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.
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BibTeX
@misc{wu2026learning,
title = {{Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing}},
author = {Jiahui Wu and Chao Zhang and Zipeng Wu and Shilin Huang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28571},
eprint = {2608.28571},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28571},
}
RIS
TY - UNPB
TI - Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing
AU - Jiahui Wu
AU - Chao Zhang
AU - Zipeng Wu
AU - Shilin Huang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28571
UR - https://arxiv.org/abs/2608.28571
AB - 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.
ER -