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Bibliographic Details
Main Authors: Okada, Koki, Kasai, Kenta
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.20838
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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