[](https://github.com/vprusso/toqito/actions/workflows/build-test-actions.yml)
[](https://toqito.readthedocs.io/en/latest/)
[](https://codecov.io/gh/vprusso/toqito)
[](https://doi.org/10.5281/zenodo.4743211)
[](https://pepy.tech/project/toqito)
[](http://unitary.fund)
<p align="center">
<picture>
<source media="(prefers-color-scheme: dark)" srcset="https://github.com/vprusso/toqito/raw/cfb62c4a5ce04b782f64229e7acd2b1c97f09801/docs/figures/logo.svg" width="60%">
<img src="https://github.com/vprusso/toqito/raw/cfb62c4a5ce04b782f64229e7acd2b1c97f09801/docs/figures/logo.svg" width="60%">
</picture>
</p>
# toqito: Theory of Quantum Information Toolkit
The `toqito` package is an open-source Python library for studying various
objects in quantum information, namely, states, channels, and measurements.
<p align="center">
<a href="https://toqito.readthedocs.io/en/latest/">
<img width=30% src="https://img.shields.io/badge/documentation-blue?style=for-the-badge&logo=read%20the%20docs" alt="Documentation" />
</a>
</p>
Specifically, `toqito` focuses on providing numerical tools to study problems
about entanglement theory, nonlocal games, matrix analysis, and other
aspects of quantum information that are often associated with computer science.
`toqito` aims to fill the needs of quantum information researchers who want
numerical and computational tools for manipulating quantum states,
measurements, and channels. It can also be used as a tool to enhance the
experience of students and instructors in classes about quantum
information.
## Getting Started
toqito is available via [PyPi](https://pypi.org/project/toqito/) for Linux, and macOS, with support for Python 3.10 to 3.12.
```console
(venv) $ pip install toqito
```
The following code gives an example on the usage:
```python
# Calculate the classical and quantum value of the CHSH game.
import numpy as np
from toqito.nonlocal_games.xor_game import XORGame
# The probability matrix.
prob_mat = np.array([[1/4, 1/4], [1/4, 1/4]])
# The predicate matrix.
pred_mat = np.array([[0, 0], [0, 1]])
# Define CHSH game from matrices.
chsh = XORGame(prob_mat, pred_mat)
chsh.classical_value()
# 0.75
chsh.quantum_value()
# 0.8535533
```
**Detailed documentation on all available methods, options, and input formats is available at [ReadTheDocs](https://toqito.readthedocs.io/en/latest/).**
## Using
Full documentation along with specific examples and tutorials are provided here:
[https://toqito.readthedocs.io/](https://toqito.readthedocs.io/).
More information can also be found on the following
[toqito homepage](https://vprusso.github.io/toqito/).
Chat with us in our `toqito` channel on [Discord](http://discord.unitary.fund/).
## Testing
The `pytest` module is used for testing. To run the suite of tests for `toqito`,
run the following command in the root directory of this project.
```
pytest --cov-report term-missing --cov=toqito
```
## Citing
You can cite `toqito` using the following DOI:
10.5281/zenodo.4743211
If you are using the `toqito` software package in research work, please include
an explicit mention of `toqito` in your publication. Something along the lines
of:
```
To solve problem "X" we used `toqito`; a package for studying certain
aspects of quantum information.
```
A BibTeX entry that you can use to cite `toqito` is provided here:
```bib
@misc{toqito,
author = {Vincent Russo},
title = {toqito: A {P}ython toolkit for quantum information, version 1.0.0},
howpublished = {\url{https://github.com/vprusso/toqito}},
month = May,
year = 2021,
doi = {10.5281/zenodo.4743211}
}
```
## References
The `toqito` project has been used or referenced in the following works:
- [](https://arxiv.org/abs/2406.13430) Bandyopadhyay, Somshubhro and Russo, Vincent
"Distinguishing a maximally entangled basis using LOCC and shared entanglement", (2024).
- [](https://arxiv.org/abs/2307.02551) Tavakoli, Armin and Pozas-Kerstjens, Alejandro and Brown, Peter and Araújo, Mateus
"Semidefinite programming relaxations for quantum correlations", (2023).
- [](https://arxiv.org/abs/2311.17047) Johnston, Nathaniel and Russo, Vincent and Sikora, Jamie
"Tight bounds for antidistinguishability and circulant sets of pure quantum states", (2023).
- [](https://arxiv.org/abs/2308.15579) Pelofske, Elijah and Bartschi, Andreas and Eidenbenz, Stephan and Garcia, Bryan and Kiefer, Boris
"Probing Quantum Telecloning on Superconducting Quantum Processors", (2023).
- [](https://arxiv.org/abs/2303.07911) Philip, Aby and Rethinasamy, Soorya and Russo, Vincent and Wilde, Mark.
