{
  "abstract": "We develop a holomorphic representation of quantum error correction codes (QECCs) within the Segal--Bargmann space. By encoding qubits into Schwinger boson modes $(z_{a_j}, z_{b_j})$ subject to a degree-one homogeneity constraint, we derive closed-form differential operator representations for stabilizers, syndrome extraction, and recovery for fundamental codes (three-, five-, seven-, and nine-qubit codes). Quantum errors are characterized as holomorphic perturbations violating this constraint, while syndrome measurement projects onto eigenspaces of commuting differential operators. Restricting to unit-magnitude variables ($|z|=1$) reveals a toroidal space $\\T^{2n}$ where error syndromes manifest as discrete translations in winding number space $\\Z^{2n}$, and recovery acts as Hamiltonian flows restoring the winding configuration. In the full Segal--Bargmann space, the code space is a holomorphic submanifold of $\\CP^{2^n-1}$, with correctable errors as transverse normal directions. Consequently, the Knill--Laflamme condition becomes a Fubini--Study orthogonality condition between the code submanifold and its error-translated images. Topological protection emerges from the $U(1)^n$ fiber bundle structure: global phase noise along fibers is unobservable, while base-space errors require active correction. Finally, we establish a path-integral formulation for semiclassical error correction dynamics and show that geometric entanglement via the Segre embedding naturally quantifies code distance. This framework unifies algebraic, geometric, and topological perspectives on fault-tolerant quantum protocols.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19162",
  "author_total": 1,
  "authors": [
    {
      "name": "M. W. AlMasri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avh8ac16748fv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19162",
  "fulltext_url": null,
  "id": "avh8ac16748fv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19162",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avh8ac16748fv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19162"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Holomorphic Quantum Error Correction Codes",
  "title_text": "Holomorphic Quantum Error Correction Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/avh8ac16748fv",
  "venue": "arXiv",
  "versions": []
}