Topological Quantum Computing: Non-Abelian Anyons, Braiding, and Majorana Qubits — E8 Intelligence Research

FINDING: Topological quantum computing uses anyons with non-Abelian braiding statistics for fault-tolerant qubits, with Microsoft's Majorana 1 chip claiming topological qubit realization. | MATH: Braiding group \( B_n \) generators satisfy \( σ_i σᵢ₊₁ σ_i = σᵢ₊₁ σ_i σᵢ₊₁ \); anyon fusion rules \( a × b = ∑_c Nab^c c \); Fibonacci anyon quantum dimension \( d = φ = (1+√5)/2 ≈ 1.618 \); Majorana zero modes obey \( γ_i^ = γ_i, \{γ_i, γ_j\} = 2δᵢⱼ \). | CONNECTION: Fibonacci anyon dimension \( d = 1.618 \) is the golden ratio; braid group representations relate to Temperley-Lieb algebras with parameter \( τ = 1/d^2 = 0.382 \); anyon fusion rules mirror SU(2)_k modular tensor categories with \( q = e2π i/(k+2) \), linking to root systems \( A_n, D_n, E_6, E_7, E_8 \). | DEPTH: 8 — Directly ties golden ratio, modular tensor categories, and non-Abelian statistics to fault-tolerant quant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com