Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913809939038208 |
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| author | Kasai, Kenta |
| author_facet | Kasai, Kenta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction Kasai, Kenta Quantum Physics Information Theory 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. |
| title | Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2504.17790 |