "source": [ + "n_batches = 1\n", + "samples_per_batch = 2\n", + "\n", + "# seed for random number generator\n", + "rand_seed = 48\n", + "\n", + "# Generate the batches\n", + "batches = postselect_and_subsample(\n", + " bitstring_matrix_full,\n", + " probs_arr_full,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " samples_per_batch,\n", + " n_batches,\n", + " rand_seed=rand_seed,\n", + ")\n", + "\n", + "print(batches[0])" + ] + }, + { + "cell_type": "markdown", + "id": "54d699ca", + "metadata": {}, + "source": [ + "### Obtain decimal representation of the spin-up and spin-down bitstrings used by the eigenstate solver\n", + "\n", + "The fist element in the tuple corresponds to the decimal representation of the spin-up configurations, while the second element in the tuple corresponds to the decimal representation of the spin-down configurations" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b40b049b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([1, 4], dtype=int64), array([2, 8], dtype=int64))\n" + ] + } + ], + "source": [ + "addresses = bitstring_matrix_to_sorted_addresses(batches[0], open_shell=open_shell)\n", + "print(addresses)" + ] + }, + { + "cell_type": "markdown", + "id": "28921e56", + "metadata": {}, + "source": [ + "If we specify that `open_shell = True`, now we do not include all unique half-bitstrings as spin-up and spin-down configurations, thus yielding a smaller basis as when specifying `open_shell = False`" + ] + }, + { + "cell_type": "markdown", + "id": "e1959b72", + "metadata": {}, + "source": [ + "### Basis of the subspace:\n", + "\n", + "The eigenstate solver takes all possible pairs of spin-up and spin-down bitstrings to construnct the basis $\\mathcal{B}$ of the subspace:\n", + " \n", + "- Element 1: $|00010010\\rangle$ \n", + "\n", + "- Element 2: $|00011000\\rangle$ \n", + "\n", + "- Element 3: $|01000010\\rangle$ \n", + "\n", + "- Element 4: $|01001000\\rangle$ \n", + "\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a550aba2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Basis elements of the subspace:\n", + "|00010010>\n", + "|00011000>\n", + "|01000010>\n", + "|01001000>\n" + ] + } + ], + "source": [ + "addresses_up = addresses[0]\n", + "addresses_dn = addresses[1]\n", + "\n", + "print(\"Basis elements of the subspace:\")\n", + "\n", + "for address_up in addresses_up:\n", + " for address_dn in addresses_dn:\n", + " format_name = \"{0:0\" + str(num_orbitals) + \"b}\"\n", + " print(\"|\" + format_name.format(address_up) + format_name.format(address_dn) + \">\")" + ] + }, + { + "cell_type": "markdown", + "id": "7317bc49", + "metadata": {}, + "source": [ + "**The subspace dimension is upper-bounded by**: (`samples_per_batch`)$^2$" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/how_tos/use_oo_to_optimize_hamiltonian_basis.ipynb b/docs/how_tos/use_oo_to_optimize_hamiltonian_basis.ipynb new file mode 100644 index 0000000..4d8d91f --- /dev/null +++ b/docs/how_tos/use_oo_to_optimize_hamiltonian_basis.ipynb @@ -0,0 +1,428 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", + "metadata": {}, + "source": [ + "# Optimize Hamiltonian basis with orbital optimization\n", + "\n", + "In this tutorial, we will show how to use the `sqd` package to post-process quantum samples using the [self-consistent configuration recovery technique](https://arxiv.org/abs/2405.05068) and then further optimize the ground state approximation using orbital optimization\n", + "\n", + "Refer to [Sec. II A 4](https://arxiv.org/pdf/2405.05068) for a more detailed discussion on this technique." + ] + }, + { + "cell_type": "markdown", + "id": "a6755afb-ca1e-4473-974b-ba89acc8abce", + "metadata": {}, + "source": [ + "### First we will specify the molecule and its properties\n", + "\n", + "In this example, we will approximate the ground state energy of an $N_2$ molecule and then improve the answer using orbital optimization. This guide studies $N_2$ at equilibrium, which is mean-field dominated. This means the MO basis is already a good choice for our integrals; therefore, we will rotate our integrals **out** of the MO basis in order to illustrate the effects of orbital optimization." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "677f54ac-b4ed-47e3-b5ba-5366d3a520f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsing ../molecules/n2_fci.txt\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from pyscf import ao2mo, tools\n", + "from qiskit_addon_sqd.fermion import rotate_integrals\n", + "\n", + "# Specify molecule properties\n", + "num_orbitals = 16\n", + "num_elec_a = num_elec_b = 5\n", + "open_shell = False\n", + "spin_sq = 0\n", + "\n", + "# Read in molecule from disk\n", + "mf_as = tools.fcidump.to_scf(\"../molecules/n2_fci.txt\")\n", + "hcore = mf_as.get_hcore()\n", + "eri = ao2mo.restore(1, mf_as._eri, num_orbitals)\n", + "\n", + "# Rotate our integrals out of MO basis\n", + "k_rot = (np.random.rand(num_orbitals**2) - 0.5) * 0.1\n", + "hcore_rot, eri_rot = rotate_integrals(hcore, eri, k_rot)\n", + "\n", + "nuclear_repulsion_energy = mf_as.mol.energy_nuc()" + ] + }, + { + "cell_type": "markdown", + "id": "c58e988c-a109-44cd-a975-9df43250c318", + "metadata": {}, + "source": [ + "### Generate a dummy counts dictionary and create the bitstring matrix and probability array" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e9506e0b-ed64-48bb-a97a-ef851b604af1", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_addon_sqd.counts import counts_to_arrays, generate_counts_uniform\n", + "\n", + "# Create a seed to control randomness throughout this workflow\n", + "rand_seed = 42\n", + "\n", + "# Generate random samples\n", + "counts_dict = generate_counts_uniform(10_000, num_orbitals * 2, rand_seed=rand_seed)\n", + "\n", + "# Convert counts into bitstring and probability arrays\n", + "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)" + ] + }, + { + "cell_type": "markdown", + "id": "eb704101-0fe8-4d12-b572-b1d844e35a90", + "metadata": {}, + "source": [ + "### Iteratively refine the samples using SQD and approximate the ground state" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b72c048e-fe8e-4fc2-b28b-03138249074e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting configuration recovery iteration 0\n", + "Subspace dimension: 4624\n", + "Starting configuration recovery iteration 1\n", + "Subspace dimension: 215296\n", + "Starting configuration recovery iteration 2\n", + "Subspace dimension: 214369\n", + "Starting configuration recovery iteration 3\n", + "Subspace dimension: 219961\n", + "Starting configuration recovery iteration 4\n", + "Subspace dimension: 217156\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n", + "from qiskit_addon_sqd.fermion import (\n", + " bitstring_matrix_to_sorted_addresses,\n", + " flip_orbital_occupancies,\n", + " solve_fermion,\n", + ")\n", + "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n", + "\n", + "# SQSD options\n", + "iterations = 5\n", + "\n", + "# Eigenstate solver options\n", + "n_batches = 10\n", + "samples_per_batch = 300\n", + "max_davidson_cycles = 200\n", + "\n", + "# Self-consistent configuration recovery loop\n", + "e_hist = np.zeros((iterations, n_batches)) # energy history\n", + "s_hist = np.zeros((iterations, n_batches)) # spin history\n", + "occupancy_hist = np.zeros((iterations, 2 * num_orbitals))\n", + "occupancies_bitwise = None # orbital i corresponds to column i in bitstring matrix\n", + "for i in range(iterations):\n", + " print(f\"Starting configuration recovery iteration {i}\")\n", + " # On the first iteration, we have no orbital occupancy information from the\n", + " # solver, so we just post-select from the full bitstring set based on hamming weight.\n", + " if occupancies_bitwise is None:\n", + " bs_mat_tmp = bitstring_matrix_full\n", + " probs_arr_tmp = probs_arr_full\n", + "\n", + " # In following iterations, we use both the occupancy info and the target hamming\n", + " # weight to refine bitstrings.\n", + " else:\n", + " bs_mat_tmp, probs_arr_tmp = recover_configurations(\n", + " bitstring_matrix_full,\n", + " probs_arr_full,\n", + " occupancies_bitwise,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Throw out samples with incorrect hamming weight and create batches of subsamples.\n", + " batches = postselect_and_subsample(\n", + " bs_mat_tmp,\n", + " probs_arr_tmp,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " samples_per_batch,\n", + " n_batches,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n", + " int_e = np.zeros(n_batches)\n", + " int_s = np.zeros(n_batches)\n", + " int_occs = np.zeros((n_batches, 2 * num_orbitals))\n", + " cs = []\n", + " for j in range(n_batches):\n", + " addresses = bitstring_matrix_to_sorted_addresses(batches[j], open_shell=open_shell)\n", + " energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n", + " addresses,\n", + " hcore_rot,\n", + " eri_rot,\n", + " spin_sq=spin_sq,\n", + " max_davidson=max_davidson_cycles,\n", + " )\n", + " energy_sci += nuclear_repulsion_energy\n", + " int_e[j] = energy_sci\n", + " int_s[j] = spin\n", + " int_occs[j, :num_orbitals] = avg_occs[0]\n", + " int_occs[j, num_orbitals:] = avg_occs[1]\n", + " cs.append(coeffs_sci)\n", + "\n", + " print(f\"Subspace dimension: {len(addresses[0]) * len(addresses[1])}\")\n", + " # Combine batch results\n", + " avg_occupancy = np.mean(int_occs, axis=0)\n", + " # The occupancies from the solver should be flipped to match the bits in the bitstring matrix.\n", + " occupancies_bitwise = flip_orbital_occupancies(avg_occupancy)\n", + "\n", + " # Track optimization history\n", + " e_hist[i, :] = int_e\n", + " s_hist[i, :] = int_s\n", + " occupancy_hist[i, :] = avg_occupancy" + ] + }, + { + "cell_type": "markdown", + "id": "9d78906b-4759-4506-9c69-85d4e67766b3", + "metadata": {}, + "source": [ + "### Visualize the results with no orbital optimization" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Data for energies plot\n", + "x1 = range(iterations)\n", + "n2_exact = -109.10288938\n", + "y1 = [np.min(energies) for energies in e_hist]\n", + "yt1 = [float(i) for i in range(-110, -106)]\n", + "\n", + "# Data for avg spatial orbital occupancy\n", + "y2 = avg_occupancy[:num_orbitals] + avg_occupancy[num_orbitals:]\n", + "x2 = range(len(y2))\n", + "\n", + "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n", + "\n", + "# Plot energies\n", + "axs[0].plot(x1, y1, label=\"Estimated\")\n", + "axs[0].set_xticks(x1)\n", + "axs[0].set_xticklabels(x1)\n", + "axs[0].set_yticks(yt1)\n", + "axs[0].set_yticklabels(yt1)\n", + "axs[0].axhline(y=n2_exact, color=\"red\", linestyle=\"--\", label=\"Exact\")\n", + "axs[0].set_title(\"Approximated Ground State Energy vs SQD Iterations\")\n", + "axs[0].set_xlabel(\"Iteration Index\")\n", + "axs[0].set_ylabel(\"Energy (Ha)\")\n", + "axs[0].legend()\n", + "\n", + "# Plot orbital occupancy\n", + "axs[1].bar(x2, y2, width=0.8)\n", + "axs[1].set_xticks(x2)\n", + "axs[1].set_xticklabels(x2)\n", + "axs[1].set_title(\"Avg Occupancy per Spatial Orbital\")\n", + "axs[1].set_xlabel(\"Orbital Index\")\n", + "axs[1].set_ylabel(\"Avg Occupancy\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e8c6d5e4", + "metadata": {}, + "source": [ + "### Orbital optimization\n", + "\n", + "We now describe how to optimize the orbitals to further improve the quality of the sqd calculation.\n", + "\n", + "The orbital rotations that are implemented in this package are those described by:\n", + "$$\n", + "U(\\kappa) = e^{\\sum_{pq, \\sigma} \\kappa_{pq} c^\\dagger_{p\\sigma} c_{q\\sigma}},\n", + "$$\n", + "where $\\kappa_{p, q} \\in \\mathbb{R}$ and $\\kappa_{p, q} = -\\kappa_{q, p}$. The orbitals are optimized to \n", + "minimize the variational energy:\n", + "$$\n", + "E(\\kappa) = \\langle \\psi | U^\\dagger(\\kappa) H U(\\kappa) |\\psi \\rangle,\n", + "$$\n", + "with respect to $\\kappa$ using gradient descent with momentum. Recall that \n", + "$|\\psi\\rangle$ is spanned in a subspace defined by determinants.\n", + "\n", + "Since the change of basis alters the Hamiltonian, we allow $|\\psi\\rangle$ to \n", + "respond to the change in the Hamiltonian. This is done by performing a number of alternating\n", + "self-consistent optimizations of $\\kappa$ and $|\\psi\\rangle$. We recall that the optimal\n", + "$|\\psi\\rangle$ is given by the lowest eigenvector of the Hamiltonian projected into the\n", + "subspace.\n", + "\n", + "The ``sqd.fermion.fermion`` module provides the tools to perform this alternating\n", + "optimization. In particular, the function ``sqd.fermion.optimize_orbitals()``.\n", + "\n", + "Some of the arguments that define the optimization are:\n", + "\n", + "- ``num_iters``: number of self-consistent iterations.\n", + "- ``num_steps_grad``: number of gradient step updates performed when optimizing \n", + "$\\kappa$ on each self-consistent iteration.