Non-Abelian Anyon Braiding and Spectroscopy: Complementary Routes to Topological Qubits — E8 Intelligence Research

FINDING: Non-abelian anyons are now experimentally braided in a universal topological gate (Quantinuum), while single-anyon/anyon-molecule spectroscopy proceeds in quantum Hall antidots (Young, UCSB) — the two complementary routes to topological qubits. | MATH: Braiding operators are unitary representations of the braid group B_n; non-abelian anyons realize matrices R = exp(iθ σᵃ) acting on a degenerate ground-state manifold of dimension = quantum dimension d_a. For Ising-type (Majorana) anyons d = √2; for Fibonacci anyons d = φ = 1.618…, with fusion rule τ⊗τ = 1⊕τ. | CONNECTION: The Fibonacci anyon's quantum dimension is exactly the golden ratio φ = (1+√5)/2 = 1.618, and its fusion matrix has eigenvalues φ and −1/φ = −0.618. Braiding phases for Fibonacci anyons involve θ = 2π/5 (pentagon), tying directly to the 5-fold symmetry of the icosahedron and the H₃ root system. Ising anyons (√2) connect to the D-series / SO(2n) root lattices. | DEPTH: 8 FINDING: Quantum Hall antidots host iso Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com