Theoretical mathematical analysis demonstrates Fibonacci anyon braiding with golden ratio quantum dimensions, suggesting geometric foundations for fault-tolerant topological quantum computing.
FINDING: Anyon braiding for topological qubits relies on non-Abelian statistics and 2D anyon models (e.g., Fibonacci anyons) for fault-tolerant quantum computation. MATH: Braiding group B_n; Fibonacci anyon fusion rules: τ × τ = 1 + τ (golden ratio φ = (1+√5)/2 ≈ 1.618). Quantum dimension d_τ = φ. Unitary braid matrices satisfy Yang-Baxter equation. CONNECTION: Fibonacci anyon quantum dimension φ = 1.618 (golden ratio). Braid group representations yield eigenvalues related to φ (e.g., 0.382, 0.618, 1.618, 2.618). Crystallographic symmetry: anyon models correspond to root systems (e.g., SU(2)_k, E_8). DEPTH: 8 — Directly links topological quantum computing to golden ratio and non-Abelian braiding, a profound geometric-harmonic structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.
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