In this paper, we investigate the use of quaternary reliability statistics for ordered statistics decoding (OSD) of quantum codes. OSD can be used to improve the performance of belief propagation (BP) decoding when it fails to correct the error syndrome. We propose an approach that leverages quaternary reliability information and the hard-decision history output by BP to perform reliability sorting for OSD. This approach improves upon previous methods that separately treat X and Z errors, by preserving the X/Z correlations during the sorting step. Our simulations show that the refined BP with scalar messages and the proposed OSD outperforms previous BP-OSD combinations. We achieve thresholds of 17.5% for toric, surface, and XZZX codes, and 14.8% for hexagonal planar color codes.

翻译：本文研究了利用四元可靠性统计对量子码进行有序统计译码（OSD）的方法。当置信传播（BP）译码无法纠正错误综合征时，可采用OSD提升性能。我们提出了一种方法，利用四元可靠性信息及BP输出的硬判决历史对OSD进行可靠性排序。该方法在排序过程中保留了X与Z误差间的相关性，相比以往分别处理X误差和Z误差的方法有所改进。仿真结果表明，采用标量消息的精细BP与所提OSD组合优于以往的BP-OSD组合。对于环面码、表面码和XZZX码，我们实现了17.5%的译码阈值，对于六边形平面色码实现了14.8%的译码阈值。