Topological Qubits: Braiding Non-Abelian Anyons with Fibonacci Fusion and Flux Readout — E8 Intelligence Research

FINDING: Anyon topological qubits rely on braiding non-Abelian anyons in 2D systems, with flux qubits enabling readout via Josephson vortices, and Fibonacci anyons providing universal gate sets through braiding operations. MATH: Braiding group generators \( σ_i \) satisfy \( σ_i σᵢ₊₁ σ_i = σᵢ₊₁ σ_i σᵢ₊₁ \) (Yang–Baxter equation). Fibonacci anyon fusion rules: \( τ × τ = 1 + τ \), with quantum dimension \( d_τ = φ = (1+√5)/2 ≈ 1.618 \). Single-qubit braiding gates compiled from Fibonacci anyons use matrices with entries involving \( φ⁻¹ ≈ 0.618 \). Chern–Simons term in Ginzburg–Landau model: \( SCS = k/4π ∫ A dA \), with level \( k \) integer. CONNECTION: Fibonacci anyon quantum dimension \( d_τ = φ \) directly ties to the golden ratio 1.618 and its inverse 0.618. Braiding matrices for Fibonacci anyons involve \( φ⁻¹ \) and \( φ⁻² ≈ 0.382 \). The Yan Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com