\n", + "- ``learning_rate``: step-size in the gradient descent optimization of $\\kappa$." + ] + }, + { + "cell_type": "markdown", + "id": "917cf2d0", + "metadata": {}, + "source": [ + "#### Setup of the subspace\n", + "\n", + "To define the subspace, we will take the addresses of the batch with the lowest energy\n", + "from the last configuration recovery step. Other strategies may be used, like taking the union \n", + "of the addresses of the batches in the last configuration recovery iteration." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2a587030", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Subspace dimension: 229441\n", + "Energy of that batch from SQD: -109.03502554132504\n" + ] + } + ], + "source": [ + "addresses = addresses = bitstring_matrix_to_sorted_addresses(\n", + " batches[np.argmin(e_hist[-1])], open_shell=open_shell\n", + ")\n", + "print(f\"Subspace dimension: {len(addresses[0]) * len(addresses[1])}\")\n", + "print(f\"Energy of that batch from SQD: {e_hist[-1, np.argmin(e_hist[-1])]}\")\n", + "\n", + "# Union strategy\n", + "\n", + "# batches_union = np.concatenate((batches[0], batches[1]), axis = 0)\n", + "# for i in range(n_batches-2):\n", + "# batches_union = np.concatenate((batches_union, batches[ i+ 2]))\n", + "# addresses = bitstring_matrix_to_sorted_addresses(\n", + "# batches_union, open_shell=open_shell\n", + "# )\n", + "# print (f\"Subspace dimension: {len(addresses[0]) * len(addresses[1])}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b5e56baf", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_addon_sqd.fermion import optimize_orbitals\n", + "\n", + "k_flat = (np.random.rand(num_orbitals**2) - 0.5) * 0.01 # initial guess for rotation params\n", + "num_iters = 10\n", + "num_steps_grad = 10_000 # relatively cheap to execute\n", + "learning_rate = 0.1\n", + "\n", + "e_improved, k_flat, orbital_occupancies = optimize_orbitals(\n", + " addresses,\n", + " hcore_rot,\n", + " eri_rot,\n", + " k_flat,\n", + " spin_sq=spin_sq,\n", + " num_iters=num_iters,\n", + " num_steps_grad=num_steps_grad,\n", + " learning_rate=learning_rate,\n", + " max_davidson=max_davidson_cycles,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "e06f5c28-83d0-4dc2-b2bd-2ec92676745d", + "metadata": {}, + "source": [ + "Here we see that by optimizing rotation parameters for our Hamiltonian, we can improve the result from SQD." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "78a80e64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "improved_energy in the new basis: -109.03585435604712\n" + ] + } + ], + "source": [ + "print(f\"improved_energy in the new basis: {e_improved + nuclear_repulsion_energy}\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/images/lucj_ansatz_zig_zag_pattern.jpg 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This allows SQD to be robust to samples corrupted by quantum noise and deal with large Hamiltonians, such as chemistry Hamiltonians with millions of interaction terms, beyond the reach of any exact diagonalization methods. + +The SQD tool can target Hamiltonians expressed as linear combination of Pauli operators, or second-quantized fermionic operators. The input samples are obtained by quantum circuits defined by the user, which are believed to be good representations of eigenstates (e.g. the ground state) of a target operator. The convergence rate of SQD as a function of the number of samples improves with the sparseness of the target eigenstate. + +The projection and diagonalization steps are performed by a classical solver. We provide here two generic solvers, one for fermionic systems and another for qubit systems. Other solvers that might be more efficient for specific systems can be interfaced by the users. + +Documentation +------------- + +All documentation is available `here `_. + +Installation +------------ + +We encourage installing this package via ``pip``, when possible: + +.. code-block:: bash + + pip install 'qiskit-addon-sqd' + + +For more installation information refer to the `installation instructions `_ in the documentation. + +System sizes and computational requirements +------------------------------------------- + +The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, `n_batches` of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this `tutorial `_, those calls are inside a `for` loop. **It is highly recommended to perform these calls in parallel**. + +The :func:`qiskit_addon_sqd.fermion.solve_fermion` function is multithreaded and capable of handling systems with ~25 spacial orbitals and ~10 electrons with subspace dimensions of ~$10^7$, using ~10-30 cores. + +Choosing subspace dimensions +---------------------------- + +The choice of the subspace dimension affects the accuracy and runtime of the eigenstate solver. The larger the subspace the more accurate the calculation, at the cost of increasing the runtime and memory requirements. It is not known *a priori* the optimal subspace size, thus a convergence study with the subspace dimension may be performed, as described in this `guide `_. + +The subspace dimension is set indirectly +---------------------------------------- + +In this package, the user controls the number of bitstrings contained in each subspace with the `samples_per_batch` argument in :func:`.qiskit_addon_sqd.subsampling.postselect_and_subsample`. The value of this argument determines an upper bound to the subspace dimension in the case of quantum chemistry applications. See this `example `_ for more details. + +Deprecation Policy +------------------ + +We follow `semantic versioning `_ and are guided by the principles in +`Qiskit's deprecation policy `_. +We may occasionally make breaking changes in order to improve the user experience. +When possible, we will keep old interfaces and mark them as deprecated, as long as they can co-exist with the +new ones. +Each substantial improvement, breaking change, or deprecation will be documented in the +release notes. + +Contributing +------------ + +The source code is available `on GitHub `_. + +The developer guide is located at `CONTRIBUTING.md `_ +in the root of this project's repository. +By participating, you are expected to uphold Qiskit's `code of conduct `_. + +We use `GitHub issues `_ for tracking requests and bugs. + +License +------- + +`Apache License 2.0 `_ + +.. _references: + +References +---------- + +[1] Javier Robledo-Moreno, et al., `Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer `_, arXiv:2405.05068 [quant-ph]. + +[2] Keita Kanno, et al., `Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers `_, arXiv:2302.11320 [quant-ph]. + +.. toctree:: + :hidden: + + Documentation Home + Installation Instructions + Tutorials + How-To Guides + API Reference + GitHub diff --git a/docs/install.rst b/docs/install.rst new file mode 100644 index 0000000..cac7005 --- /dev/null +++ b/docs/install.rst @@ -0,0 +1,81 @@ +Installation Instructions +========================= + +Let's see how to install the package. The first +thing to do is choose how you're going to run and install the +packages. There are two primary ways to do this: + +- :ref:`Option 1` +- :ref:`Option 2` + +Pre-Installation +^^^^^^^^^^^^^^^^ + +First, create a minimal environment with only Python installed in it. We recommend using `Python virtual environments `__. + +.. code:: sh + + python3 -m venv /path/to/virtual/environment + +Activate your new environment. + +.. code:: sh + + source /path/to/virtual/environment/bin/activate + +Note: If you are using Windows, use the following commands in PowerShell: + +.. code:: pwsh + + python3 -m venv c:\path\to\virtual\environment + c:\path\to\virtual\environment\Scripts\Activate.ps1 + + +.. _Option 1: + +Option 1: Install from PyPI +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The most straightforward way to install the ``qiskit-addon-sqd`` package is via ``PyPI``. + +.. code:: sh + + pip install 'qiskit-addon-sqd' + + +.. _Option 2: + +Option 2: Install from Source +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Users who wish to develop in the repository or run the notebooks locally may want to install from source. + +If so, the first step is to clone the ``qiskit-addon-sqd`` repository. + +.. code:: sh + + git clone git@github.com:Qiskit/qiskit-addon-sqd.git + +Next, upgrade pip and enter the repository. + +.. code:: sh + + pip install --upgrade pip + cd qiskit-addon-sqd + +The next step is to install ``qiskit-addon-sqd`` to the virtual environment. If you plan on running the notebooks, install the +notebook dependencies in order to run all the visualizations in the notebooks. If you plan on developing in the repository, you +may want to install the ``dev`` dependencies. + +Adjust the options below to suit your needs. + +.. code:: sh + + pip install tox notebook -e '.[notebook-dependencies,dev]' + +If you installed the notebook dependencies, you can get started by running the notebooks in the docs. + +.. code:: + + cd docs/ + jupyter lab diff --git a/docs/molecules/n2_fci.txt b/docs/molecules/n2_fci.txt new file mode 100644 index 0000000..74f72f2 --- /dev/null +++ b/docs/molecules/n2_fci.txt @@ -0,0 +1,1611 @@ +&FCI NORB= 16,NELEC=10,MS2=0, + ORBSYM=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 + ISYM=1, + &END + 0.8227153295684669 1 1 1 1 + 0.05187587577524144 2 1 2 1 + 0.5219201962559413 2 2 1 1 + 0.535263084520174 2 2 2 2 + -0.1347836972470542 3 1 1 1 + -0.008657841512417053 3 1 2 2 + 0.05793493716089329 3 1 3 1 + 0.08632998383785331 3 2 2 1 + 0.2097929322213681 3 2 3 2 + 0.5579235002150018 3 3 1 1 + 0.5400470008931167 3 3 2 2 + -0.03025371939317356 3 3 3 1 + 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0000000..44f6684 --- /dev/null +++ b/docs/tutorials/01_getting_started_fermionic.ipynb @@ -0,0 +1,531 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9e40af77-7f0f-4dd6-ab0a-420cf396050e", + "metadata": {}, + "source": [ + "# Improving energy estimation of a Fermionic Hamiltonian with SQD\n", + "\n", + "In this tutorial, we will show how to use the `sqd` package to post-process quantum samples using the [self-consistent configuration recovery technique](https://arxiv.org/abs/2405.05068).\n", + "\n", + "This technique can be done iteratively by repeating 4 steps:\n", + "\n", + "- Correct the full set of bitstring samples, using *a priori* knowledge of particle number and the most updated orbital occupancy information obtained from the ground state approximations at each iteration.\n", + " \n", + "- Probabilistically create batches of subsamples from corrected bitstrings.\n", + " \n", + "- Project and diagonalize the molecular Hamiltonian over each sampled subspace.\n", + " \n", + "- Save the minimum ground state energy found across all batches and update the avg orbital occupancy.\n", + "\n", + "In this tutorial we implement a [Qiskit patterns](https://docs.quantum.ibm.com/guides/intro-to-patterns) for post-processing quantum samples to find good ground state approximations:\n", + "1. **Map** problem to a quantum circuit\n", + "2. **Optimize** for target hardware\n", + "3. **Execute** on target hardware\n", + "4. **Post-process** results (using *SQD*)" + ] + }, + { + "cell_type": "markdown", + "id": "afeb054c", + "metadata": {}, + "source": [ + "## Step 1: Map problem to a quantum circuit\n", + "\n", + "In this tutorial, we will approximate the ground state energy of an $N_2$ molecule. First, we will specify the molecule and its properties. Next, we will create a [local unitary cluster Jastrow (LUCJ)](https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc02516k) ansatz (quantum circuit) to generate samples from a quantum computer for ground state energy estimation." + ] + }, + { + "cell_type": "markdown", + "id": "a6755afb-ca1e-4473-974b-ba89acc8abce", + "metadata": {}, + "source": [ + "### Specify the molecule and its properties" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "677f54ac-b4ed-47e3-b5ba-5366d3a520f9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parsing ../molecules/n2_fci.txt\n" + ] + } + ], + "source": [ + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "from pyscf import ao2mo, tools\n", + "\n", + "# Specify molecule properties\n", + "num_orbitals = 16\n", + "num_elec_a = num_elec_b = 5\n", + "open_shell = False\n", + "spin_sq = 0\n", + "\n", + "# Read in molecule from disk\n", + "mf_as = tools.fcidump.to_scf(\"../molecules/n2_fci.txt\")\n", + "hcore = mf_as.get_hcore()\n", + "eri = ao2mo.restore(1, mf_as._eri, num_orbitals)\n", + "nuclear_repulsion_energy = mf_as.mol.energy_nuc()" + ] + }, + { + "cell_type": "markdown", + "id": "96bfe018", + "metadata": {}, + "source": [ + "### Create the `LUCJ` Ansatz\n", + "\n", + "The `LUCJ` ansatz is a parameterized quantum circuit, and we will initialize it with `t2` and `t1` amplitudes obtained from a CCSD calculation." