Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction
Abstract
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth 12, our method employs affine permutation matrices and a randomized sequential selection procedure to eliminate short cycles and achieve girth 16. Numerical experiments show that the proposed codes significantly reduce the number of low-weight codewords. Joint belief propagation decoding over depolarizing channels reveals that although a slight degradation appears in the waterfall region, a substantial improvement is achieved in the error floor performance. We also evaluated the minimum distance and found that the proposed codes achieve a larger upper bound compared to conventional constructions.
Cite
@article{arxiv.2504.17790,
title = {Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction},
author = {Kenta Kasai},
journal= {arXiv preprint arXiv:2504.17790},
year = {2025}
}
Comments
This version corrects an error in the experimental results reported in the previous version. Specifically, a bug in the error floor detection process led to incorrect conclusions regarding the performance comparison. The issue has been fixed, and updated numerical results are provided