论文标题
捕获量子LDPC代码集
Trapping Sets of Quantum LDPC Codes
论文作者
论文摘要
有限长度量子低密度平价检查（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数的数量线性缩放。但是，它们受到短周期的影响，有害的图形配置被称为捕获集（TSS）（TSS），以及错误的误差的对称退化。这些因素显着降低解码器解码概率性能并导致所谓的误差地面。在本文中，我们建立了一种系统的方法，可以根据其拓扑结构和使用的解码器来识别和对量子陷阱集（QTSS）进行分类。经典错误校正的TS的常规定义被推广，以解决QLDPC代码的综合征解码方案。我们表明，QTSS的知识可用于设计更好的QLDPC代码和解码器。对于某些实际有限长度的QLDPC代码，在不需要任何后处理的情况下，证明了误差率提高两个数量级的误差率。
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.