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "66270387", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "converged SCF energy = -108.867773675638\n", + "E(CCSD) = -109.0935188821144 E_corr = -0.2257452064762984\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Overwritten attributes get_hcore get_ovlp of \n" + ] + } + ], + "source": [ + "from pyscf import cc\n", + "\n", + "mf_as.kernel()\n", + "mc = cc.CCSD(mf_as)\n", + "mc.kernel()\n", + "t1 = mc.t1\n", + "t2 = mc.t2" + ] + }, + { + "attachments": { + "lucj_ansatz_zig-zag-pattern-rsz.jpg": { + "image/jpeg": 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" + } + }, + "cell_type": "markdown", + "id": "f4d882fa", + "metadata": {}, + "source": [ + "We will use the [ffsim](https://github.com/qiskit-community/ffsim/tree/main) package to create and initialize the ansatz with `t2` and `t1` amplitudes computed above. Since our molecule has a closed-shell Hartree-Fock state, we will use the spin-balanced variant of the UCJ ansatz, [UCJOpSpinBalanced](https://qiskit-community.github.io/ffsim/api/ffsim.html#ffsim.UCJOpSpinBalanced).\n", + "\n", + "As our target IBM hardware has a heavy-hex topology, we will adopt the _zig-zag_ pattern used in [this paper](https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc02516k) for qubit interactions. In this pattern, orbitals (represented by qubits) with the same spin are connected with a line topology (red and blue circles) where each line take a zig-zag shape due the heavy-hex connectivity of the target hardware. Again, due to the heavy-hex topology, orbitals for different spins have connections between every 4th orbital (0, 4, 8, etc.) (purple circles).\n", + "\n", + "![lucj_ansatz_zig-zag-pattern-rsz.jpg](attachment:lucj_ansatz_zig-zag-pattern-rsz.jpg)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "dd69a86c", + "metadata": {}, + "outputs": [], + "source": [ + "import ffsim\n", + "from qiskit import QuantumCircuit, QuantumRegister\n", + "\n", + "n_reps = 2\n", + "alpha_alpha_indices = [(p, p + 1) for p in range(num_orbitals - 1)]\n", + "alpha_beta_indices = [(p, p) for p in range(0, num_orbitals, 4)]\n", + "\n", + "ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes(\n", + " t2=t2,\n", + " t1=t1,\n", + " n_reps=n_reps,\n", + " interaction_pairs=(alpha_alpha_indices, alpha_beta_indices),\n", + ")\n", + "\n", + "nelec = (num_elec_a, num_elec_b)\n", + "\n", + "# create an empty quantum circuit\n", + "qubits = QuantumRegister(2 * num_orbitals, name=\"q\")\n", + "circuit = QuantumCircuit(qubits)\n", + "\n", + "# prepare Hartree-Fock state as the reference state and append it to the quantum circuit\n", + "circuit.append(ffsim.qiskit.PrepareHartreeFockJW(num_orbitals, nelec), qubits)\n", + "\n", + "# apply the UCJ operator to the reference state\n", + "circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n", + "circuit.measure_all()" + ] + }, + { + "cell_type": "markdown", + "id": "db11bf6d", + "metadata": {}, + "source": [ + "## Step 2: Optimize for target hardware" + ] + }, + { + "cell_type": "markdown", + "id": "0760b3f3", + "metadata": {}, + "source": [ + "Next, we will optimize our circuit for a target hardware. We need to choose the hardware device to use before optimizing our circuit. We will use a fake 127-qubit backend from ``qiskit_ibm_runtime`` to emulate a real device." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "53a039d8", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime.fake_provider import FakeSherbrooke\n", + "\n", + "backend = FakeSherbrooke()" + ] + }, + { + "cell_type": "markdown", + "id": "057ebbf6", + "metadata": {}, + "source": [ + "Next, we recommend the following steps to optimize the ansatz and make it hardware-compatible.\n", + "\n", + "- Select physical qubits (`initial_layout`) from the target harware that adheres to the zig-zag pattern described above. Laying out qubits in this pattern leads to an efficient hardware-compatible circuit with less gates.\n", + "- Generate a staged pass manager using the [generate_preset_pass_manager](https://docs.quantum.ibm.com/api/qiskit/transpiler_preset#generate_preset_pass_manager) function from qiskit with your choice of `backend` and `initial_layout`.\n", + "- Set the `pre_init` stage of your staged pass manager to `ffsim.qiskit.PRE_INIT`. `ffsim.qiskit.PRE_INIT` includes qiskit transpiler passes that decompose and merge orbitals resulting in fewer gates in the final circuit.\n", + "- Run the pass manager on your circuit. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7d554aa5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gate counts (w/o pre-init passes): OrderedDict({'rz': 7421, 'sx': 6016, 'ecr': 2240, 'x': 324, 'measure': 32, 'barrier': 1})\n", + "Gate counts (w/ pre-init passes): OrderedDict({'rz': 4155, 'sx': 3186, 'ecr': 1262, 'x': 210, 'measure': 32, 'barrier': 1})\n" + ] + } + ], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "spin_a_layout = [0, 14, 18, 19, 20, 33, 39, 40, 41, 53, 60, 61, 62, 72, 81, 82]\n", + "spin_b_layout = [2, 3, 4, 15, 22, 23, 24, 34, 43, 44, 45, 54, 64, 65, 66, 73]\n", + "initial_layout = spin_a_layout + spin_b_layout\n", + "\n", + "pass_manager = generate_preset_pass_manager(\n", + " optimization_level=3, backend=backend, initial_layout=initial_layout\n", + ")\n", + "\n", + "# without PRE_INIT passes\n", + "isa_circuit = pass_manager.run(circuit)\n", + "print(f\"Gate counts (w/o pre-init passes): {isa_circuit.count_ops()}\")\n", + "\n", + "# with PRE_INIT passes\n", + "# We will use the circuit generated by this pass manager for hardware execution\n", + "pass_manager.pre_init = ffsim.qiskit.PRE_INIT\n", + "isa_circuit = pass_manager.run(circuit)\n", + "print(f\"Gate counts (w/ pre-init passes): {isa_circuit.count_ops()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "0cc1edef", + "metadata": {}, + "source": [ + "## Step 3: Execute on target hardware" + ] + }, + { + "cell_type": "markdown", + "id": "cbf7ef9f", + "metadata": {}, + "source": [ + "After optimizing the circuit for hardware execution, we are ready to run it on the target hardware and collect samples for ground state energy estimation. As we only have one circuit, we will use Qiskit Runtime's [Job execution mode](https://docs.quantum.ibm.com/guides/execution-modes) and execute our circuit.\n", + "\n", + "**Note: We have commented out the code for running the circuit on a QPU and left it for the user's reference. Instead of running on real hardware in this guide, we will just generate random samples drawn from the uniform distribution.**" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3da09100", + "metadata": {}, + "outputs": [], + "source": [ + "# from qiskit_ibm_runtime import SamplerV2 as Sampler\n", + "\n", + "# sampler = Sampler(mode=backend)\n", + "# job = sampler.run([isa_circuit], shots=10_000)\n", + "# primitive_result = job.result()\n", + "# pub_result = primitive_result[0]\n", + "# counts = pub_result.data.meas.get_counts()\n", + "\n", + "from qiskit_addon_sqd.counts import generate_counts_uniform\n", + "\n", + "rand_seed = 42\n", + "counts = generate_counts_uniform(10_000, num_orbitals * 2, rand_seed=rand_seed)" + ] + }, + { + "cell_type": "markdown", + "id": "6df05b6e", + "metadata": {}, + "source": [ + "## Step 4: Post-process results" + ] + }, + { + "cell_type": "markdown", + "id": "851bc98e-9c08-4e78-9472-36301abc11d8", + "metadata": {}, + "source": [ + "### Transform the counts into a bitstring matrix and probability array for post-processing\n", + "\n", + "In order to speed up the bitwise processing required in this workflow, we use Numpy arrays to hold representations of the bitstrings and sampling frequencies." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "7a102a7f-aae6-4583-ab82-ae40fcb5496a", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qiskit_addon_sqd.counts import counts_to_arrays\n", + "\n", + "# Convert counts into bitstring and probability arrays\n", + "bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts)" + ] + }, + { + "cell_type": "markdown", + "id": "eb704101-0fe8-4d12-b572-b1d844e35a90", + "metadata": {}, + "source": [ + "### Iteratively refine the samples using SQD and approximate the ground state\n", + "\n", + "There are a few user-controlled options which are important for this technique:\n", + "- ``iterations``: Number of self-consistent configuration recovery iterations\n", + "- ``n_batches``: Number of batches of configurations used by the different calls to the eigenstate solver\n", + "- ``samples_per_batch``: Number of unique configurations to include in each batch\n", + "- ``max_davidson_cycles``: Maximum number of Davidson cycles run by each eigensolver" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b72c048e-fe8e-4fc2-b28b-03138249074e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting configuration recovery iteration 0\n", + "Starting configuration recovery iteration 1\n", + "Starting configuration recovery iteration 2\n", + "Starting configuration recovery iteration 3\n", + "Starting configuration recovery iteration 4\n" + ] + } + ], + "source": [ + "from qiskit_addon_sqd.configuration_recovery import recover_configurations\n", + "from qiskit_addon_sqd.fermion import (\n", + " bitstring_matrix_to_sorted_addresses,\n", + " flip_orbital_occupancies,\n", + " solve_fermion,\n", + ")\n", + "from qiskit_addon_sqd.subsampling import postselect_and_subsample\n", + "\n", + "# SQD options\n", + "iterations = 5\n", + "\n", + "# Eigenstate solver options\n", + "n_batches = 10\n", + "samples_per_batch = 300\n", + "max_davidson_cycles = 200\n", + "\n", + "# Self-consistent configuration recovery loop\n", + "e_hist = np.zeros((iterations, n_batches)) # energy history\n", + "s_hist = np.zeros((iterations, n_batches)) # spin history\n", + "occupancy_hist = np.zeros((iterations, 2 * num_orbitals))\n", + "occupancies_bitwise = None # orbital i corresponds to column i in bitstring matrix\n", + "for i in range(iterations):\n", + " print(f\"Starting configuration recovery iteration {i}\")\n", + " # On the first iteration, we have no orbital occupancy information from the\n", + " # solver, so we just post-select from the full bitstring set based on hamming weight.\n", + " if occupancies_bitwise is None:\n", + " bs_mat_tmp = bitstring_matrix_full\n", + " probs_arr_tmp = probs_arr_full\n", + "\n", + " # In following iterations, we use both the occupancy info and the target hamming\n", + " # weight to refine bitstrings.\n", + " else:\n", + " bs_mat_tmp, probs_arr_tmp = recover_configurations(\n", + " bitstring_matrix_full,\n", + " probs_arr_full,\n", + " occupancies_bitwise,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Throw out samples with incorrect hamming weight and create batches of subsamples.\n", + " batches = postselect_and_subsample(\n", + " bs_mat_tmp,\n", + " probs_arr_tmp,\n", + " num_elec_a,\n", + " num_elec_b,\n", + " samples_per_batch,\n", + " n_batches,\n", + " rand_seed=rand_seed,\n", + " )\n", + "\n", + " # Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.\n", + " int_e = np.zeros(n_batches)\n", + " int_s = np.zeros(n_batches)\n", + " int_occs = np.zeros((n_batches, 2 * num_orbitals))\n", + " cs = []\n", + " for j in range(n_batches):\n", + " addresses = bitstring_matrix_to_sorted_addresses(batches[j], open_shell=open_shell)\n", + " energy_sci, coeffs_sci, avg_occs, spin = solve_fermion(\n", + " addresses,\n", + " hcore,\n", + " eri,\n", + " spin_sq=spin_sq,\n", + " max_davidson=max_davidson_cycles,\n", + " )\n", + " energy_sci += nuclear_repulsion_energy\n", + " int_e[j] = energy_sci\n", + " int_s[j] = spin\n", + " int_occs[j, :num_orbitals] = avg_occs[0]\n", + " int_occs[j, num_orbitals:] = avg_occs[1]\n", + " cs.append(coeffs_sci)\n", + "\n", + " # Combine batch results\n", + " avg_occupancy = np.mean(int_occs, axis=0)\n", + " # The occupancies from the solver should be flipped to match the bits in the bitstring matrix.\n", + " occupancies_bitwise = flip_orbital_occupancies(avg_occupancy)\n", + "\n", + " # Track optimization history\n", + " e_hist[i, :] = int_e\n", + " s_hist[i, :] = int_s\n", + " occupancy_hist[i, :] = avg_occupancy" + ] + }, + { + "cell_type": "markdown", + "id": "9d78906b-4759-4506-9c69-85d4e67766b3", + "metadata": {}, + "source": [ + "### Visualize the results\n", + "\n", + "The first plot shows that after a couple of iterations we estimate the ground state energy within ``~200 mH``. Remember, the quantum samples in this demo were pure noise. The signal here comes from *a priori* knowledge of the electronic structure and molecular Hamiltonian.\n", + "\n", + "The second plot shows the average occupancy of each spatial orbital after the final iteration. We can see that both the spin-up and spin-down electrons occupy the first five orbitals with high probability in our solutions." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "caffd888-e89c-4aa9-8bae-4d1bb723b35e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Data for energies plot\n", + "x1 = range(iterations)\n", + "n2_exact = -109.10288938\n", + "y1 = [np.min(energies) for energies in e_hist]\n", + "yt1 = [float(i) for i in range(-110, -106)]\n", + "\n", + "# Data for avg spatial orbital occupancy\n", + "y2 = avg_occupancy[:num_orbitals] + avg_occupancy[num_orbitals:]\n", + "x2 = range(len(y2))\n", + "\n", + "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n", + "\n", + "# Plot energies\n", + "axs[0].plot(x1, y1, label=\"Estimated\")\n", + "axs[0].set_xticks(x1)\n", + "axs[0].set_xticklabels(x1)\n", + "axs[0].set_yticks(yt1)\n", + "axs[0].set_yticklabels(yt1)\n", + "axs[0].axhline(y=n2_exact, color=\"red\", linestyle=\"--\", label=\"Exact\")\n", + "axs[0].set_title(\"Approximated Ground State Energy vs SQD Iterations\")\n", + "axs[0].set_xlabel(\"Iteration Index\")\n", + "axs[0].set_ylabel(\"Energy (Ha)\")\n", + "axs[0].legend()\n", + "\n", + "# Plot orbital occupancy\n", + "axs[1].bar(x2, y2, width=0.8)\n", + "axs[1].set_xticks(x2)\n", + "axs[1].set_xticklabels(x2)\n", + "axs[1].set_title(\"Avg Occupancy per Spatial Orbital\")\n", + "axs[1].set_xlabel(\"Orbital Index\")\n", + "axs[1].set_ylabel(\"Avg Occupancy\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/tutorials/index.rst b/docs/tutorials/index.rst new file mode 100644 index 0000000..ba7fbd6 --- /dev/null +++ b/docs/tutorials/index.rst @@ -0,0 +1,10 @@ +######### +Tutorials +######### + +This page summarizes the available tutorials. + +.. nbgallery:: + :glob: + + * diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..84dc6c6 --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,146 @@ +[build-system] +requires = ["hatchling"] +build-backend = "hatchling.build" + +[project] +name = "qiskit-addon-sqd" +version = "0.3.0" +readme = "README.md" +license = {file = "LICENSE.txt"} +classifiers = [ + "Intended Audience :: Developers", + "Intended Audience :: Science/Research", + "License :: OSI Approved :: Apache Software License", + "Natural Language :: English", + "Operating System :: POSIX :: Linux", + "Programming Language :: Python :: 3.9", + "Programming Language :: Python :: 3.10", + "Programming Language :: Python :: 3.11", + "Programming Language :: Python :: 3.12", + "Topic :: Scientific/Engineering :: Physics", +] + + +requires-python = ">=3.10" + +dependencies = [ + "numpy>=1.26", + "pyscf>=2.5", + "jaxlib>=0.4.17", + "jax>=0.4", + "scipy>=0.13", +] + +[project.optional-dependencies] +dev = [ + "qiskit-addon-sqd[test,nbtest,lint,docs]", +] +basetest = [ + "tox>=4.0", + "pytest>=8.0", + "pytest-cov>=5.0", +] +test = [ + "qiskit-addon-sqd[basetest]", +] +nbtest = [ + "qiskit-addon-sqd[basetest]", + "nbmake>=1.5.0", +] +style = [ + "ruff==0.6.4", + "nbqa>=1.8.5", +] +lint = [ + "qiskit-addon-sqd[style]", + "mypy==1.11.2", + "pylint>=3.2.7", + "pydocstyle==6.3", + "reno>=4.1", + "toml>=0.9.6", +] +notebook-dependencies = [ + "qiskit-addon-sqd", + "matplotlib", + "ffsim", + "qiskit", + "qiskit-ibm-runtime", +] +docs = [ + "qiskit-addon-sqd[basetest,notebook-dependencies]", + "qiskit-sphinx-theme~=2.0.0", + "jupyter-sphinx", + "sphinx-design", + "sphinx-autodoc-typehints", + "sphinx-copybutton", + "nbsphinx>=0.9.4", + "reno>=4.1", +] + +[tool.hatch.build.targets.wheel] +only-include = [ + "qiskit_addon_sqd", +] + +[tool.hatch.metadata] +allow-direct-references = true + +[tool.mypy] +python_version = "3.10" +show_error_codes = true +warn_return_any = true +warn_unused_configs = true +ignore_missing_imports = true + +[tool.pylint.main] +py-version = "3.10" + +[tool.pylint."messages control"] +disable = ["all"] +enable = [ + "reimported", + "no-self-use", + "no-else-raise", + "redefined-argument-from-local", + "redefined-builtin", + "raise-missing-from", + "cyclic-import", + "unused-argument", + "attribute-defined-outside-init", + "no-else-return", +] + +[tool.pytest.ini_options] +testpaths = ["./qiskit_addon_sqd/", "./test/"] + +[tool.ruff] +line-length = 100 +src = ["qiskit_addon_sqd", "test"] +target-version = "py39" + +[tool.ruff.lint] +select = [ + "I", # isort + "E", # pycodestyle + "W", # pycodestyle + "F", # pyflakes + "RUF", # ruff + "UP", # pyupgrade + "SIM", # flake8-simplify + "B", # flake8-bugbear + "A", # flake8-builtins +] +ignore = [ + "E501", # line too long +] + +[tool.ruff.lint.pylint] +max-args = 6 + +[tool.ruff.lint.extend-per-file-ignores] +"docs/**/*" = [ + "E402", # module level import not at top of file +] + +[tool.typos.default.extend-words] +IY = "IY" diff --git a/qiskit_addon_sqd/__init__.py b/qiskit_addon_sqd/__init__.py new file mode 100644 index 0000000..f823093 --- /dev/null +++ b/qiskit_addon_sqd/__init__.py @@ -0,0 +1,31 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Primary SQD functionality. + +.. currentmodule:: qiskit_addon_sqd + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + +Modules +======= +.. autosummary:: + :toctree: + + configuration_recovery + subsampling + counts + fermion + qubit +""" diff --git a/qiskit_addon_sqd/configuration_recovery.py b/qiskit_addon_sqd/configuration_recovery.py new file mode 100644 index 0000000..f2040bb --- /dev/null +++ b/qiskit_addon_sqd/configuration_recovery.py @@ -0,0 +1,297 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Functions for performing self-consistent configuration recovery. + +.. currentmodule:: qiskit_addon_sqd.configuration_recovery + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + post_select_by_hamming_weight + recover_configurations +""" + +from __future__ import annotations + +from collections.abc import Sequence + +import numpy as np + + +def post_select_by_hamming_weight( + bitstring_matrix: np.ndarray, hamming_left: int, hamming_right: int +) -> np.ndarray: + """ + Post-select bitstrings based on the hamming weight of each half. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring + hamming_left: The target hamming weight of the left half of bitstrings + hamming_right: The target hamming weight of the right half of bitstrings + + Returns: + A mask signifying which samples were selected from the input matrix. + """ + if hamming_left < 0 or hamming_right < 0: + raise ValueError("Hamming weights must be non-negative integers.") + num_bits = bitstring_matrix.shape[1] + + # Find the bitstrings with correct hamming weight on both halves + up_keepers = np.sum(bitstring_matrix[:, : num_bits // 2], axis=1) == hamming_left + down_keepers = np.sum(bitstring_matrix[:, num_bits // 2 :], axis=1) == hamming_right + correct_bs_mask = np.array(np.logical_and(up_keepers, down_keepers)) + + return correct_bs_mask + + +def recover_configurations( + bitstring_matrix: np.ndarray, + probabilities: Sequence[float], + avg_occupancies: np.ndarray, + hamming_left: int, + hamming_right: int, + rand_seed: int | None = None, +) -> tuple[np.ndarray, np.ndarray]: + """ + Refine bitstrings based on average orbital occupancy and a target hamming weight. + + This function makes the assumption that bit ``i`` represents the same orbital as + bit ``i + # orbitals`` in all input bitstrings, s.t. ``i < # orbitals``. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring + probabilities: A 1D array specifying a probability distribution over the bitstrings + avg_occupancies: A 1D array containing the mean occupancy of each orbital. It is assumed + that ``avg_occupancies[i]`` corresponds to the orbital represented by column + ``i`` in ``bitstring_matrix``. + hamming_left: The target hamming weight used for the left half of the bitstring + hamming_right: The target hamming weight used for the right half of the bitstring + rand_seed: A seed to control random behavior + + Returns: + A corrected bitstring matrix and an updated probability array + """ + if hamming_left < 0 or hamming_right < 0: + raise ValueError("Hamming weights must be non-negative integers.") + + # First, we need to flip the orbitals such that + + corrected_dict: dict[str, float] = {} + for bitstring, freq in zip(bitstring_matrix, probabilities): + bs_corrected = _bipartite_bitstring_correcting( + bitstring, + avg_occupancies, + hamming_left, + hamming_right, + rand_seed=rand_seed, + ) + bs_str = np.array2string(bs_corrected.astype(int), separator="")[1:-1] + corrected_dict[bs_str] = corrected_dict.get(bs_str, 0.0) + freq + bs_mat_out = np.array([[bit == "1" for bit in bs] for bs in corrected_dict]) + freqs_out = np.array([f for f in corrected_dict.values()]) + freqs_out = np.abs(freqs_out) / np.sum(np.abs(freqs_out)) + + return bs_mat_out, freqs_out + + +def _p_flip_0_to_1(ratio_exp: float, occ: float, eps: float = 0.01) -> float: + """ + Calculate the probability of flipping a bit from 0 to 1. + + This function will more aggressively flip bits which are in disagreement + with the occupation information. + + Args: + ratio_exp: The ratio of 1's expected in the set of bits + occ: The occupancy of a particular bit, based estimated ground + state found at the end of each configuration recovery iteration. + eps: A value for controlling how aggressively to flip bits + + Returns: + The probability with which to flip the bit + """ + # Occupancy is < than naive expectation. + # Flip 0s to 1 with small (~eps) probability in this case + if occ < ratio_exp: + return occ * eps / ratio_exp + + # Occupancy is >= naive expectation. + # The probability to flip the bit increases linearly from ``eps`` to + # ``~1.0`` as the occupation deviates further from the expected ratio + slope = (1 - eps) / (1 - ratio_exp) + intercept = 1 - slope + return occ * slope + intercept + + +def _p_flip_1_to_0(ratio_exp: float, occ: float, eps: float = 0.01) -> float: + """ + Calculate the probability of flipping a bit from 1 to 0. + + This function will more aggressively flip bits which are in disagreement + with the occupation information. + + Args: + ratio_exp: The ratio of 1's expected in the set of bits + occ: The occupancy of a particular bit, based estimated ground + state found at the end of each configuration recovery iteration. + eps: A value for controlling how aggressively to flip bits + + Returns: + The probability with which to flip the bit + """ + # Occupancy is < naive expectation. + # The probability to flip the bit increases linearly from ``eps`` to + # ``~1.0`` as the occupation deviates further from the expected ratio + if occ < 1.0 - ratio_exp: + slope = (1.0 - eps) / (1.0 - ratio_exp) + return 1.0 - occ * slope + + # Occupancy is >= naive expectation. + # Flip 1s to 0 with small (~eps) probability in this case + slope = -eps / ratio_exp + intercept = eps / ratio_exp + return occ * slope + intercept + + +def _bipartite_bitstring_correcting( + bit_array: np.ndarray, + avg_occupancies: np.ndarray, + hamming_left: int, + hamming_right: int, + rand_seed: int | None = None, +) -> np.ndarray: + """ + Use occupancy information and target hamming weight to correct a bitstring. + + Args: + bit_array: A 1D array of ``bool`` representations of bit values + avg_occupancies: A 1D array containing the mean occupancy of each orbital. + hamming_left: The target hamming weight used for the left half of the bitstring + hamming_right: The target hamming weight used for the right half of the bitstring + rand_seed: A seed to control random behavior + + Returns: + A corrected bitstring + """ + # This function must not mutate the input arrays. + bit_array = bit_array.copy() + + np.random.seed(rand_seed) + + # The number of bits should be even + num_bits = bit_array.shape[0] + partition_size = num_bits // 2 + + # Get the probability of flipping each bit, separated into LEFT and RIGHT subsystems, + # based on the avg occupancy of each bit and the target hamming weight + probs_left = np.zeros(partition_size) + probs_right = np.zeros(partition_size) + for i in range(partition_size): + if bit_array[i]: + probs_left[i] = _p_flip_1_to_0( + hamming_left / float(partition_size), avg_occupancies[i], 0.01 + ) + else: + probs_left[i] = _p_flip_0_to_1( + hamming_left / float(partition_size), avg_occupancies[i], 0.01 + ) + + if bit_array[i + partition_size]: + probs_right[i] = _p_flip_1_to_0( + hamming_right / float(partition_size), avg_occupancies[i], 0.01 + ) + else: + probs_right[i] = _p_flip_0_to_1( + hamming_right / float(partition_size), avg_occupancies[i], 0.01 + ) + + # Normalize + probs_left = np.absolute(probs_left) + probs_right = np.absolute(probs_right) + probs_left = probs_left / np.sum(probs_left) + probs_right = probs_right / np.sum(probs_right) + + ######################## Handle LEFT bits ######################## + + # Get difference between # of 1s and expected # of 1s in LEFT bits + n_left = np.sum(bit_array[:partition_size]) + n_diff = n_left - hamming_left + + # Too many electrons in LEFT bits + if n_diff > 0: + indices_occupied = np.where(bit_array[:partition_size])[0] + # Get the probabilities that each 1 should be flipped to 0 + p_choice = probs_left[bit_array[:partition_size]] / np.sum( + probs_left[bit_array[:partition_size]] + ) + # Correct the hamming by probabilistically flipping some bits to flip to 0 + indices_to_flip = np.random.choice( + indices_occupied, size=round(n_diff), replace=False, p=p_choice + ) + bit_array[:partition_size][indices_to_flip] = False + + # too few electrons in LEFT bits + if n_diff < 0: + indices_empty = np.where(np.logical_not(bit_array[:partition_size]))[0] + # Get the probabilities that each 0 should be flipped to 1 + p_choice = probs_left[np.logical_not(bit_array[:partition_size])] / np.sum( + probs_left[np.logical_not(bit_array[:partition_size])] + ) + # Correct the hamming by probabilistically flipping some bits to flip to 1 + indices_to_flip = np.random.choice( + indices_empty, size=round(np.abs(n_diff)), replace=False, p=p_choice + ) + bit_array[:partition_size][indices_to_flip] = np.logical_not( + bit_array[:partition_size][indices_to_flip] + ) + + ######################## Handle RIGHT bits ######################## + + # Get difference between # of 1s and expected # of 1s in RIGHT bits + n_right = np.sum(bit_array[partition_size:]) + n_diff = n_right - hamming_right + + # too many electrons in RIGHT bits + if n_diff > 0: + indices_occupied = np.where(bit_array[partition_size:])[0] + # Get the probabilities that each 1 should be flipped to 0 + p_choice = probs_right[bit_array[partition_size:]] / np.sum( + probs_right[bit_array[partition_size:]] + ) + # Correct the hamming by probabilistically flipping some bits to flip to 0 + indices_to_flip = np.random.choice( + indices_occupied, size=round(n_diff), replace=False, p=p_choice + ) + bit_array[partition_size:][indices_to_flip] = np.logical_not( + bit_array[partition_size:][indices_to_flip] + ) + + # too few electrons in RIGHT bits + if n_diff < 0: + indices_empty = np.where(np.logical_not(bit_array[partition_size:]))[0] + # Get the probabilities that each 1 should be flipped to 0 + p_choice = probs_right[np.logical_not(bit_array[partition_size:])] / np.sum( + probs_right[np.logical_not(bit_array[partition_size:])] + ) + # Correct the hamming by probabilistically flipping some bits to flip to 1 + indices_to_flip = np.random.choice( + indices_empty, size=round(np.abs(n_diff)), replace=False, p=p_choice + ) + bit_array[partition_size:][indices_to_flip] = np.logical_not( + bit_array[partition_size:][indices_to_flip] + ) + + return bit_array diff --git a/qiskit_addon_sqd/counts.py b/qiskit_addon_sqd/counts.py new file mode 100644 index 0000000..b4063e1 --- /dev/null +++ b/qiskit_addon_sqd/counts.py @@ -0,0 +1,158 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Functions for transforming counts dictionaries. + +.. currentmodule:: qiskit_addon_sqd.counts + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + counts_to_arrays + generate_counts_uniform + generate_counts_bipartite_hamming + normalize_counts_dict +""" + +from __future__ import annotations + +import numpy as np + + +def counts_to_arrays(counts: dict[str, float | int]) -> tuple[np.ndarray, np.ndarray]: + """ + Convert a counts dictionary into arrays. + + Args: + counts: The dictionary to convert + + Returns: + A tuple containing: + - A 2D array representing the sampled bitstrings. Each row represents a + bitstring, and each element is a ``bool`` representation of the + bit's value + - A 1D array containing the probability with which each bitstring was sampled + """ + if counts == {}: + return np.array([]), np.array([]) + prob_dict = normalize_counts_dict(counts) + bs_mat = np.array([[bit == "1" for bit in bitstring] for bitstring in prob_dict]) + freq_arr = np.array(list(prob_dict.values())) + + return bs_mat, freq_arr + + +def generate_counts_uniform( + num_samples: int, num_bits: int, rand_seed: None | int = None +) -> dict[str, int]: + """ + Generate a bitstring counts dictionary of samples drawn from the uniform distribution. + + Args: + num_samples: The number of samples to draw + num_bits: The number of bits in the bitstrings + rand_seed: A seed for controlling randomness + + Returns: + A dictionary mapping bitstrings of length ``num_bits`` to the + number of times they were sampled. + + Raises: + ValueError: ``num_samples`` and ``num_bits`` must be positive integers. + """ + if num_samples < 1: + raise ValueError("The number of samples must be specified with a positive integer.") + if num_bits < 1: + raise ValueError("The number of bits must be specified with a positive integer.") + np.random.seed(rand_seed) + sample_dict: dict[str, int] = {} + # Use numpy to generate a random matrix of bit values and + # convert it to a dictionary of bitstring samples + bts_matrix = np.random.choice([0, 1], size=(num_samples, num_bits)) + for i in range(num_samples): + bts_arr = bts_matrix[i, :].astype("int") + bts = np.array2string(bts_arr, separator="")[1:-1] + sample_dict[bts] = sample_dict.get(bts, 0) + 1 + + return sample_dict + + +def generate_counts_bipartite_hamming( + num_samples: int, + num_bits: int, + hamming_left: int, + hamming_right: int, + rand_seed: None | int = None, +) -> dict[str, int]: + """ + Generate a bitstring counts dictionary with specified bipartite hamming weight. + + Args: + num_samples: The number of samples to draw + num_bits: The number of bits in the bitstrings + hamming_left: The hamming weight on the left half of each bitstring + hamming_right: The hamming weight on the right half of each bitstring + rand_seed: A seed for controlling randomness + + Returns: + A dictionary mapping bitstrings to the number of times they were sampled. + Each half of each bitstring in the output dictionary will have a hamming + weight as specified by the inputs. + + Raises: + ValueError: ``num_bits`` and ``num_samples`` must be positive integers. + ValueError: Hamming weights must be specified as non-negative integers. + ValueError: ``num_bits`` must be even. + """ + if num_bits % 2 != 0: + raise ValueError("The number of bits must be specified with an even integer.") + if num_samples < 1: + raise ValueError("The number of samples must be specified with a positive integer.") + if num_bits < 1: + raise ValueError("The number of bits must be specified with a positive integer.") + if hamming_left < 0 or hamming_right < 0: + raise ValueError("Hamming weights must be specified as non-negative integers.") + + np.random.seed(rand_seed) + + sample_dict: dict[str, int] = {} + for _ in range(num_samples): + # Pick random bits to flip such that the left and right hamming weights are correct + up_flips = np.random.choice(np.arange(num_bits // 2), hamming_left, replace=False).astype( + "int" + ) + dn_flips = np.random.choice(np.arange(num_bits // 2), hamming_right, replace=False).astype( + "int" + ) + + # Create a bitstring with the chosen bits flipped + bts_arr = np.zeros(num_bits) + bts_arr[up_flips] = 1 + bts_arr[dn_flips + num_bits // 2] = 1 + bts_arr = bts_arr.astype("int") + bts = np.array2string(bts_arr, separator="")[1:-1] + + # Add the bitstring to the sample dict + sample_dict[bts] = sample_dict.get(bts, 0) + 1 + + return sample_dict + + +def normalize_counts_dict(counts: dict[str, float | int]) -> dict[str, float]: + """Convert a counts dictionary into a probability dictionary.""" + if counts == {}: + return counts + + total_counts = float(sum(counts.values())) + + return {bs: count / total_counts for bs, count in counts.items()} diff --git a/qiskit_addon_sqd/fermion.py b/qiskit_addon_sqd/fermion.py new file mode 100644 index 0000000..9ffeb78 --- /dev/null +++ b/qiskit_addon_sqd/fermion.py @@ -0,0 +1,452 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Functions for the study of fermionic systems. + +.. currentmodule:: qiskit_addon_sqd.fermion + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + bitstring_matrix_to_sorted_addresses + enlarge_batch_from_transitions + flip_orbital_occupancies + solve_fermion + optimize_orbitals + rotate_integrals +""" + +from __future__ import annotations + +import numpy as np +from jax import Array, config, grad, jit, vmap +from jax import numpy as jnp +from jax.scipy.linalg import expm +from pyscf import fci +from scipy import linalg as LA + +config.update("jax_enable_x64", True) # To deal with large integers + + +def solve_fermion( + addresses: tuple[np.ndarray, np.ndarray], + hcore: np.ndarray, + eri: np.ndarray, + spin_sq: int | None = None, + max_davidson: int = 100, + verbose: int | None = None, +) -> tuple[float, np.ndarray, list[np.ndarray], float]: + """ + Approximate the ground state given molecular integrals and Slater determinant addresses. + + .. note:: + The ``addresses`` are expected to be unique and sorted. While this will be handled + for the user automatically, this function could become slower if the input + addresses are not sorted or nearly-sorted. + + Args: + addresses: A length-2 tuple of 1D arrays containing sorted, base-10 + representations of bitstrings. The first array represents configurations of the + alpha particles, and the second array represents that of the beta particles. + hcore: Core Hamiltonian matrix representing single-electron integrals + eri: Electronic repulsion integrals representing two-electron integrals + spin_sq: Target value for the total spin squared for the ground state. + If ``None``, no spin will be imposed. + max_davidson: The maximum number of cycles of Davidson's algorithm + verbose: A verbosity level between 0 and 10 + + Returns: + A tuple containing: + - Minimum energy from SCI calculation + - SCI coefficients + - Average orbital occupancy + - Expectation value of spin-squared + + Raises: + ValueError: The input determinant ``addresses`` must be non-empty, sorted arrays of integers. + """ + addresses = _check_addresses(addresses) + + num_up = bin(addresses[0][0])[2:].count("1") + num_dn = bin(addresses[1][0])[2:].count("1") + + # Number of molecular orbitals + norb = hcore.shape[0] + # Call the projection + eigenstate finder + myci = fci.selected_ci.SelectedCI() + if spin_sq is not None: + myci = fci.addons.fix_spin_(myci, ss=spin_sq) + e_sci, coeffs_sci = fci.selected_ci.kernel_fixed_space( + myci, + hcore, + eri, + norb, + (num_up, num_dn), + ci_strs=addresses, + verbose=verbose, + max_cycle=max_davidson, + ) + # Calculate the avg occupancy of each orbital + dm1 = myci.make_rdm1s(coeffs_sci, norb, (num_up, num_dn)) + avg_occupancy = [np.diagonal(dm1[0]), np.diagonal(dm1[1])] + + # Compute total spin + spin_squared = myci.spin_square(coeffs_sci, norb, (num_up, num_dn))[0] + + return e_sci, coeffs_sci, avg_occupancy, spin_squared + + +def optimize_orbitals( + addresses: tuple[np.ndarray, np.ndarray], + hcore: np.ndarray, + eri: np.ndarray, + k_flat: np.ndarray, + *, + spin_sq: float = 0.0, + num_iters: int = 10, + num_steps_grad: int = 10_000, + learning_rate: float = 0.01, + max_davidson: int = 100, +) -> tuple[float, np.ndarray, list[np.ndarray]]: + """ + Optimize orbitals to produce a minimal ground state. + + The process involves iterating over 3 steps: + + For ``num_iters`` iterations: + - Rotate the integrals with respect to the parameters, ``k_flat`` + - Diagonalize and approximate the groundstate energy and wavefunction amplitudes + - Optimize ``k_flat`` using gradient descent and the wavefunction + amplitudes found in Step 2 + + Refer to `Sec. II A 4 `_ for more detailed + discussion on this orbital optimization technique. + + .. note:: + The input ``addresses`` are expected to be unique and sorted. While this will be + handled for the user automatically, this function may become slower if the input + addresses are not sorted or nearly-sorted. + + Args: + addresses: A length-2 tuple of 1D arrays containing sorted, base-10 + representations of bitstrings. The first array represents configurations of the + alpha particles, and the second array represents that of the beta particles. + hcore: Core Hamiltonian matrix representing single-electron integrals + eri: Electronic repulsion integrals representing two-electron integrals + k_flat: 1D array defining the orbital transform. This array will be reshaped + to be of shape (# orbitals, # orbitals) before being used as a + similarity transform operator on the orbitals. Thus ``len(k_flat)=# orbitals**2``. + spin_sq: Target value for the total spin squared for the ground state + num_iters: The number of iterations of orbital optimization to perform + max_davidson: The maximum number of cycles of Davidson's algorithm to + perform during diagonalization. + num_steps_grad: The number of steps of gradient descent to perform + during each optimization iteration + learning_rate: The learning rate to use during gradient descent + + Returns: + A tuple containing: + - The groundstate energy found during the last optimization iteration + - An optimized 1D array defining the orbital transform + - Average orbital occupancy + """ + addresses = _check_addresses(addresses) + + num_up = bin(addresses[0][0])[2:].count("1") + num_dn = bin(addresses[1][0])[2:].count("1") + + # TODO: Need metadata showing the optimization history + ## hcore and eri in physicist ordering + num_orbitals = hcore.shape[0] + k_flat = k_flat.copy() + eri_phys = np.asarray(eri.transpose(0, 2, 3, 1), order="C") # physicist ordering + for _ in range(num_iters): + # Rotate integrals + hcore_rot, eri_rot = rotate_integrals(hcore, eri_phys, k_flat) + eri_rot_chem = np.asarray(eri_rot.transpose(0, 3, 1, 2), order="C") # chemist ordering + + # Solve for ground state with respect to optimized integrals + myci = fci.selected_ci.SelectedCI() + myci = fci.addons.fix_spin_(myci, ss=spin_sq) + e_qsci, amplitudes = fci.selected_ci.kernel_fixed_space( + myci, + hcore_rot, + eri_rot_chem, + num_orbitals, + (num_up, num_dn), + ci_strs=addresses, + max_cycle=max_davidson, + ) + + # Generate the one and two-body reduced density matrices from latest