https://github.com/vprusso/toqito
|toqito> (Theory of Quantum Information Toolkit) in Python :snake:
https://github.com/vprusso/toqito
matrix-analysis physics python python-3 quantum quantum-computing quantum-information unitaryhack
Last synced: 12 days ago
JSON representation
|toqito> (Theory of Quantum Information Toolkit) in Python :snake:
- Host: GitHub
- URL: https://github.com/vprusso/toqito
- Owner: vprusso
- License: mit
- Created: 2020-01-22T03:47:16.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2025-04-08T01:17:32.000Z (12 days ago)
- Last Synced: 2025-04-08T02:25:09.489Z (12 days ago)
- Topics: matrix-analysis, physics, python, python-3, quantum, quantum-computing, quantum-information, unitaryhack
- Language: Python
- Homepage: https://toqito.readthedocs.io
- Size: 4.3 MB
- Stars: 241
- Watchers: 8
- Forks: 110
- Open Issues: 77
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: docs/contributing.rst
- Funding: .github/FUNDING.yml
- License: LICENSE
- Code of conduct: docs/code_of_conduct.rst
- Citation: CITATION.bib
Awesome Lists containing this project
- quantum-awesome - https://github.com/vprusso/toqito
README
# |toqito⟩: Theory of Quantum Information Toolkit
[](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)
[](https://unitary.foundation)
The |toqito⟩ package is an open-source Python library for studying various
objects in quantum information, namely, states, channels, and measurements.
|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.
## Installing
|toqito⟩ is available via [PyPi](https://pypi.org/project/toqito/) for Linux, and macOS, with support for Python 3.10 to
3.12.
```sh
pip install toqito
```
## Examples
Full documentation, along with specific examples and tutorials, is provided here:
[https://toqito.readthedocs.io/](https://toqito.readthedocs.io/).
Chat with us in our |toqito⟩ channel on [Discord](http://discord.unitary.fund/).
### Example: Nonlocal games
[Nonlocal games](https://toqito.readthedocs.io/en/latest/tutorials.nonlocal_games.html) are a mathematical framework
that abstractly models a physical system. The CHSH game is a subtype of nonlocal game referred to as an XOR game that
characterizes the seminal [CHSH inequality](https://en.wikipedia.org/wiki/CHSH_inequality).
For XOR games, there exist optimization problems (that are provided via |toqito⟩) that one can compute to attain the
optimal values of such games when the players use either a classical or quantum strategy.
```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
```
Indeed, using a quantum strategy for the CHSH game gives the known optimal result of $\frac{1}{4}\left(2 +
\sqrt{2}\right) \approx 0.8535...$
### Example: Quantum state distinguishability
Quantum state distinguishability is a fundamental task in quantum information theory. Consider the set of four [Bell
states](https://en.wikipedia.org/wiki/Bell_state):
$$
\begin{equation}
\begin{aligned}
|\psi_0\rangle = \frac{1}{\sqrt{2}} \left(|00\rangle + |11\rangle\right), \quad
|\psi_1\rangle = \frac{1}{\sqrt{2}} \left(|00\rangle - |11\rangle\right), \\
|\psi_2\rangle = \frac{1}{\sqrt{2}} \left(|01\rangle + |10\rangle\right), \quad
|\psi_3\rangle = \frac{1}{\sqrt{2}} \left(|01\rangle - |10\rangle\right).
\end{aligned}
\end{equation}
$$
The optimal probability of globally distinguishing the four Bell states (assuming an equal weighting of probability) is
1 (i.e., it can be performed perfectly). However, under a more restrictive set of measurements (such as PPT measurement
operators), the optimal probability of distinguishing the four Bell states using PPT operators is 1/2.
|toqito⟩ offers a wide suite of functionality for computing the distinguishability of quantum states:
```python
from toqito.states import bell
from toqito.state_opt import state_distinguishability, ppt_distinguishability
# Define the set of states as the four Bell states:
states = [bell(0), bell(1), bell(2), bell(3)]
# Distinguishing four Bell states (global measurements): 0.9999999999767388
pos_res, _ = state_distinguishability(states)
print(f"Distinguishing four Bell states (global measurements): {pos_res}")
# Distinguishing four Bell states (PPT measurements): 0.5000000000098367
ppt_res, _ = ppt_distinguishability(states, subsystems=[0], dimensions=[2, 2])
print(f"Distinguishing four Bell states (PPT measurements): {ppt_res}")
```
Consult the [tutorials](https://toqito.readthedocs.io/en/latest/tutorials.html#quantum-state-distinguishability) for
additional examples and information.
## 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},
howpublished = {\url{https://github.com/vprusso/toqito}},
month = May,
year = 2021,
doi = {10.5281/zenodo.4743211}
}
```
## Research
The |toqito⟩ project is, first and foremost, a quantum information theory research tool. Consult the following [open
problems wiki
page](https://github.com/vprusso/toqito/wiki/Research-open-problems-in-quantum-information-theory-using-%7Ctoqito%E2%9F%A9)
for a list of certain solved and unsolved problems in quantum information theory in which |toqito⟩ could be potentially
helpful in probing. Feel free to add to this list and/or contribute solutions!
The |toqito⟩ project has been used or referenced in the following works:
- [](https://www.proquest.com/openview/eb0021dd3eb463b5fb12b7fc71d920eb/1?cbl=18750&diss=y&pq-origsite=gscholar) Philip, Aby
"On Multipartite Entanglement and Its Use", (2024).
- [](https://arxiv.org/abs/2409.08705)
Gupta, Tathagata and Mushid, Shayeef and Russo, Vincent and Bandyopadhyay, Somshubhro
"Optimal discrimination of quantum sequences", (2024).
- [](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/contributing.html#contrib-guide-reference-label).
## License
[MIT License](http://opensource.org/licenses/mit-license.php>)