{
  "abstract": "We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over $\\mathbb{H}$ is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over $\\mathbb{H}$, we construct a complete model---quaternionic qubits on right $\\mathbb{H}$-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets---and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding $99\\%$ via pulse-level synthesis on current hardware are discussed. Over $\\mathbb{O}$, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, $G_{2}$-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Quantum Reports 2025, 7(4), 55",
  "arxiv": "2611.03348",
  "author_total": 3,
  "authors": [
    {
      "name": "Johan Heriberto Rúa Muñoz"
    },
    {
      "name": "Jorge Eduardo Mahecha Gómez"
    },
    {
      "name": "Santiago Pineda Montoya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bq7d2c9pzr64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03348",
  "fulltext_url": null,
  "id": "4bq7d2c9pzr64",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03348",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bq7d2c9pzr64.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quaternionic and Octonionic Frameworks for Quantum Computation: Mathematical Structures, Models, and Fundamental Limitations",
  "title_text": "Quaternionic and Octonionic Frameworks for Quantum Computation: Mathematical Structures, Models, and Fundamental Limitations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/4bq7d2c9pzr64",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.3390/quantum7040055",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}