{
  "abstract": "We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11457",
  "author_total": 3,
  "authors": [
    {
      "name": "Nathaniel Selub"
    },
    {
      "name": "Aditya Bhardwaj"
    },
    {
      "name": "Ethan Lake"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4s5x74hq9vdkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11457",
  "fulltext_url": null,
  "id": "4s5x74hq9vdkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11457",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.CG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212281517",
  "pdf_url": "https://arxiv.org/pdf/2609.11457",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4s5x74hq9vdkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.11457",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11457"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes",
  "title_text": "Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/4s5x74hq9vdkf",
  "venue": "arXiv",
  "versions": []
}