"Quantum Steering Algorithm for Estimating Fidelity of Separability.", Quantum 8, 1366, (2023).
- [](https://arxiv.org/abs/2302.09401) Miszczak, Jarosław Adam.
"Symbolic quantum programming for supporting applications of quantum computing technologies.", (2023).
- [](https://arxiv.org/abs/2306.09444) Casalé, Balthazar and Di Molfetta, Giuseppe and Anthoine, Sandrine and Kadri, Hachem.
"Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens.", (2023).
- [](https://arxiv.org/abs/2206.08313) Russo, Vincent and Sikora, Jamie "Inner products of pure states and their antidistinguishability", Physical Review A, Vol. 107, No. 3, (2023).
## Contributing
All contributions, bug reports, bug fixes, documentation improvements,
enhancements, and ideas are welcome.
A detailed overview of how to contribute can be found in the
[contributing guide](https://toqito.readthedocs.io/en/latest/getting_started.html#contributing).
## License
[MIT License](http://opensource.org/licenses/mit-license.php>)
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"description": "[](https://github.com/vprusso/toqito/actions/workflows/build-test-actions.yml)\n[](https://toqito.readthedocs.io/en/latest/)\n[](https://codecov.io/gh/vprusso/toqito)\n[](https://doi.org/10.5281/zenodo.4743211)\n[](https://pepy.tech/project/toqito)\n[](http://unitary.fund)\n\n\n<p align=\"center\">\n <picture>\n <source media=\"(prefers-color-scheme: dark)\" srcset=\"https://github.com/vprusso/toqito/raw/cfb62c4a5ce04b782f64229e7acd2b1c97f09801/docs/figures/logo.svg\" width=\"60%\">\n <img src=\"https://github.com/vprusso/toqito/raw/cfb62c4a5ce04b782f64229e7acd2b1c97f09801/docs/figures/logo.svg\" width=\"60%\">\n </picture>\n </p>\n\n\n# toqito: Theory of Quantum Information Toolkit\n\nThe `toqito` package is an open-source Python library for studying various\nobjects in quantum information, namely, states, channels, and measurements.\n\n<p align=\"center\">\n <a href=\"https://toqito.readthedocs.io/en/latest/\">\n <img width=30% src=\"https://img.shields.io/badge/documentation-blue?style=for-the-badge&logo=read%20the%20docs\" alt=\"Documentation\" />\n </a>\n</p>\n\nSpecifically, `toqito` focuses on providing numerical tools to study problems\nabout entanglement theory, nonlocal games, matrix analysis, and other\naspects of quantum information that are often associated with computer science.\n\n`toqito` aims to fill the needs of quantum information researchers who want\nnumerical and computational tools for manipulating quantum states,\nmeasurements, and channels. It can also be used as a tool to enhance the\nexperience of students and instructors in classes about quantum\ninformation.\n\n\n## Getting Started\n\ntoqito is available via [PyPi](https://pypi.org/project/toqito/) for Linux, and macOS, with support for Python 3.10 to 3.12.\n\n```console\n(venv) $ pip install toqito\n```\n\nThe following code gives an example on the usage:\n\n```python\n# Calculate the classical and quantum value of the CHSH game.\nimport numpy as np\nfrom toqito.nonlocal_games.xor_game import XORGame\n\n# The probability matrix.\nprob_mat = np.array([[1/4, 1/4], [1/4, 1/4]])\n\n# The predicate matrix.\npred_mat = np.array([[0, 0], [0, 1]])\n\n# Define CHSH game from matrices.\nchsh = XORGame(prob_mat, pred_mat)\n\nchsh.classical_value()\n# 0.75\nchsh.quantum_value()\n# 0.8535533\n\n```\n\n**Detailed documentation on all available methods, options, and input formats is available at [ReadTheDocs](https://toqito.readthedocs.io/en/latest/).**\n\n## Using\n\nFull documentation along with specific examples and tutorials are provided here:\n[https://toqito.readthedocs.io/](https://toqito.readthedocs.io/). \n\nMore information can also be found on the following\n[toqito homepage](https://vprusso.github.io/toqito/).\n\nChat with us in our `toqito` channel on [Discord](http://discord.unitary.fund/). \n\n## Testing\n\nThe `pytest` module is used for testing. To run the suite of tests for `toqito`,\nrun the following command in the root directory of this project.\n\n```\npytest --cov-report term-missing --cov=toqito\n```\n\n## Citing\n\nYou can cite `toqito` using the following DOI:\n10.5281/zenodo.4743211\n\n\nIf you are using the `toqito` software package in research work, please include\nan explicit mention of `toqito` in your publication. 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