Topological Quantum Computing with Non-Abelian Anyons and Braid Group Operations — E8 Intelligence Research

FINDING: Topological quantum computing uses non-Abelian anyons (Majorana zero modes) to encode qubits in braiding operations, immune to local decoherence. | MATH: Braid group \( B_n \) generators \( σ_i \) satisfy \( σ_i σᵢ₊₁ σ_i = σᵢ₊₁ σ_i σᵢ₊₁ \); anyon fusion rules: \( σ × σ = 1 + ψ \) (Ising model); Majorana operators \( γ_i \) with \( \{γ_i, γ_j\} = 2δᵢⱼ \); topological qubit encoded in parity \( iγ_1γ_2 = ± 1 \). | CONNECTION: Braid group is related to the Fibonacci sequence via the Burau representation; the golden ratio \( φ = 1.618 \) appears in the quantum dimension of Fibonacci anyons: \( d_τ = φ \). The Ising anyon quantum dimension is \( √2 \), linking to \( √2 ≈ 1.414 \), close to 1.4142 (no direct golden ratio). Crystallographic symmetry: Anyon braiding corresponds to the mapping class group of a punctured surface, related to root systems of Lie alge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com