Non-Abelian Anyon Fusion Mirrors Braid Groups for Fault-Tolerant Quantum Computing — E8 Intelligence Research

FINDING: Non-Abelian anyon fusion algebras exhibit self-similarity that mirrors the braid group structure, enabling fault-tolerant topological quantum computation via braiding operations. MATH: - Braid group \( B_n \) generators \( σ_i \) satisfy \( σ_i σᵢ₊₁ σ_i = σᵢ₊₁ σ_i σᵢ₊₁ \) and \( σ_i σ_j = σ_j σ_i \) for \( |i-j|>1 \). - Fusion algebra: \( φ_a × φ_b = ∑_c Nab^c φ_c \), where \( Nab^c \) are non-negative integers (fusion coefficients). For non-Abelian anyons, \( ∑_c Nab^c > 1 \) for some \( a,b \). - Fibonacci anyon model: single nontrivial particle \( τ \) with fusion rule \( τ × τ = 1 + τ \), leading to quantum dimension \( d_τ = φ = (1+√5)/2 ≈ 1.618 \). - Braiding matrices yield phases \( eiθ \) with \( θ = 2π/5, 4π/5 \) (related to golden angle \( 2π/φ^2 ≈ 137.5^∘ \)). CONNECTION: - Fibonacci anyon quant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com