Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some fashion. However, the use of BP decoding for degenerate QLDPC codes is known to face issues with convergence. These issues are commonly attributed to short cycles in the Tanner graph and multiple syndrome-matching error patterns due to code degeneracy. Although various methods have been proposed to mitigate the non-convergence issue, such as BP with ordered statistics decoding (BP-OSD) and BP with stabilizer inactivation (BP-SI), achieving better performance with lower complexity remains an active area of research. In this work, we propose to decode QLDPC codes with BP guided decimation (BPGD), which has been previously studied for constraint satisfaction and lossy compression problems. The decimation process is applicable to both binary BP and quaternary BP and involves sequentially freezing the value of the most reliable qubits to encourage BP convergence. Despite its simplicity, we find that BPGD significantly reduces BP failures due to non-convergence while maintaining a low probability of error given convergence, achieving performance on par with BP-OSD and BP-SI. To better understand how and why BPGD improves performance, we discuss several interpretations of BPGD and their connection to BP syndrome decoding.

翻译：量子低密度奇偶校验（QLDPC）码已成为量子纠错领域一种前景广阔的技术。针对QLDPC码已提出多种译码器，其中许多以某种方式采用置信传播（BP）译码。然而，将BP译码用于简并QLDPC码时，已知会面临收敛问题。这些问题通常归因于Tanner图中的短环以及由码简并性导致的多重综合征匹配错误模式。尽管已有多种方法被提出以缓解非收敛问题，例如基于有序统计译码的BP（BP-OSD）和基于稳定子失活的BP（BP-SI），但在更低复杂度下实现更优性能仍是当前研究的热点。本文提出采用先前已在约束满足和有损压缩问题中研究过的引导判决BP（BPGD）来译码QLDPC码。该判决过程适用于二进制BP和四进制BP，涉及顺序冻结最可靠量子比特的值以促进BP收敛。尽管方法简单，我们发现BPGD在维持低收敛错误概率的同时显著减少了因非收敛导致的BP失败，其性能与BP-OSD和BP-SI相当。为深入理解BPGD改进性能的机制与原因，本文讨论了BPGD的多种解释及其与BP综合征译码的联系。