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 classicalBitCodes.- Includes options for applying local Pauli transformations (i.e., Pauli deformations of the code), which is useful for tailoring a
CSSCodeto biased noise (see arXiv:2202.01702). CSSCode.get_logical_ops: method (from arXiv:0903.5256) to construct a basis of nontrivial logical operators for aCSSCode.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 underlyingBitCodes), an upper bound (with the method of arXiv:2308.07915), and the exact code distance (with an integer linear program, which has exponential complexity).
- Includes options for applying local Pauli transformations (i.e., Pauli deformations of the code), which is useful for tailoring a
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 classicalBitCodes. 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 subsetsAandBof a groupG, and (b) two classicalBitCodes 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.
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