qLDPC

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 a local version from source:

git clone [email protected]: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:

• 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 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.

In the meantime, 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/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.