Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, though they are not always correctly measured. Most of the existing decoding algorithms for surface codes are not equipped to handle erroneous syndrome information or need additional measurements to correct syndromes with errors, which implies a potential increase in inference complexity and decoding latency. In this paper, we propose a high-performance list decoding algorithm for surface codes with erroneous syndromes. More specifically, to cope with erroneous syndrome information, we incorporate syndrome soft information, allowing the syndrome to be listed as well. To enhance the efficiency of the list decoding algorithm, we use LCOSD, which can significantly reduce the average list size in classical error correction compared with the conventional ordered statistics decoding (OSD). Numerical results demonstrate that our proposed algorithm significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM) and BP decoders.

翻译：量子纠错码（QECC）是实现容错量子计算的必要条件。表面码是一类拓扑量子纠错码，因其优异的纠错能力和易于实现的特点而备受关注。在表面码的译码过程中，综合征对于纠错至关重要，但它们并非总能被正确测量。现有的大多数表面码译码算法无法处理错误的综合征信息，或者需要额外的测量来纠正含错误的综合征，这可能导致推理复杂度和译码延迟的增加。本文提出了一种针对含错误综合征的表面码的高性能列表译码算法。具体而言，为应对错误的综合征信息，我们引入了综合征软信息，允许将综合征也列入列表。为提高列表译码算法的效率，我们采用了LCOSD，与传统的有序统计译码（OSD）相比，它能在经典纠错中显著降低平均列表大小。数值结果表明，与最小权重完美匹配（MWPM）和BP译码器相比，我们提出的算法显著提升了含错误综合征表面码的译码性能。