High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures

• URL: http://arxiv.org/abs/2604.20838v2
• Date: Fri, 24 Apr 2026 16:41:21 GMT
• Title: High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures
• Abstract summary: We construct a quantum low-density parity-check code family from a length-$512$ Calderbank-Shor--Steane base matrix pair.<n>The base pair is permutation-equivalent to the known SPC(3) product CSS code.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $d\le 40$.

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