|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.

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 for Linux, and macOS, with support for Python 3.10 to 3.12.

pip install toqito

The following code gives an example on the usage:

# 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

Using

Full documentation, along with specific examples and tutorials, are provided here: https://toqito.readthedocs.io/.

Chat with us in our |toqito⟩ channel on Discord.

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:

@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 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:

• Philip, Aby "On Multipartite Entanglement and Its Use", (2024).

• Bandyopadhyay, Somshubhro and Russo, Vincent "Distinguishing a maximally entangled basis using LOCC and shared entanglement", (2024).

• Tavakoli, Armin and Pozas-Kerstjens, Alejandro and Brown, Peter and Araújo, Mateus "Semidefinite programming relaxations for quantum correlations", (2023).

• Johnston, Nathaniel and Russo, Vincent and Sikora, Jamie "Tight bounds for antidistinguishability and circulant sets of pure quantum states", (2023).

• Pelofske, Elijah and Bartschi, Andreas and Eidenbenz, Stephan and Garcia, Bryan and Kiefer, Boris "Probing Quantum Telecloning on Superconducting Quantum Processors", (2023).

• Philip, Aby and Rethinasamy, Soorya and Russo, Vincent and Wilde, Mark. "Quantum Steering Algorithm for Estimating Fidelity of Separability.", Quantum 8, 1366, (2023).

• Miszczak, Jarosław Adam. "Symbolic quantum programming for supporting applications of quantum computing technologies.", (2023).

• Casalé, Balthazar and Di Molfetta, Giuseppe and Anthoine, Sandrine and Kadri, Hachem. "Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens.", (2023).

• 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.

License

MIT License