用于量子低密度奇偶校验码BP解码的辅助节点
Auxiliary Nodes for BP Decoding of Quantum LDPC Codes
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中文总结 AI 辅助
研究针对CSS量子低密度奇偶校验码BP解码性能受其构造特性影响的问题，提出引入辅助节点的通用框架，4循环消除等技术可视为该框架实例，还基于此框架提出解码器，能降低逻辑错误率。
中文摘要 AI 辅助
许多最近提出的Calderbank-Shor-Steane（CSS）量子低密度奇偶校验（QLDPC）码具有稀疏解码图，能以低复杂度进行基于校验子的置信传播（BP）解码。但其构造常导致损害BP性能的特性，如短循环和退化。本文提出将辅助变量节点（AVN）和辅助校验节点（ACN）引入CSS码解码图的通用框架，与标准稳定器测量框架兼容。这为解码图设计提供额外自由度，可解决上述缺点。还表明近期技术4循环消除和子码集合解码可视为该框架实例。基于此框架进一步提出图衍生子码集合解码器，在电路级噪声下证明其与相应无4循环解码图上的BP相比大幅降低每轮逻辑错误率。
英文摘要
Many recently proposed Calderbank-Shor-Steane (CSS) quantum low-density parity-check (QLDPC) codes have sparse decoding graphs, enabling syndrome-based belief propagation (BP) decoding at low complexity. Their construction, however, often results in properties that impair BP performance, such as short cycles and degeneracy. In this work, we propose a general framework for introducing auxiliary variable nodes (AVNs) and auxiliary check nodes (ACNs) into the decoding graph of CSS codes, compatible with the standard stabilizer measurement framework. This provides an additional degree of freedom in the design of the decoding graph itself and can be used to tackle the aforementioned shortcomings. We show that recently proposed techniques, 4-cycle removal and subcode ensemble decoding, can be interpreted as instances of this framework. For 4-cycle removal, we find that the gains depend strongly on the BP iteration count and check-node message scaling. Building on this framework, we further propose a graph-derived subcode ensemble decoder and demonstrate under circuit-level noise that it substantially reduces the per-round logical error rate compared with BP on the corresponding 4-cycle-free decoding graph.
