Abstract:Quantum error correcting codes are essential to achieve fault-tolerant quantum computation. This work introduces two constructions of high-rate, dual-containing (DC) Calderbank--Shor--Steane low-density parity-check (LDPC) codes based on quasi-dyadic matrices. We characterize the automorphism group of such codes, investigate their minimum distance behavior, and provide several theoretical results on their cycle properties. Monte Carlo simulations under depolarizing and phenomenological noise show better finite-length logical error rates than the considered DC benchmark codes and competitive performance against several state-of-the-art quantum LDPC code families. Finally, we employ an automorphism-ensemble belief propagation decoder to improve their decoding performance.
From: Alessio Baldelli [view email]
[v1]
Tue, 5 May 2026 11:00:37 UTC (87 KB)
[v2]
Tue, 12 May 2026 08:51:44 UTC (87 KB)
[v3]
Wed, 22 Jul 2026 13:39:45 UTC (71 KB)
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