Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing

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.

arXiv:2608.28571 [quant-ph]

(or arXiv:2608.28571v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.28571 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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