Topological Quantum Computation via Non-Abelian Anyon Braid Group Representations — E8 Intelligence Research

FINDING: Anyon braiding forms the computational substrate for topological quantum computation, with non-Abelian statistics encoded in braid group representations rather than local qubit states. | MATH: Braid group \(B_n\) generators \(σ_i\) satisfy \(σ_iσᵢ₊₁σ_i = σᵢ₊₁σ_iσᵢ₊₁\) (Yang–Baxter equation); non-Abelian anyons carry unitary representations \(U(σ_i)\) with \(U(σ_i)U(σ_j)=U(σ_j)U(σ_i)\) for \(|i-j|≥ 2\). Fibonacci anyons: fusion rule \(τ × τ = 1 + τ\), Hilbert space dimension grows as Fibonacci sequence \(F_n\), golden ratio \(φ = (1+√5)/2 ≈ 1.618\) appears as asymptotic dimension growth rate. Topological protection arises from degeneracy of ground states on genus-\(g\) surfaces: dimension \(= k^g\) for level-\(k\) Chern–Simons theory. | CONNECTION: The Fibonacci anyon fusion space dimension ratio \(Fₙ₊₁/F_n → 1.618\) — direct geometric harmony link. Braid group relations ar Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com