High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913058901721088 |
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| author | Okada, Koki Kasai, Kenta |
| author_facet | Okada, Koki Kasai, Kenta |
| contents | We construct a quantum low-density parity-check code family from a length-$512$ Calderbank--Shor--Steane base matrix pair. The base pair is permutation-equivalent to the known SPC(3) product CSS code, and the present affine-coset description gives a direct proof that both Tanner graphs are $(3,8)$-regular with girth $8$. The base code has parameters $[[512,174,8]]$. We then apply circulant permutation matrix (CPM) lifts. The main decoding experiment uses the CPM-lifted code with lift factor $P=32$, which has parameters $[[16384,4142,\le 40]]$, under the code-capacity depolarizing model. A belief-propagation decoder with post-processing achieved frame error rate about $10^{-8}$ at $p=0.085$, and one observed logical residual of weight $40$ gives a decoder-derived upper bound $d\le 40$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20838 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures Okada, Koki Kasai, Kenta Quantum Physics We construct a quantum low-density parity-check code family from a length-$512$ Calderbank--Shor--Steane base matrix pair. The base pair is permutation-equivalent to the known SPC(3) product CSS code, and the present affine-coset description gives a direct proof that both Tanner graphs are $(3,8)$-regular with girth $8$. The base code has parameters $[[512,174,8]]$. We then apply circulant permutation matrix (CPM) lifts. The main decoding experiment uses the CPM-lifted code with lift factor $P=32$, which has parameters $[[16384,4142,\le 40]]$, under the code-capacity depolarizing model. A belief-propagation decoder with post-processing achieved frame error rate about $10^{-8}$ at $p=0.085$, and one observed logical residual of weight $40$ gives a decoder-derived upper bound $d\le 40$. |
| title | High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.20838 |