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.

翻译：量子协议中的容错性依赖于纠错码及其相应译码器的贡献。量子低密度奇偶校验（QLDPC）码是研究最深入的量子码之一，具有良好的编码率和高效的译码器。然而，基于迭代消息传递的译码器虽然速度快，但因这类码固有的巨大简并度和短环问题，难以达到理想的成功率。本文提出一种改进置信传播（BP）译码（特别是最小和算法）性能的策略。我们设计了一个协同译码框架，将消息传递与稳定子校验节点移除相结合。进一步引入"量子比特分离"概念，证明译码性能的提升直接源于高度分离的被困数据量子比特的生成。为引导更具选择性地移除限制被困数据量子比特分离度的校验节点，我们引入了数据量子比特及其相邻稳定子校验的信息度量（IMs）。通过在广义超图乘积（GHP）码上评估所提协同译码器的性能，结果表明适当的译码器配置可在不显著增加开销的情况下缓解最小和译码中的陷阱集问题。