{
  "abstract": "Achieving passive protection of quantum information at finite temperature is a central problem at the intersection of quantum information and quantum many-body physics. Yet a general, computable criterion for determining self-correcting behavior directly from the form of local interactions remains elusive. Here we develop a unified algebraic-geometric framework for certifying partial self-correction in three-dimensional translation-invariant local stabilizer codes, encompassing the cubic code as a special case. From the algebraic curves defined by the codes' defining polynomials, we construct valuation matrices on the boundaries of their normalized projective closures and derive a computable rank criterion. Together with a polynomial-time decoder, this criterion guarantees super-Arrhenius memory lifetimes for code families satisfying it under the specified local Davies dynamics. We apply the framework to certify several classes of partially self-correcting quantum memories, including nearest-neighbor models with stabilizer weight as low as six and long memory lifetimes at modest system sizes. These results establish an algebraic-geometric connection between local stabilizer structure and the recoverability of quantum information at finite temperature, providing a systematic approach to certifying and designing passive quantum memories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06469",
  "author_total": 2,
  "authors": [
    {
      "name": "Chong-Yuan Xu"
    },
    {
      "name": "Yong Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkescth9b9pkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06469",
  "fulltext_url": null,
  "id": "fkescth9b9pkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06469",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkescth9b9pkb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06469"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Universally Certifying Partially Self-Correcting Quantum Memories in 3D Translation-Invariant Stabilizer Codes",
  "title_text": "Universally Certifying Partially Self-Correcting Quantum Memories in 3D Translation-Invariant Stabilizer Codes",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:20Z",
  "url": "https://research.draconitic.com/paper/fkescth9b9pkb",
  "venue": "arXiv",
  "versions": []
}