Jiahui Wu, Chao Zhang, Zipeng Wu, Shilin Huang (Aug 31 2026).
Abstract: 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.
