发表机构
Tsinghua University; Jinan Institute of Quantum Technology and Jinan branch, Hefei National Laboratory; Frontier Science Center for Quantum Information（清华大学; 济南量子技术研究院及合肥国家实验室济南分部; 量子信息前沿科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对电路级量子纠错中的超边故障，提出综合征基序投影（SMP）框架，以线性复杂度提取超边信息并兼容匹配解码器，显著降低表面码、色码及逻辑门电路的故障概率。
AI 中文摘要
超边故障仍然是电路级量子纠错中的一个主要挑战。准确利用超边相关性通常需要大量的计算资源，这使得实时解码变得复杂。基于匹配的解码器快速且可扩展，但其成对图表示限制了对高阶故障信息的利用。在此，我们引入综合征基序投影（SMP），这是一个将超边信息纳入基于匹配的解码的通用框架。关键思想是，超边故障会产生特征性的局部综合征基序。观察到这样的基序为相应的故障提供了证据。SMP直接从测量的综合征中提取此信息，预处理复杂度为线性，同时保留匹配后端。因此，它可以作为现有可扩展且实时的匹配解码器的轻量级前端。我们在表面码存储器、色码存储器和逻辑门电路上展示了SMP。在谷歌的Willow实验表面码数据上，SMP改进了标准和相关匹配，并优于测试的置信度匹配基线。对于色码存储器，SMP与Chromobius结合可将逻辑故障概率降低高达77.8%。对于逻辑门电路，SMP相对于逻辑可观测匹配将六CNOT电路的故障概率降低了35.5%，同时实现了与迭代置信度匹配相当的性能。这些结果表明，SMP为超边解码提供了一种轻量级且可迁移的方法，并具有集成到容错量子计算的可扩展实时解码架构中的清晰路径。
英文摘要
Hyperedge faults remain a major challenge in circuit-level quantum error correction. Accurately exploiting hyperedge correlations often requires substantial computational resources, which complicates real-time decoding. Matching-based decoders are fast and scalable, but their pairwise graph representation limits the use of higher-order fault information. Here, we introduce Syndrome Motif Projection (SMP), a general framework for incorporating hyperedge information into matching-based decoding. The key idea is that a hyperedge fault produces a characteristic local syndrome motif. Observing such a motif provides evidence for the corresponding fault. SMP extracts this information directly from the measured syndrome with linear-complexity preprocessing while preserving the matching backend. It can therefore serve as a lightweight front end to existing scalable and real-time matching decoders. We demonstrate SMP across surface code memories, color code memories, and logical gate circuits. On Google's Willow experimental surface code data, SMP improves both standard and correlated matching and outperforms the tested belief matching baseline. For color code memories, SMP combined with Chromobius reduces logical failure probabilities by up to 77.8\%. For logical gate circuits, SMP reduces the failure probability of a six-CNOT circuit by 35.5\% relative to logical observable matching while achieving performance comparable to iterative belief matching. These results demonstrate that SMP provides a lightweight and transferable approach to hyperedge decoding, with a clear path toward integration into scalable real-time decoding architectures for fault-tolerant quantum computation.
