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 \( \sigma_i \) satisfy \( \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} \); anyon fusion rules: \( \sigma \times \sigma = 1 + \psi \) (Ising model); Majorana operators \( \gamma_i \) with \( \{\gamma_i, \gamma_j\} = 2\delta_{ij} \); topological qubit encoded in parity \( i\gamma_1\gamma_2 = \pm 1 \). | CONNECTION: Braid group is related to the Fibonacci sequence via the Burau representation; the golden ratio \( \phi = 1.618 \) appears in the quantum dimension of Fibonacci anyons: \( d_\tau = \phi \). The Ising anyon quantum dimension is \( \sqrt{2} \), linking to \( \sqrt{2} \approx 1.414 \), 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