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.
翻译:限制长度量低密度对等检查(QLDPC)代码的迭代解码器具有吸引力,因为它们的硬件复杂度仅与物理当量计数成线,但受到短周期、代码图中称为陷阱装置(TS)的有害图形配置以及误差的对称分解码装置的影响。这些因素大大降低了解码器解码概率性能,并导致所谓的差错下层。在本文件中,我们确立了一种系统的方法,使人们可以根据它们使用的表层结构和解码来辨别和分类量子捕获装置(QTS)。传统错误校正对TS的传统定义被广泛用来处理QLDPC代码的综合解码假设。我们表明,QTS的知识可用于设计更好的QLDPC代码和解码器。在错误下层系统中对两个数量级的改进框架错误率,用于某些实用的定值QLDPC代码,无需任何后处理。