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 \( \sigma_i \) satisfy \( \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} \) (Yang–Baxter equation). Fibonacci anyon fusion rules: \( \tau \times \tau = 1 + \tau \), with quantum dimension \( d_\tau = \phi = (1+\sqrt{5})/2 \approx 1.618 \). Single-qubit braiding gates compiled from Fibonacci anyons use matrices with entries involving \( \phi^{-1} \approx 0.618 \). Chern–Simons term in Ginzburg–Landau model: \( S_{CS} = \frac{k}{4\pi} \int A \wedge dA \), with level \( k \) integer. CONNECTION: Fibonacci anyon quantum dimension \( d_\tau = \phi \) directly ties to the golden ratio 1.618 and its inverse 0.618. Braiding matrices for Fibonacci anyons involve \( \phi^{-1} \) and \( \phi^{-2} \approx 0.382 \). The Yan Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com