利用协同检查节点移除解码量子低密度奇偶校验码
Decoding Quantum LDPC Codes using Collaborative Check Node Removal
AI总结：
本文提出一种协同解码框架，通过结合消息传递与稳定子检查节点移除，提升Belief Propagation解码性能，特别是最小和算法，通过引入量子比特分离概念和信息测量，有效减少陷阱集。
摘要：
量子协议的容错性需要纠错码及其合适解码器的贡献。量子低密度奇偶校验（QLDPC）码是研究最广泛的量子码之一，具有良好的编码率和高效的解码器。基于迭代消息传递的解码器虽然速度快，但因这些码固有的巨大退化性和短环而无法产生合适的成功率。本文提出了一种策略来改进Belief Propagation解码，特别是最小和算法。我们提出了一种协同解码框架，将消息传递与稳定子检查节点移除相结合。我们进一步引入“量子比特分离”概念，并展示改进的解码性能直接与高分离度的被困数据量子比特的生成相关。为了指导更选择性的检查节点移除，以约束被困数据量子比特的分离，我们为数据量子比特及其相邻稳定子检查引入信息测量（IMs）。我们评估了所提出的协同解码器在广义超图积（GHP）码上的性能，并证明适当的解码器配置可以在不引起显著开销的情况下减少最小和解码中的陷阱集。
英文摘要：
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and efficient decoders. Iterative message passing-based decoders, although fast, fail to produce suitable success rates due to the colossal degeneracy and short cycles intrinsic to these codes. In this work we present a strategy to improve the performance of the Belief Propagation (BP) decoding, specifically the min-sum algorithm. We propose a collaborative decoding framework that integrates message passing with stabilizer check node removals. We further introduce the concept of ``qubit separation" and show that the improved decoding performance is directly related to the generation of highly separated trapped data qubits. To guide a more selective removal of check nodes that constrain the separation of the trapped data qubits, we introduce information measurements (IMs) for the data qubits and their adjacent stabilizer checks. We evaluate the performance of the proposed collaborative decoder on Generalized Hypergraph Product (GHP) codes and demonstrate that appropriate decoder configurations mitigate trapping sets in min-sum decoding without significant overhead.
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