qLDPC 0.0.3

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

qLDPC (PREVIEW)

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

Installation

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

pip install qldpc

To install from source:

git clone https://github.com/perlinm/qLDPC.git
pip install -e qLDPC

Features

Notable features include:

• abstract.py: module for basic abstract algebra (groups, algebras, and representations thereof).
• BitCode: class for representing {classical, linear, binary} error-correcting codes.
• CSSCode: general class for constructing quantum CSS codes out of two classical BitCodes.
  • Includes options for applying local Pauli transformations (i.e., Pauli deformations of the code), which is useful for tailoring a CSSCode to biased noise (see arXiv:2202.01702).
  • CSSCode.get_logical_ops: method (from arXiv:0903.5256) to construct a 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). Includes options for computing a lower bound (determined by the distances of the underlying BitCodes), an upper bound (with the method of arXiv:2308.07915), and the exact code distance (with an integer linear program, which has exponential complexity).
• 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 classical BitCodes. Follows the conventions of arXiv:2202.01702.
• 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 classical BitCodes with block lengths |A| and |B|. See arXiv:2202.13641 and arXiv:2206.07571.

Questions and issues

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

If you have any questions or requests, please open an issue!

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/perlinm/qLDPC}},
}

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

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