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This research presents novel constructions of high-rate dual-containing CSS LDPC codes using quasi-dyadic matrices to advance fault-tolerant quantum computation. Theoretical analysis and Monte Carlo simulations demonstrate superior finite-length logical error rates compared to existing benchmarks, while an optimized belief propagation decoder further enhances performance under various noise models. These findings offer significant theoretical progress for building scalable quantum hardware by improving the efficiency of error correction protocols.

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Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices

arXiv23 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2605.03631v3 Announce Type: replace-cross 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.

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.

Information Theory (cs.IT); Quantum Physics (quant-ph)

arXiv:2605.03631 [cs.IT]

(or arXiv:2605.03631v3 [cs.IT] for this version)

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