wavefunction amplitudes + dm1, dm2_chem = myci.make_rdm12(amplitudes, num_orbitals, (num_up, num_up)) + dm2 = np.asarray(dm2_chem.transpose(0, 2, 3, 1), order="C") + + # TODO: Expose the momentum parameter as an input option + # Optimize the basis rotations + _optimize_orbitals_sci( + k_flat, learning_rate, 0.9, num_steps_grad, dm1, dm2, hcore, eri_phys + ) + + return e_qsci, k_flat, [np.diagonal(dm1), np.diagonal(dm1)] + + +def rotate_integrals( + hcore: np.ndarray, eri: np.ndarray, k_flat: np.ndarray +) -> tuple[np.ndarray, np.ndarray]: + r""" + Perform a similarity transform on the integrals. + + The transformation is described as: + + .. math:: + + \hat{\widetilde{H}} = \hat{U^{\dagger}}(k)\hat{H}\hat{U}(k) + + For more information on how :math:`\hat{U}` and :math:`\hat{U^{\dagger}}` are generated from ``k_flat`` + and applied to the one- and two-body integrals, refer to `Sec. II A 4 `_. + + Args: + hcore: Core Hamiltonian matrix representing single-electron integrals + eri: Electronic repulsion integrals representing two-electron integrals + k_flat: 1D array defining the orbital transform. Refer to `Sec. II A 4 `_ + for more information on how these values are used to generate the transform operator. + + Returns: + - The rotated core Hamiltonian matrix + - The rotated ERI matrix + """ + num_orbitals = hcore.shape[0] + p = np.reshape(k_flat, (num_orbitals, num_orbitals)) + K = (p - np.transpose(p)) / 2.0 + U = LA.expm(K) + hcore_rot = np.matmul(np.transpose(U), np.matmul(hcore, U)) + eri_rot = np.einsum("pqrs, pi, qj, rk, sl->ijkl", eri, U, U, U, U, optimize=True) + + return np.array(hcore_rot), np.array(eri_rot) + + +def flip_orbital_occupancies(occupancies: np.ndarray) -> np.ndarray: + """ + Flip an orbital occupancy array to match the indexing of a bitstring. + + This function reformats a 1D array of spin-orbital occupancies formatted like: + + ``[occ_a_0, occ_a_1, occ_a_N, occ_b_0, ..., occ_b_N]`` + + To an array formatted like: + + ``[occ_a_N, ..., occ_a_0, occ_b_N, ..., occ_b_0]`` + + where ``N`` is the number of spatial orbitals. + """ + num_orbitals = occupancies.shape[0] // 2 + occ_up = occupancies[:num_orbitals] + occ_dn = occupancies[num_orbitals:] + occ_out = np.zeros(2 * num_orbitals) + occ_out[:num_orbitals] = np.flip(occ_up) + occ_out[num_orbitals:] = np.flip(occ_dn) + + return occ_out + + +def bitstring_matrix_to_sorted_addresses( + bitstring_matrix: np.ndarray, open_shell: bool = False +) -> tuple[np.ndarray, np.ndarray]: + """ + Convert a bitstring matrix into base-10 address representation. + + This function separates each bitstring in ``bitstring_matrix`` in half, translates + each set of bits into integer representations, and appends them to their respective + lists. Those lists are sorted and output from this function. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring + open_shell: A flag specifying whether unique addresses from the left and right + halves of the bitstrings should be kept separate. If ``False``, addresses + from the left and right halves of the bitstrings are combined into a single + set of unique addresses. That combined set will be returned for both the left + and right bitstrings. + + Returns: + A length-2 tuple of sorted, base-10 determinant addresses representing the left + and right halves of the bitstrings, respectively. + """ + num_orbitals = bitstring_matrix.shape[1] // 2 + num_configs = bitstring_matrix.shape[0] + + address_left = np.zeros(num_configs) + address_right = np.zeros(num_configs) + bts_matrix_left = bitstring_matrix[:, :num_orbitals] + bts_matrix_right = bitstring_matrix[:, num_orbitals:] + + # For performance, we accumulate the left and right addresses together, column-wise, + # across the two halves of the input bitstring matrix. + for i in range(num_orbitals): + address_left[:] += bts_matrix_left[:, i] * 2 ** (num_orbitals - 1 - i) + address_right[:] += bts_matrix_right[:, i] * 2 ** (num_orbitals - 1 - i) + + addresses_right = np.unique(address_right.astype("longlong")) + addresses_left = np.unique(address_left.astype("longlong")) + + if not open_shell: + addresses_left = addresses_right = np.union1d(addresses_left, addresses_right) + + return addresses_left, addresses_right + + +def enlarge_batch_from_transitions( + bitstring_matrix: np.ndarray, transition_operators: np.ndarray +) -> np.ndarray: + """ + Apply the set of transition operators to the configurations represented in ``bitstring_matrix``. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring. + transition_operators: A 1D or 2D array ``I``, ``+``, ``-``, and ``n`` strings + representing the action of the identity, creation, annihilation, or number operators. + Each row represents a transition operator. + + Returns: + Bitstring matrix representing the augmented set of electronic configurations after applying + the excitation operators. + """ + diag, create, annihilate = _transition_str_to_bool(transition_operators) + + bitstring_matrix_augmented, mask = apply_excitations(bitstring_matrix, diag, create, annihilate) + + bitstring_matrix_augmented = bitstring_matrix_augmented[mask] + + return np.array(bitstring_matrix_augmented) + + +def _check_addresses( + addresses: tuple[np.ndarray, np.ndarray], +) -> tuple[np.ndarray, np.ndarray]: + """Make sure the hamming weight is consistent in all determinants.""" + addr_up, addr_dn = addresses + addr_up_ham = bin(addr_up[0])[2:].count("1") + for i, addr in enumerate(addr_up): + ham = bin(addr)[2:].count("1") + if ham != addr_up_ham: + raise ValueError( + f"Spin-up address in index 0 has hamming weight {addr_up_ham}, but address in " + f"index {i} has hamming weight {ham}." + ) + addr_dn_ham = bin(addr_dn[0])[2:].count("1") + for i, addr in enumerate(addr_dn): + ham = bin(addr)[2:].count("1") + if ham != addr_dn_ham: + raise ValueError( + f"Spin-down address in index 0 has hamming weight {addr_dn_ham}, but address in " + f"index {i} has hamming weight {ham}." + ) + + return np.sort(np.unique(addr_up)), np.sort(np.unique(addr_dn)) + + +def _optimize_orbitals_sci( + k_flat: np.ndarray, + learning_rate: float, + momentum: float, + num_steps: int, + dm1: np.ndarray, + dm2: np.ndarray, + hcore: np.ndarray, + eri: np.ndarray, +) -> None: + """ + Optimize orbital rotation parameters in-place using gradient descent. + + This procedure is described in `Sec. II A 4 `_. + """ + prev_update = np.zeros(len(k_flat)) + num_orbitals = dm1.shape[0] + for _ in range(num_steps): + grad = _SCISCF_Energy_contract_grad(dm1, dm2, hcore, eri, num_orbitals, k_flat) + prev_update = learning_rate * grad + momentum * prev_update + k_flat -= prev_update + + +def _SCISCF_Energy_contract( + dm1: np.ndarray, + dm2: np.ndarray, + hcore: np.ndarray, + eri: np.ndarray, + num_orbitals: int, + k_flat: np.ndarray, +) -> Array: + """ + Calculate gradient. + + The gradient can be calculated by contracting the bare one and two-body + reduced density matrices with the gradients of the of the one and two-body + integrals with respect to the rotation parameters, ``k_flat``. + """ + p = jnp.reshape(k_flat, (num_orbitals, num_orbitals)) + K = (p - jnp.transpose(p)) / 2.0 + U = expm(K) + hcore_rot = jnp.matmul(jnp.transpose(U), jnp.matmul(hcore, U)) + eri_rot = jnp.einsum("pqrs, pi, qj, rk, sl->ijkl", eri, U, U, U, U) + grad = jnp.sum(dm1 * hcore_rot) + jnp.sum(dm2 * eri_rot / 2.0) + + return grad + + +_SCISCF_Energy_contract_grad = jit(grad(_SCISCF_Energy_contract, argnums=5), static_argnums=4) + + +def _apply_excitation_single( + single_bts: np.ndarray, diag: np.ndarray, create: np.ndarray, annihilate: np.ndarray +) -> tuple[jnp.ndarray, Array]: + falses = jnp.array([False for _ in range(len(diag))]) + + bts_ret = single_bts == diag + create_crit = jnp.all(jnp.logical_or(diag, falses == jnp.logical_and(single_bts, create))) + annihilate_crit = jnp.all(falses == jnp.logical_and(falses == single_bts, annihilate)) + + include_crit = jnp.logical_and(create_crit, annihilate_crit) + + return bts_ret, include_crit + + +_apply_excitation = jit(vmap(_apply_excitation_single, (0, None, None, None), 0)) + +apply_excitations = jit(vmap(_apply_excitation, (None, 0, 0, 0), 0)) + + +def _transition_str_to_bool(string_rep: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Transform string representations of a transition operator into bool representation. + + Transform sequences of identity ("I"), creation ("+"), annihilation ("-"), and number ("n") + characters into the internal representation used to apply the transitions into electronic + configurations. + + Args: + string_rep: A 1D or 2D array of ``I``, ``+``, ``-``, ``n`` strings representing + the action of the identity, creation, annihilation, or number operators. + + Returns: + A 3-tuple: + - A mask signifying the diagonal terms (I). + - A mask signifying whether there is a creation operator (+). + - A mask signifying whether there is an annihilation operator (-). + """ + diag = np.logical_or(string_rep == "I", string_rep == "n") + create = np.logical_or(string_rep == "+", string_rep == "n") + annihilate = np.logical_or(string_rep == "-", string_rep == "n") + + return diag, create, annihilate diff --git a/qiskit_addon_sqd/qubit.py b/qiskit_addon_sqd/qubit.py new file mode 100644 index 0000000..853e66d --- /dev/null +++ b/qiskit_addon_sqd/qubit.py @@ -0,0 +1,220 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Functions for handling quantum samples. + +.. currentmodule:: qiskit_addon_sqd.qubit + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + matrix_elements_from_pauli_string + sort_and_remove_duplicates +""" + +from collections.abc import Sequence +from typing import Any + +import jax.numpy as jnp +import numpy as np +from jax import Array, config, jit, vmap +from numpy.typing import NDArray + +config.update("jax_enable_x64", True) # To deal with large integers + + +def sort_and_remove_duplicates(bitstring_matrix: np.ndarray, inplace: bool = True) -> np.ndarray: + """ + Sort a bitstring matrix and remove duplicate entries. + + The lowest bitstring values will be placed in the lowest-indexed rows. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring. + inplace: Whether to modify the input array in place. + + Returns: + Sorted version of ``bitstring_matrix`` without repeated rows. + """ + if not inplace: + bitstring_matrix = bitstring_matrix.copy() + + base_10 = _base_10_conversion_from_bts_matrix_vmap(bitstring_matrix) + + _, indices = np.unique(base_10, return_index=True) + + return bitstring_matrix[indices, :] + + +def matrix_elements_from_pauli_string( + bitstring_matrix: np.ndarray, pauli_str: Sequence[str] +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Find the matrix elements of a Pauli operator in the subspace defined by the bitstrings. + + .. note:: + The bitstrings in the ``bitstring_matrix`` must be sorted and unique according + to their base-10 representation. Otherwise the projection will return wrong + results. We do not explicitly check for uniqueness and order because this + can be rather time consuming. + + .. note:: + This function relies on ``jax`` to efficiently perform some calculations. ``jax`` + converts the bit arrays to ``int64_t``, which means the bit arrays in + ``bitstring_matrix`` may not have length greater than ``63``. