{
  "abstract": "Erasures are used to model faults at a subset of known locations in various platforms used to construct fault-tolerant quantum computers. Beyond the utility in erasure recovery, efficient decoders for erasures are useful to both understand error decoders and as a subroutine for error decoding. Classical expander codes, which belong to the family of low-density parity-check (LDPC) codes, can be equipped with the Peeling decoder which works in linear time. Our main result is the algorithm Small-Set-Peeling, a quantum generalization of the classical Peeling decoder for erasures, that applies to quantum expander codes (Tillich, Zémor, IEEE T-IT 2013; Leverrier, Tillich, Zémor, FOCS 2015). This decoder can correct up to $D-1$ erasures, where $D$ is the (design) distance of the code and, importantly, is the first decoder that is guaranteed to do so in linear time. Combining with the erasure-conversion algorithm Small-Set-Find (Krishna, Livni-Navon, Wootters, SODA 2024), our result also implies the existence of a novel graph-local linear-time decoder for Pauli errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06818",
  "author_total": 2,
  "authors": [
    {
      "name": "Anirudh Krishna"
    },
    {
      "name": "Christopher A. Pattison"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwjn8fnaccx8c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06818",
  "fulltext_url": null,
  "id": "bwjn8fnaccx8c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06818",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06818",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwjn8fnaccx8c.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06818"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Linear-time erasure recovery for quantum expander codes",
  "title_text": "Linear-time erasure recovery for quantum expander codes",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/bwjn8fnaccx8c",
  "venue": "arXiv",
  "versions": []
}