{
  "abstract": "FINDING: Braiding of Ising anyons generates only Clifford gates, not universal quantum computation; two-qubit braiding exhausts the full two-qubit Clifford group. | MATH: Ising anyon braid group representation → Clifford group (generated by H, S, CNOT). Key matrices: H = (1/√2)[[1,1],[1,-1]], S = diag(1, i), CNOT. Braid generators σ_i satisfy σ_i² = -1 (fermion parity), σ_i σ_j = σ_j σ_i for |i-j|≥2. The π/8 gate (T = diag(1, e^{iπ/4})) is *not* in the Clifford group — hence not reachable by braiding alone. | CONNECTION: The Clifford group is the normalizer of the Pauli group, isomorphic to the binary symplectic group Sp(2n, F₂) — a root system of type C_n over F₂. The π/8 gate corresponds to a 45° rotation in the Bloch sphere — a geometric angle of π/4, which is *not* a multiple of the golden-ratio-derived angles (π/5, 2π/5) nor of the crystallographic 60° (π/3) or 90° (π/2). The Ising braid matrices live in SU(2) with level-2 Kac-Moody algebra — whose fusion rules (1/2 ⊗ 1/2 = 0 ⊕ 1)\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/303bpwym91j71.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447093",
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  "id": "303bpwym91j71",
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  "language": "eng",
  "licence": "CC-BY-4.0",
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  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/303bpwym91j71.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:47Z",
      "native_id": "23447093",
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  "title": "Ising Anyon Braiding Generates Only Clifford Gates, Not Universal Quantum Computation — E8 Intelligence Research",
  "title_text": "Ising Anyon Braiding Generates Only Clifford Gates, Not Universal Quantum Computation — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:47Z",
  "url": "https://research.draconitic.com/paper/303bpwym91j71",
  "venue": "Zenodo",
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}