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring. + The bitstrings in the matrix must be sorted according to + their base-10 representation. Otherwise the projection will return + wrong results. + pauli_str: A length-N sequence of single-qubit Pauli strings representing + an N-qubit Pauli operator. The Pauli term for qubit ``i`` should be + in ``pauli_str[i]`` (e.g. ``qiskit.quantum_info.Pauli("XYZ") = ["Z", "Y", "X"]``). + + Returns: + First array corresponds to the nonzero matrix elements + Second array corresponds to the row indices of the elements + Third array corresponds to the column indices of the elements + + Raises: + ValueError: Input bit arrays must have length < ``64``. + """ + d, n_qubits = bitstring_matrix.shape + row_array = np.arange(d) + + if n_qubits > 63: + raise ValueError("Bit arrays must have length < 64.") + + diag, sign, imag = _pauli_str_to_bool(pauli_str) + + base_10_array_rows = _base_10_conversion_from_bts_matrix_vmap(bitstring_matrix) + + bs_mat_conn, matrix_elements = _connected_elements_and_amplitudes_bool_vmap( + bitstring_matrix, diag, sign, imag + ) + + base_10_array_cols = _base_10_conversion_from_bts_matrix_vmap(bs_mat_conn) + + indices = np.isin(base_10_array_cols, base_10_array_rows, assume_unique=True, kind="sort") + + matrix_elements = matrix_elements[indices] + row_array = row_array[indices] + base_10_array_cols = base_10_array_cols[indices] + + col_array = np.searchsorted(base_10_array_rows, base_10_array_cols) + + return matrix_elements, row_array, col_array + + +def _pauli_str_to_bool( + pauli_str: Sequence[str], +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Transform sequences of Pauli strings into arrays. + + An N-qubit Pauli string will be transformed into 3 arrays which represent + the diagonal terms of the Pauli operator. + + Args: + pauli_str: A sequence of single-qubit Pauli strings. + + Returns: + A 3-tuple: + - A mask signifying the diagonal Pauli terms (I, Z). + - A mask signifying whether there is a change in sign between the two rows + of the Pauli matrix (Y, Z). + - A mask signifying whether the Pauli matrix elements are purely imaginary. + """ + diag = [] + sign = [] + imag = [] + for p in pauli_str: + if p == "I" or p == "i": + diag.append(True) + sign.append(False) + imag.append(False) + if p == "X" or p == "x": + diag.append(False) + sign.append(False) + imag.append(False) + if p == "Y" or p == "y": + diag.append(False) + sign.append(True) + imag.append(True) + if p == "Z" or p == "z": + diag.append(True) + sign.append(True) + imag.append(False) + + return np.array(diag), np.array(sign), np.array(imag) + + +def _connected_elements_and_amplitudes_bool( + bit_array: np.ndarray, diag: np.ndarray, sign: np.ndarray, imag: np.ndarray +) -> tuple[NDArray[np.bool_], Array]: + """ + Find the connected element to computational basis state |X>. + + Given a Pauli operator represented by ``{diag, sign, imag}``. + Args: + bit_array: A 1D array of ``bool`` representations of bits. + diag: ``bool`` whether the Pauli operator is diagonal. Only ``True`` + for I and Z. + sign: ``bool`` Whether there is a change of sign in the matrix elements + of the different rows of the Pauli operators. Only True for Y and Z. + imag: ``bool`` whether the matrix elements of the Pauli operator are + purely imaginary + + Returns: + A matrix of bitstrings where each row is the connected element to the + input the matrix element. + """ + bit_array_mask: NDArray[np.bool_] = bit_array == diag + return bit_array_mask, jnp.prod( + (-1) ** (jnp.logical_and(bit_array, sign)) * jnp.array(1j, dtype="complex64") ** (imag) + ) + + +"""Same as ``_connected_elements_and_amplitudes_jnp_bool()`` but allows to deal +with 2D arrays of bitstrings through the ``vmap`` transformation of Jax. Also +JIT compiled. +""" +_connected_elements_and_amplitudes_bool_vmap = jit( + vmap(_connected_elements_and_amplitudes_bool, (0, None, None, None), 0) +) + + +def _base_10_conversion_from_bts_array(bit_array: np.ndarray) -> Any: + """ + Convert a bit array to a base-10 representation. + + NOTE: This can only handle up to 63 qubits. Then the integer will overflow + + Args: + bit_array: A 1D array of ``bool`` representations of bit values. + + Returns: + Base-10 representation of the bit array. + """ + n_qubits = len(bit_array) + base_10_array = 0.0 + for i in range(n_qubits): + base_10_array = base_10_array + bit_array[i] * 2 ** (n_qubits - 1 - i) + + return base_10_array.astype("longlong") # type: ignore + + +_base_10_conversion_from_bts_matrix_vmap = jit(vmap(_base_10_conversion_from_bts_array, 0, 0)) diff --git a/qiskit_addon_sqd/subsampling.py b/qiskit_addon_sqd/subsampling.py new file mode 100644 index 0000000..67c1c88 --- /dev/null +++ b/qiskit_addon_sqd/subsampling.py @@ -0,0 +1,153 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Functions for creating batches of samples from a bitstring matrix. + +.. currentmodule:: qiskit_addon_sqd.subsampling + +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: + + subsample + postselect_and_subsample +""" + +from __future__ import annotations + +import numpy as np + +from .configuration_recovery import post_select_by_hamming_weight + + +def postselect_and_subsample( + bitstring_matrix: np.ndarray, + probabilities: np.ndarray, + hamming_left: int, + hamming_right: int, + samples_per_batch: int, + num_batches: int, + rand_seed: int | None = None, +) -> list[np.ndarray]: + """ + Subsample batches of bit arrays with correct hamming weight from an input ``bitstring_matrix``. + + Bitstring samples with incorrect hamming weight on either their left or right half will not + be sampled. + + Each individual batch will be sampled without replacement from the input ``bitstring_matrix``. + Samples will be replaced after creation of each batch, so different batches may contain + identical samples. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring. + probabilities: A 1D array specifying a probability distribution over the bitstrings + hamming_left: The target hamming weight for the left half of sampled bitstrings + hamming_right: The target hamming weight for the right half of sampled bitstrings + samples_per_batch: The number of samples to draw for each batch + num_batches: The number of batches to generate + rand_seed: A seed to control random behavior + + Returns: + A list of bitstring matrices with correct hamming weight subsampled from the input bitstring matrix + + Raises: + ValueError: The number of elements in ``probabilities`` must equal the number of rows in ``bitstring_matrix``. + ValueError: Hamming weights must be non-negative integers. + ValueError: Samples per batch and number of batches must be positive integers. + """ + if bitstring_matrix.shape[0] < 1: + return [np.array([])] * num_batches + if len(probabilities) != bitstring_matrix.shape[0]: + raise ValueError( + "The number of elements in the probabilities array must match the number of rows in the bitstring matrix." + ) + if hamming_left < 0 or hamming_right < 0: + raise ValueError("Hamming weight must be specified with a non-negative integer.") + + # Post-select only bitstrings with correct hamming weight + mask_postsel = post_select_by_hamming_weight(bitstring_matrix, hamming_left, hamming_right) + bs_mat_postsel = bitstring_matrix[mask_postsel] + probs_postsel = probabilities[mask_postsel] + probs_postsel = np.abs(probs_postsel) / np.sum(np.abs(probs_postsel)) + + if len(probs_postsel) == 0: + return [np.array([])] * num_batches + + return subsample(bs_mat_postsel, probs_postsel, samples_per_batch, num_batches, rand_seed) + + +def subsample( + bitstring_matrix: np.ndarray, + probabilities: np.ndarray, + samples_per_batch: int, + num_batches: int, + rand_seed: int | None = None, +) -> list[np.ndarray]: + """ + Subsample batches of bit arrays from an input ``bitstring_matrix``. + + Each individual batch will be sampled without replacement from the input ``bitstring_matrix``. + Samples will be replaced after creation of each batch, so different batches may contain + identical samples. + + Args: + bitstring_matrix: A 2D array of ``bool`` representations of bit + values such that each row represents a single bitstring. + probabilities: A 1D array specifying a probability distribution over the bitstrings + samples_per_batch: The number of samples to draw for each batch + num_batches: The number of batches to generate + rand_seed: A seed to control random behavior + + Returns: + A list of bitstring matrices subsampled from the input bitstring matrix. + + Raises: + ValueError: The number of elements in ``probabilities`` must equal the number of rows in ``bitstring_matrix``. + ValueError: Samples per batch and number of batches must be positive integers. + """ + if bitstring_matrix.shape[0] < 1: + return [np.array([])] * num_batches + if len(probabilities) != bitstring_matrix.shape[0]: + raise ValueError( + "The number of elements in the probabilities array must match the number of rows in the bitstring matrix." + ) + if samples_per_batch < 1: + raise ValueError("Samples per batch must be specified with a positive integer.") + if num_batches < 1: + raise ValueError("The number of batches must be specified with a positive integer.") + + np.random.seed(rand_seed) + num_bitstrings = bitstring_matrix.shape[0] + + # If the number of requested samples is >= the number of bitstrings, return + # num_batches copies of the input array. + randomly_sample = True + if samples_per_batch >= num_bitstrings: + randomly_sample = False + indices = np.arange(num_bitstrings).astype("int") + + # Create batches of samples + batches = [] + for _ in range(num_batches): + if randomly_sample: + indices = np.random.choice( + np.arange(num_bitstrings).astype("int"), + samples_per_batch, + replace=False, + p=probabilities, + ) + + batches.append(bitstring_matrix[indices]) + + return batches diff --git a/test/README.md b/test/README.md new file mode 100644 index 0000000..30e619e --- /dev/null +++ b/test/README.md @@ -0,0 +1,95 @@ +# Test environments + +This repository's tests and development automation tasks are organized using [tox], a command-line CI frontend for Python projects. tox is typically used during local development and is also invoked from this repository's GitHub Actions [workflows](../.github/workflows/). + +tox can be installed by running `pip install tox`. + +tox is organized around various "environments," each of which is described below. To run _all_ test environments, run `tox` without any arguments: + +```sh +$ tox +``` + +Environments for this repository are configured in [`tox.ini`] as described below. + +## Lint environment + +The `lint` environment ensures that the code meets basic coding standards, including + +- [_Black_] formatting style +- Style checking with [ruff], [autoflake], and [pydocstyle] +- [mypy] type annotation checker, as configured by [`.mypy.ini`] + +The _Black_ and mypy passes are applied also to [Jupyter] notebooks (via [nbqa]). + +To run: + +```sh +$ tox -e lint +``` + +## Style environment + +The command `tox -e style` will apply automated style fixes. This includes: + +- Automated fixes from [ruff] and [autoflake] +- Reformatting of all files in the repository according to _Black_ style + +## Test (py##) environments + +The `py##` environments are the main test environments. tox defines one for each version of Python. For instance, the following command will run the tests on Python 3.10, Python 3.11, and Python 3.12: + +```sh +$ tox -e py310,py311,py312 +``` + +These environments execute all tests using [pytest], which supports its own simple style of tests, in addition to [unittest]-style tests. + +## Notebook environments + +The `notebook` and `py##-notebook` environments invoke [nbmake] to ensure that all the Jupyter notebooks in the [`docs/`](/docs/tutorials) directory execute successfully. + +```sh +$ tox -e py310-notebook +``` + +## Coverage environment + +The `coverage` environment uses [Coverage.py] to ensure that the fraction of code tested by pytest is above some threshold (enforced to be 100% for new modules). A detailed, line-by-line coverage report can be viewed by navigating to `htmlcov/index.html` in a web browser. + +To run: + +```sh +$ tox -e coverage +``` + +## Documentation environment + +The `docs` environment builds the [Sphinx] documentation locally. + +For the documentation build to succeed, [pandoc](https://pandoc.org/) must be installed. Pandoc is not available via pip, so must be installed through some other means. Linux users are encouraged to install it through their package manager (e.g., `sudo apt-get install -y pandoc`), while macOS users are encouraged to install it via [Homebrew](https://brew.sh/) (`brew install pandoc`). Full instructions are available on [pandoc's installation page](https://pandoc.org/installing.html). + +To run this environment: + +```sh +$ tox -e docs +``` + +If the build succeeds, it can be viewed by navigating to `docs/_build/html/index.html` in a web browser. + +[tox]: https://github.com/tox-dev/tox +[`tox.ini`]: ../tox.ini +[mypy]: https://mypy.readthedocs.io/en/stable/ +[`.mypy.ini`]: ../.mypy.ini +[nbmake]: https://github.com/treebeardtech/nbmake +[_Black_]: https://github.com/psf/black +[ruff]: https://github.com/charliermarsh/ruff +[autoflake]: https://github.com/PyCQA/autoflake +[pydocstyle]: https://www.pydocstyle.org/en/stable/ +[pylint]: https://github.com/PyCQA/pylint +[nbqa]: https://github.com/nbQA-dev/nbQA +[Jupyter]: https://jupyter.org/ +[pytest]: https://docs.pytest.org/ +[unittest]: https://docs.python.org/3/library/unittest.html +[Coverage.py]: https://coverage.readthedocs.io/ +[Sphinx]: https://www.sphinx-doc.org/ diff --git a/test/__init__.py b/test/__init__.py new file mode 100644 index 0000000..75efffe --- /dev/null +++ b/test/__init__.py @@ -0,0 +1,10 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. diff --git a/test/test_configuration_recovery.py b/test/test_configuration_recovery.py new file mode 100644 index 0000000..74d0e73 --- /dev/null +++ b/test/test_configuration_recovery.py @@ -0,0 +1,19 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for configuration_recovery submodule.""" + +import unittest + + +class TestConfigurationRecovery(unittest.TestCase): + def test_configuration_recovery(self): + pass diff --git a/test/test_counts.py b/test/test_counts.py new file mode 100644 index 0000000..a48f446 --- /dev/null +++ b/test/test_counts.py @@ -0,0 +1,148 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for the counts module.""" + +import unittest + +import pytest +from qiskit_addon_sqd.counts import ( + counts_to_arrays, + generate_counts_bipartite_hamming, + generate_counts_uniform, + normalize_counts_dict, +) + + +class TestCounts(unittest.TestCase): + def setUp(self): + self.max_val = 16 + self.counts = {bin(i)[2:].zfill(4): 100 for i in range(self.max_val)} + + def