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.
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BibTeX
@misc{gokduman2026chromatic,
title = {{Chromatic Block-Gibbs p-Bit Decoding of QLDPC Codes}},
author = {Mert Gökduman and Cyril Guyot and Henry D. Pfister},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17520},
eprint = {2610.17520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17520},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chromatic Block-Gibbs p-Bit Decoding of QLDPC Codes
AU - Mert Gökduman
AU - Cyril Guyot
AU - Henry D. Pfister
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17520
UR - https://arxiv.org/abs/2610.17520
AB - 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.
ER -