{
  "abstract": "FINDING: The Solovay-Kitaev theorem guarantees efficient approximation of any single-qubit unitary using finite gate sets; its optimal implementations (\"golden gates\") are deeply tied to algebraic number theory and, for Fibonacci anyons, to the golden ratio. | MATH: The theorem states: For any finite set \\(S \\subset SU(2)\\) generating a dense subgroup, any \\(U \\in SU(2)\\) can be \\(\\varepsilon\\)-approximated in \\(O(\\log^c(1/\\varepsilon))\\) gates, \\(c \\approx 3.97\\) (improved to \\(c=1\\) for certain sets). Exact synthesis for Fibonacci anyons uses the braid group \\(B_3\\) representation where the fusion space dimension grows as \\(F_n\\) (Fibonacci numbers). The key constant: the golden ratio \\(\\varphi = (1+\\sqrt{5})/2 = 1.618...\\), with its inverse \\(\\varphi^{-1} = 0.618...\\), and the related \\(\\varphi^{-2} = 0.382...\\). The Fibonacci anyon braid matrices have entries in \\(\\mathbb{Z}[\\varphi]\\), the ring of integers of \\(\\mathbb{Q}(\\sqrt{5})\\). | CONNECTION: Direct and explicit. The Fibonac\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2evm65y20tjd1.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464948",
  "fulltext_url": null,
  "id": "2evm65y20tjd1",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23464948",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2evm65y20tjd1.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:50Z",
      "native_id": "23464948",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23464948"
    }
  ],
  "subjects": [],
  "title": "Golden Gates: Solovay-Kitaev, Fibonacci Anyons, and the Golden Ratio — E8 Intelligence Research",
  "title_text": "Golden Gates: Solovay-Kitaev, Fibonacci Anyons, and the Golden Ratio — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:50Z",
  "url": "https://research.draconitic.com/paper/2evm65y20tjd1",
  "venue": "Zenodo",
  "versions": []
}