Majorana 1 and Braid-Based Topological Quantum Computing — E8 Intelligence Research

FINDING: Topological quantum computing leverages non-Abelian anyons (Majorana zero modes) for fault-tolerant braid-based computation, with Microsoft's Majorana 1 chip claiming hardware realization. MATH: - Braid group \( B_n \) generators \( σ_i \) satisfy \( σ_iσᵢ₊₁σ_i = σᵢ₊₁σ_iσᵢ₊₁ \) (Yang–Baxter equation). - Non-Abelian anyon fusion rules: \( σ × σ = 1 + ψ \) (Ising anyons) or Fibonacci anyons: \( τ × τ = 1 + τ \). - Topological quantum number: \( ν = 1/2π∮ A· dl \) (Chern number for Majorana modes). - Majorana condition: \( γ^ = γ \), \( \{γ_i,γ_j\} = 2δᵢⱼ \). - Braid matrices yield phases \( eiθ \) with \( θ = π/8 \) for Ising (Clifford) and \( θ = 2π/5 \) for Fibonacci (universal). CONNECTION: - Fibonacci anyons: golden ratio \( φ = 1.618 \) appears in fusion dimension \( d_τ = φ \), an Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com