qLDPC 0.0.9

Tools for constructing and analyzing quantum low density parity check (qLDPC) codes.

qLDPC

This package contains tools for constructing and analyzing quantum low density parity check (qLDPC) codes.

📦 Installation

This package requires Python>=3.10, and can be installed from PyPI with

pip install qldpc

To install a local version from source:

git clone [e-mail]:Infleqtion/qLDPC.git
pip install -e qLDPC

You can also pip install -e 'qLDPC[dev]' to additionally install some development tools.

🚀 Features

Notable features include:

• ClassicalCode: class for representing classical linear error-correcting codes over finite fields.
  • Various pre-defined classical code families.
  • Communication with the GAP/GUAVA package for even more codes.
• QuditCode: general class for constructing Galois-qudit codes.
• CSSCode: general class for constructing quantum CSS codes out of two mutually compatible ClassicalCodes.
  • CSSCode.get_logical_ops: method to construct a complete basis of nontrivial logical operators for a CSSCode.
  • CSSCode.get_distance: method to compute the code distance (i.e., the minimum weight of a nontrivial logical operator) of a CSSCode. Includes options for computing the exact code distance by brute force, as well as an estimate (or upper bound) with the method of arXiv:2308.07915.
  • Includes options for applying local Hadamard transformations, which is useful for tailoring a CSSCode to biased noise (see arXiv:2202.01702). Options to apply more general Clifford code deformations are pending.
• GBCode: class for constructing generalized bicycle codes, as described in arXiv:1904.02703.
• QCCode: class for constructing the quasi-cyclic codes in arXiv:2308.07915.
• HGPCode: class for constructing hypergraph product codes out of two ClassicalCodes.
• LPCode: class for constructing lifted product codes out of two protographs (i.e., matrices whose entries are elements of a group algebra). See arXiv:2012.04068 and arXiv:2202.01702.
• QTCode: class for constructing quantum Tanner codes out of (a) two symmetric subsets A and B of a group G, and (b) two ClassicalCodes with block lengths |A| and |B|. See arXiv:2202.13641 and arXiv:2206.07571.
• abstract.py: module for basic abstract algebra (groups, algebras, and representations thereof).
  • Various pre-defined groups (mostly borrowed from SymPy).
  • Communication with the GAP computer algebra system and GroupNames.org for constructing even more groups.
• objects.py: module for constructing and helper objects such as Cayley complexes and chain complexes, which are instrumental for the construction of various quantum codes.

🤔 Questions and issues

If this project gains interest and traction, I'll add a documentation webpage and material to help users get started quickly. I am also planning to write a paper that presents and explains this project. In the meantime, you can explore the documentation and explanations in the source code. qldpc/codes_test.py contains some examples of using the classes and methods described above.

If you have any questions, feedback, or requests, please open an issue on GitHub or email me at [e-mail]!

⚓ Attribution

If you use this software in your work, please cite with:

@misc{perlin2023qldpc,
  author = {Perlin, Michael A.},
  title = {{qLDPC}},
  year = {2023},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/Infleqtion/qLDPC}},
}

This may require adding \usepackage{url} to your LaTeX file header. Alternatively, you can cite

Michael A. Perlin. qLDPC. https://github.com/Infleqtion/qLDPC, 2023.