AI 中文总结
该研究提出分层消息传递神经框架解码级联量子码，在[[15,7,3]]量子汉明码上提升去极化伪阈值，在多超立方体码上降低逻辑-CNOT失效率，为级联码设计提供通用解码工具。
AI 中文摘要
我们提出一种用于解码通用级联稳定子码的神经消息传递框架。软置信度在级联层级间双向传播，轻量级神经网络仅需学习聚合传入消息。针对级联[[15,7,3]]量子汉明码，所提解码器在比特翻转噪声和去极化噪声下均达到远超当前最优双向硬判决解码器的阈值，其中去极化伪阈值几乎翻倍，从6.5%升至12.3%。针对多超立方体码，在Knill teleportation型纠错的电路级错误上微调的解码器，使用固定次数的消息传递迭代而非大规模组合搜索，可实现比专用解码器更低的逻辑-CNOT失效率。该框架为探索级联码（包括非CSS结构）的设计空间提供通用解码工具，以实现低开销容错。
英文摘要
We introduce a neural message-passing framework for decoding general concatenated stabilizer codes. Soft beliefs propagate bidirectionally across concatenation levels, and lightweight neural networks learn only to aggregate incoming messages. For the concatenated $[[15,7,3]]$ quantum Hamming code, the resulting decoder achieves substantially higher thresholds than the state-of-the-art bidirectional hard-decision decoder under both bit-flip and depolarizing noise. In particular, the depolarizing pseudo-threshold nearly doubles, from $6.5\%$ to $12.3\%$. For many-hypercube codes, a decoder fine-tuned on circuit-level errors in Knill's teleportation-based error correction can achieve lower logical-CNOT failure rates than their dedicated decoder, using a fixed number of message-passing iterations instead of extensive combinatorial search. Our framework provides a generic decoding tool for exploring the design space of concatenated codes, including non-CSS constructions, toward low-overhead fault tolerance.
