{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28571",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiahui Wu"
    },
    {
      "name": "Chao Zhang"
    },
    {
      "name": "Zipeng Wu"
    },
    {
      "name": "Shilin Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mjt696907rv5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28571",
  "fulltext_url": null,
  "id": "7mjt696907rv5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28571",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204745456",
  "pdf_url": "https://arxiv.org/pdf/2608.28571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mjt696907rv5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28571"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing",
  "title_text": "Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/7mjt696907rv5",
  "venue": "arXiv",
  "versions": []
}