{
  "abstract": "We develop normal factor graph (NFG) representations of stabilizer quantum error-correcting codes and entanglement-assisted quantum error-correcting codes. We introduce two complementary representations. Quantum-code NFGs describe stabilizer and normalizer label codes and provide a graphical framework for establishing self-orthogonality, constructing codes from component codes, and identifying encoding and decoding circuits. Quantum-probability NFGs represent the quantum-mechanical probabilities associated with encoding, noise, and measurement. We also introduce a doubleedge formulation that makes the relationship between these two representations explicit. We apply the framework to convolutional and tail-biting convolutional stabilizer codes, as well as to two classes of low-density parity-check stabilizer codes. Finally, we extend the quantum-probability representation to entanglementassisted codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00985",
  "author_total": 2,
  "authors": [
    {
      "name": "July X. Li"
    },
    {
      "name": "Pascal O. Vontobel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2vfejg8q61dr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00985",
  "fulltext_url": null,
  "id": "a2vfejg8q61dr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00985",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2vfejg8q61dr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00985"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications",
  "title_text": "Normal Factor Graph Representations of Stabilizer Quantum Codes with Applications",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/a2vfejg8q61dr",
  "venue": "arXiv",
  "versions": []
}