{
  "abstract": "The codeword stabilized (CWS) framework provides a systematic method for constructing quantum error correcting codes from a simple undirected graph and a classical code. When the underlying classical code is linear, the resulting quantum code is a stabilizer code. In this work, we investigate the conditions under which an arbitrary $[n,k,d]$ classical binary linear code can be lifted to an $[[n,k,d]]$ quantum stabilizer code using the CWS framework. We analyze the random CWS code constructed from a given $[n,k,d]$ binary linear code $\\mathcal{C}$ and an Erdős-Rényi random graph $\\mathrm{G}(n, \\frac12)$. We establish a lower bound on the probability that the resulting quantum code preserves the minimum distance $d$ of the classical code. This probabilistic analysis yields a Gilbert-Varshamov-type condition on the $n,k,d$ parameters of the classical code that guarantees the existence of a graph resulting in a quantum code with the same $n,k,d$ parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14192",
  "author_total": 2,
  "authors": [
    {
      "name": "Thamadathil Aswanth"
    },
    {
      "name": "Navin Kashyap"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bppjt1bmv71gh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14192",
  "fulltext_url": null,
  "id": "bppjt1bmv71gh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14192",
  "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": "W7221758335",
  "pdf_url": "https://arxiv.org/pdf/2610.14192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bppjt1bmv71gh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.14192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Lifting an $[n,k,d]$ Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code",
  "title_text": "Lifting an [n,k,d] Binary Linear Code to an $[[n,k,d]]$ Quantum Stabilizer Code",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bppjt1bmv71gh",
  "venue": "arXiv",
  "versions": []
}