Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles, detrimental graphical configurations known as trapping sets (TSs) present in a code graph as well as symmetric degeneracy of errors. These factors significantly degrade the decoder decoding probability performance and cause so-called error floor. In this paper, we establish a systematic methodology by which one can identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. The conventional definition of a TS from classical error correction is generalized to address the syndrome decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders. Frame error rate improvements of two orders of magnitude in the error floor regime are demonstrated for some practical finite-length QLDPC codes without requiring any post-processing.

中文翻译：

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捕获量子 LDPC 码集

用于有限长度量子低密度奇偶校验 (QLDPC) 代码的迭代解码器很有吸引力，因为它们的硬件复杂性仅与物理量子位的数量成线性关系。然而，它们受到短周期、被称为陷阱集 (TS) 的有害图形配置以及错误的对称退化的影响。这些因素会显着降低解码器的解码概率性能并导致所谓的错误底线。在本文中，我们建立了一种系统方法，可以根据量子捕获集（QTS）的拓扑结构和使用的解码器对其进行识别和分类。来自经典纠错的 TS 的传统定义被推广以解决 QLDPC 码的校正子解码场景。我们表明 QTS 的知识可用于设计更好的 QLDPC 代码和解码器。对于一些实用的有限长度 QLDPC 码，证明了错误底限机制中两个数量级的帧错误率改进，无需任何后处理。