{
  "abstract": "We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes with the goal of reducing decoding latency. We target two major bottlenecks of decoding under the \\emph{circuit-level} noise model: (i) post-processing via order-statistics decoding (OSD), and (ii) the large number of auxiliary variable nodes commonly introduced to represent CNOT-induced correlations during syndrome extraction. Our key observation is that propagating CNOT faults (\\emph{hook errors}) create \\emph{stabilizer-induced} trapping sets (TSs) that are intrinsic to hypergraph-product (HGP) and lifted-product (LP) constructions. Therefore, instead of modeling each such fault with an explicit correlation node and relying on OSD to clean up the resulting failures, we design message-passing decoders that resolve the corresponding \\emph{stabilizer-induced} TSs directly. We obtain these decoders by deriving QLDPC decoders from decoders for the parent classical LDPC codes and using them collectively to correct broad families of \\emph{stabilizer-induced} TSs. For CNOT faults that manifest primarily as syndrome errors, we show that their effect is equivalent to a data error together with syndrome-bit measurement errors. Consequently, given repeated measurements and a decoding graph that already includes nodes representing syndrome-bit errors, no distinct variable node is needed for each CNOT fault. Using a \\emph{phenomenological} Tanner graph with nodes representing only data errors and syndrome-bit errors, simulations on LP codes show a significant improvement in logical error rate relative to BP+OSD. Moreover, the improved error correction relies on low-complexity finite-state iterative decoders, targeted for fast and low-latency FPGA implementation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31040",
  "author_total": 4,
  "authors": [
    {
      "name": "Asit Kumar Pradhan"
    },
    {
      "name": "Nithin Raveendran"
    },
    {
      "name": "David Declercq"
    },
    {
      "name": "Bane Vasić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cd19er1k9t5we.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31040",
  "fulltext_url": null,
  "id": "cd19er1k9t5we",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31040",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204961082",
  "pdf_url": "https://arxiv.org/pdf/2608.31040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cd19er1k9t5we.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2608.31040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31040"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes",
  "title_text": "Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/cd19er1k9t5we",
  "venue": "arXiv",
  "versions": []
}