test_counts_to_arrays(self): + with self.subTest("Basic test"): + bitstring_matrix, probs = counts_to_arrays(self.counts) + self.assertEqual(self.max_val, bitstring_matrix.shape[0]) + self.assertEqual(4, bitstring_matrix.shape[1]) + self.assertEqual(self.max_val, len(probs)) + uniform_prob = 1 / bitstring_matrix.shape[0] + for p in probs: + self.assertEqual(uniform_prob, p) + with self.subTest("Null test"): + counts = {} + bitstring_matrix, probs = counts_to_arrays(counts) + self.assertEqual((0,), bitstring_matrix.shape) + self.assertEqual((0,), probs.shape) + + def test_generate_counts_uniform(self): + with self.subTest("Basic test"): + num_samples = 10 + num_bits = 4 + counts = generate_counts_uniform(num_samples, num_bits) + self.assertLessEqual(len(counts), num_samples) + for bs in counts: + self.assertEqual(num_bits, len(bs)) + with self.subTest("Non-positive num_bits"): + num_samples = 10 + num_bits = 0 + with pytest.raises(ValueError) as e_info: + generate_counts_uniform(num_samples, num_bits) + self.assertEqual( + "The number of bits must be specified with a positive integer.", + e_info.value.args[0], + ) + with self.subTest("Non-positive num_samples"): + num_samples = 0 + num_bits = 4 + with pytest.raises(ValueError) as e_info: + generate_counts_uniform(num_samples, num_bits) + self.assertEqual( + "The number of samples must be specified with a positive integer.", + e_info.value.args[0], + ) + + def test_generate_counts_bipartite_hamming(self): + with self.subTest("Basic test"): + num_samples = 10 + num_bits = 8 + hamming_left = 3 + hamming_right = 2 + counts = generate_counts_bipartite_hamming( + num_samples, num_bits, hamming_left, hamming_right + ) + self.assertLessEqual(len(counts), num_samples) + for bs in counts: + ham_l = sum([b == "1" for b in bs[: num_bits // 2]]) + ham_r = sum([b == "1" for b in bs[num_bits // 2 :]]) + self.assertEqual(num_bits, len(bs)) + self.assertEqual(hamming_left, ham_l) + self.assertEqual(hamming_right, ham_r) + with self.subTest("Uneven num bits"): + num_samples = 10 + num_bits = 7 + hamming_left = 3 + hamming_right = 2 + with pytest.raises(ValueError) as e_info: + generate_counts_bipartite_hamming( + num_samples, num_bits, hamming_left, hamming_right + ) + self.assertEqual( + "The number of bits must be specified with an even integer.", e_info.value.args[0] + ) + with self.subTest("Non-positive num_samples"): + num_samples = 0 + num_bits = 8 + hamming_left = 3 + hamming_right = 2 + with pytest.raises(ValueError) as e_info: + generate_counts_bipartite_hamming( + num_samples, num_bits, hamming_left, hamming_right + ) + self.assertEqual( + "The number of samples must be specified with a positive integer.", + e_info.value.args[0], + ) + with self.subTest("Non-positive num_bits"): + num_samples = 10 + num_bits = 0 + hamming_left = 3 + hamming_right = 2 + with pytest.raises(ValueError) as e_info: + generate_counts_bipartite_hamming( + num_samples, num_bits, hamming_left, hamming_right + ) + self.assertEqual( + "The number of bits must be specified with a positive integer.", + e_info.value.args[0], + ) + with self.subTest("Negative hamming"): + num_samples = 10 + num_bits = 8 + hamming_left = -1 + hamming_right = -1 + with pytest.raises(ValueError) as e_info: + generate_counts_bipartite_hamming( + num_samples, num_bits, hamming_left, hamming_right + ) + self.assertEqual( + "Hamming weights must be specified as non-negative integers.", e_info.value.args[0] + ) + + def test_normalize_counts(self): + with self.subTest("Basic test"): + counts_norm = normalize_counts_dict(self.counts) + uniform_prob = 1 / self.max_val + for prob in counts_norm.values(): + self.assertEqual(uniform_prob, prob) + with self.subTest("Null test"): + counts = {} + counts_norm = normalize_counts_dict(counts) + self.assertEqual(counts_norm, counts) diff --git a/test/test_fermion.py b/test/test_fermion.py new file mode 100644 index 0000000..e41c5b9 --- /dev/null +++ b/test/test_fermion.py @@ -0,0 +1,19 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for the fermion module.""" + +import unittest + + +class TestFermion(unittest.TestCase): + def test_fermion(self): + pass diff --git a/test/test_qubit.py b/test/test_qubit.py new file mode 100644 index 0000000..dde3c5b --- /dev/null +++ b/test/test_qubit.py @@ -0,0 +1,19 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for the qubit module.""" + +import unittest + + +class TestQubit(unittest.TestCase): + def test_qubit(self): + pass diff --git a/test/test_subsampling.py b/test/test_subsampling.py new file mode 100644 index 0000000..174715d --- /dev/null +++ b/test/test_subsampling.py @@ -0,0 +1,275 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Unit tests for subsampling module.""" + +import unittest + +import numpy as np +import pytest +from qiskit_addon_sqd.subsampling import postselect_and_subsample, subsample + + +class TestSubsampling(unittest.TestCase): + def setUp(self): + # 4 qubit full sampling + self.bitstring_matrix = np.array( + [ + [False, False, False, False], + [False, False, False, True], + [False, False, True, False], + [False, False, True, True], + [False, True, False, False], + [False, True, False, True], + [False, True, True, False], + [False, True, True, True], + [True, False, False, False], + [True, False, False, True], + [True, False, True, False], + [True, False, True, True], + [True, True, False, False], + [True, True, False, True], + [True, True, True, False], + [True, True, True, True], + ] + ) + self.uniform_probs = np.array( + [1 / self.bitstring_matrix.shape[0] for _ in self.bitstring_matrix] + ) + + def test_subsample(self): + with self.subTest("Basic test"): + samples_per_batch = 2 + num_batches = 10 + batches = subsample( + self.bitstring_matrix, self.uniform_probs, samples_per_batch, num_batches + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(samples_per_batch, batch.shape[0]) + with self.subTest("Test probability specification"): + samples_per_batch = 2 + num_batches = 10 + batches = subsample( + self.bitstring_matrix, self.uniform_probs, samples_per_batch, num_batches + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(samples_per_batch, batch.shape[0]) + with self.subTest("Full sampling"): + samples_per_batch = 20 + num_batches = 1 + batches = subsample( + self.bitstring_matrix, self.uniform_probs, samples_per_batch, num_batches + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(self.bitstring_matrix.shape[0], batch.shape[0]) + + with self.subTest("Non-positive batch size"): + samples_per_batch = 0 + num_batches = 10 + with pytest.raises(ValueError) as e_info: + subsample( + self.bitstring_matrix, + self.uniform_probs, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "Samples per batch must be specified with a positive integer." + ) + with self.subTest("Non-positive num batches"): + samples_per_batch = 1 + num_batches = 0 + with pytest.raises(ValueError) as e_info: + subsample( + self.bitstring_matrix, + self.uniform_probs, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "The number of batches must be specified with a positive integer." + ) + with self.subTest("Mismatching probs"): + samples_per_batch = 1 + num_batches = 1 + with pytest.raises(ValueError) as e_info: + subsample( + self.bitstring_matrix, + np.array([]), + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "The number of elements in the probabilities array must match the number of rows in the bitstring matrix." + ) + with self.subTest("Empty matrix"): + samples_per_batch = 1 + num_batches = 1 + batches = subsample( + np.array([]), + np.array([]), + samples_per_batch, + num_batches, + ) + self.assertEqual(num_batches, len(batches)) + self.assertEqual(0, batches[0].shape[0]) + + def test_postselect_and_subsample(self): + with self.subTest("Basic test"): + samples_per_batch = 2 + num_batches = 10 + hamming_left = 1 + hamming_right = 1 + partition_len = self.bitstring_matrix.shape[1] // 2 + batches = postselect_and_subsample( + self.bitstring_matrix, + self.uniform_probs, + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(samples_per_batch, batch.shape[0]) + for bitstring in batch: + self.assertEqual(hamming_left, np.sum(bitstring[:partition_len])) + self.assertEqual(hamming_right, np.sum(bitstring[partition_len:])) + with self.subTest("Zero hamming"): + samples_per_batch = 2 + num_batches = 10 + hamming_left = 0 + hamming_right = 0 + partition_len = self.bitstring_matrix.shape[1] // 2 + batches = postselect_and_subsample( + self.bitstring_matrix, + self.uniform_probs, + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(1, batch.shape[0]) + bitstring = batch[0] + self.assertEqual(hamming_left, np.sum(bitstring[:partition_len])) + self.assertEqual(hamming_right, np.sum(bitstring[partition_len:])) + with self.subTest("Empty after postselection"): + samples_per_batch = 2 + num_batches = 10 + hamming_left = 0 + hamming_right = 0 + partition_len = self.bitstring_matrix.shape[1] // 2 + batches = postselect_and_subsample( + self.bitstring_matrix[1:], + self.uniform_probs[1:], + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + self.assertEqual(num_batches, len(batches)) + for batch in batches: + self.assertEqual(0, batch.shape[0]) + with self.subTest("Negative hamming"): + samples_per_batch = 2 + num_batches = 10 + hamming_left = -1 + hamming_right = -1 + with pytest.raises(ValueError) as e_info: + postselect_and_subsample( + self.bitstring_matrix, + self.uniform_probs, + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "Hamming weight must be specified with a non-negative integer." + ) + with self.subTest("Non-positive batch size"): + samples_per_batch = 0 + num_batches = 10 + hamming_left = 1 + hamming_right = 1 + with pytest.raises(ValueError) as e_info: + postselect_and_subsample( + self.bitstring_matrix, + self.uniform_probs, + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "Samples per batch must be specified with a positive integer." + ) + with self.subTest("Non-positive num batches"): + samples_per_batch = 1 + num_batches = 0 + hamming_left = 1 + hamming_right = 1 + with pytest.raises(ValueError) as e_info: + postselect_and_subsample( + self.bitstring_matrix, + self.uniform_probs, + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "The number of batches must be specified with a positive integer." + ) + with self.subTest("Mismatching probs"): + samples_per_batch = 1 + num_batches = 1 + hamming_left = 1 + hamming_right = 1 + with pytest.raises(ValueError) as e_info: + postselect_and_subsample( + self.bitstring_matrix, + np.array([]), + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + assert ( + e_info.value.args[0] + == "The number of elements in the probabilities array must match the number of rows in the bitstring matrix." + ) + with self.subTest("Empty matrix"): + samples_per_batch = 1 + num_batches = 1 + hamming_left = 1 + hamming_right = 1 + batches = postselect_and_subsample( + np.array([]), + np.array([]), + hamming_left, + hamming_right, + samples_per_batch, + num_batches, + ) + self.assertEqual(num_batches, len(batches)) + self.assertEqual(0, batches[0].shape[0]) diff --git a/test/test_workflow.py b/test/test_workflow.py new file mode 100644 index 0000000..ab616e7 --- /dev/null +++ b/test/test_workflow.py @@ -0,0 +1,19 @@ +# This code is a Qiskit project. + +# (C) Copyright IBM 2024. + +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Full test of workflow on minimal N2 example.""" + +import unittest + + +class TestSQD(unittest.TestCase): + def test_sqd(self): + pass diff --git a/tox.ini b/tox.ini new file mode 100644 index 0000000..0508dd3 --- /dev/null +++ b/tox.ini @@ -0,0 +1,67 @@ +[tox] +minversion = 4.0 +envlist = py{39,310,311,312}{,-notebook}, lint +isolated_build = True + +[testenv] +passenv = + SSH_AUTH_SOCK +extras = + test +commands = + pytest {posargs} + +[testenv:style] +extras = + style +commands = + ruff format qiskit_addon_sqd/ docs/ test/ + ruff check --fix qiskit_addon_sqd/ docs/ test/ + nbqa ruff --fix docs/ + +[testenv:lint] +basepython = python3.10 +extras = + lint +commands = + ruff format --check qiskit_addon_sqd/ docs/ test/ + ruff check qiskit_addon_sqd/ docs/ test/ + nbqa ruff docs/ + mypy qiskit_addon_sqd/ + #reno lint + pylint -rn qiskit_addon_sqd/ test/ + nbqa pylint -rn docs/ + pydocstyle qiskit_addon_sqd/ + +[testenv:{,py-,py3-,py39-,py310-,py311-,py312-}notebook] +extras = + nbtest + notebook-dependencies +commands = + pytest --nbmake --nbmake-timeout=3000 {posargs} docs/tutorials/ + +[testenv:coverage] +deps = + coverage>=7.5 +extras = + test +commands = + coverage3 run --source qiskit_addon_sqd --parallel-mode -m pytest test/ {posargs} + coverage3 combine + coverage3 html + coverage3 report --fail-under=100 --show-missing + +[testenv:docs] +basepython = python3.10 +extras = + docs +commands = + sphinx-build -j auto -W -T --keep-going -b html {posargs} {toxinidir}/docs/ {toxinidir}/docs/_build/html + +[testenv:docs-clean] +skip_install = true +allowlist_externals = + rm + mypy +commands = + rm -rf {toxinidir}/docs/stubs/ {toxinidir}/docs/_build/