Chromatic Block-Gibbs p-Bit Decoding of QLDPC Codes

Abstract:We introduce a parallel decoder for quantum low-density parity-check (QLDPC) codes based on probabilistic bits (p-bits), tunable stochastic binary units controlled by local fields. The idea is that predicted error configurations, interpreted as explanations of the observed syndrome, are updated stochastically using local Gibbs conditionals, while a progressively strengthened parity penalty drives the search toward syndrome-valid configurations. A coloring of the decoding graph enables parallel block updates, and independent replicas and restarts provide trajectory diversity. The best candidate encountered during the search is returned, mirroring the candidate-selection strategy of recent ensemble decoders. At the stated update budgets, the resulting logical error rates are on par with leading decoders under both code-capacity and circuit-level noise. While the total number of variable resamplings can be substantially larger than the message-update count of BP-based alternatives, the numerical results establish constraint-annealed p-bit dynamics as a competitive stochastic alternative for QLDPC decoding and motivate further study of hardware-native implementations.

arXiv:2610.17520 [quant-ph]

(or arXiv:2610.17520v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.17520 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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