AI 中文总结
本研究提出基于陷阱集的框架，可预测量子纠错迭代解码器的错误平层，揭示码距与解码性能的差距，为解码算法设计提供指导。
AI 中文摘要
消息传递解码器是可扩展量子纠错最具前景的候选方案之一，但在实际电路级噪声下，其在低错误率区域的行为仍知之甚少。本研究引入了一套系统框架，用于识别决定解码器失效的图结构，并利用这些结构预测由此产生的错误平层。我们将详尽的陷阱集枚举直接应用于二元自行车码（bivariate bicycle code）的检测器错误模型，对所得结构支持的所有低重量故障配置进行测试。这将对极罕见逻辑失效的分析转化为有限结构搜索，避免了直接蒙特卡洛模拟的 prohibitive 成本。我们在三个架构和解码启发式方法差异显著的迭代解码器上评估该框架。值得注意的是，对于\ exttt{RelayBP}，所得预测准确复现了模拟的错误平层；对于其他解码器，其结果仍处于同一数量级。尽管存在差异，无叶基本陷阱集捕获了所有三个解码器低重量错误平层贡献的大部分。此外，每个解码器都存在由远低于电路级距离所隐含的纠错能力的故障配置导致的失效，这揭示了码距与实际迭代解码性能之间存在显著差距。这些结果确立了陷阱集分析作为预测错误平层、揭示迭代解码器结构弱点以及指导解码算法联合设计的实用框架。
英文摘要
Message-passing decoders are among the most promising candidates for scalable quantum error correction, yet their behavior in the low-error-rate regime remains poorly understood under realistic circuit-level noise. In this work, we introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor. We apply exhaustive trapping-set enumeration directly to the detector error model of a bivariate bicycle code and test all low-weight fault configurations supported on the resulting structures. This converts the analysis of extremely rare logical failures into a finite structural search, avoiding the prohibitive cost of direct Monte Carlo simulation. We evaluate the framework on three iterative decoders with substantially different architectures and decoding heuristics. Remarkably, for \texttt{RelayBP}, the resulting prediction accurately reproduces the simulated error floor; for the others, it remains within the same order of magnitude. Despite their differences, leafless elementary trapping sets capture a substantial part of the low-weight error-floor contribution for all three decoders. Moreover, each decoder admits failures caused by fault configurations well below the correction capability implied by the circuit-level distance, revealing a substantial gap between code distance and practical iterative-decoding performance. These results establish trapping-set analysis as a practical framework for predicting error floors, exposing the structural weaknesses of iterative decoders, and guiding the joint design of decoding algorithms.
Comments21 pages, 5 figures, 7 tables
