Quantum low-density parity-check (QLDPC) codes are a leading approach to quantum error correction, yet conventional belief propagation (BP) decoders often perform poorly, primarily due to non-convergence exacerbated by stabilizer constraints, which induce short cycles and degeneracy. We propose two scheduling variants, sequential check node scheduling (SCNS) and sequential variable node scheduling (SVNS), that improve BP's error-correction ability by processing check nodes (CNs) or variable nodes (VNs), respectively, in a fixed order, stabilizing message updates and reducing stalls. We also employ this technique to an improved BP-variant called BP guided decimation (BPGD), where symbols are progressively fixed during decoding iterations. Here, we demonstrate that the sequential BPGD (SBPGD) decoder can further improve the convergence properties and performance of the decoder. On standard QLDPC benchmarks under a Pauli-X noise model, our sequential schedules are shown to lower the block error rate relative to conventional BP, and SBPGD outperforms BPGD while using significantly fewer decimation rounds, translating to lower computational cost. These results demonstrate that changing the update schedule, without altering the code, can improve both the reliability and efficiency of BP-based decoding for QLDPC codes. For the [[1922,50,16]] C2 hypergraph-product code with independent X errors, SVNS-BP surpasses BP-OSD-0 in error correction at roughly the same complexity as standard BP.

翻译：量子低密度奇偶校验（QLDPC）码是量子纠错的主流方案，然而传统置信传播（BP）译码器常因稳定子约束引发的短循环和简并性问题导致非收敛，性能普遍不佳。本文提出两种调度变体——序列化校验节点调度（SCNS）与序列化变量节点调度（SVNS），分别通过固定顺序处理校验节点（CN）或变量节点（VN）来稳定消息更新、减少停滞，从而提升BP的纠错能力。我们还将该技术应用于改进型BP变体BP引导确定（BPGD）中，该算法在译码迭代过程中逐步固定符号位。实验表明，序列化BPGD（SBPGD）译码器能进一步改善译码器的收敛特性与性能。在Pauli-X噪声模型下的标准QLDPC基准测试中，所提序列化调度相比传统BP降低了块错误率；SBPGD在显著减少确定轮数的同时性能优于BPGD，这意味着更低的计算成本。这些结果表明，在不改变编码结构的前提下，调整更新调度策略能够同时提升QLDPC码基于BP译码的可靠性与效率。对于存在独立X错误的[[1922,50,16]] C2超图乘积码，SVNS-BP在复杂度与标准BP相近的情况下，其纠错能力超越了BP-OSD-0。