Topological Qubits via Anyon Braiding: Majorana 1 and Braid Group Gates — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Abstract

FINDING: Topological quantum computing encodes logical qubits in non-local, global degrees of freedom of matter — braiding anyonic excitations — making them immune to local decoherence; Microsoft's Majorana 1 is the first hardware claim of this paradigm. | MATH: Braiding operators are unitary representations of the braid group B_n, generated by σ_i with relations σ_iσ_{i+1}σ_i = σ_{i+1}σ_iσ_{i+1} (Yang–Baxter) and σ_iσ_j = σ_jσ_i (|i−j|≥2). Gates = images of B_n in U(N). Fibonacci anyons: braiding matrices have entries in ℤ[φ], φ = (1+√5)/2 = 1.618…; the Fibonacci F-matrix and R-matrix satisfy (R^F)^3 = 1, and the quantum dimension d_τ = φ. Ising anyons: d_σ = √2, braiding generates only the Clifford group (not universal). | CONNECTION: The Fibonacci anyon model is literally named for the golden ratio — its Hilbert-space dimension grows as φ^n, and the Jones polynomial evaluated at roots of unity (e.g., e^{2πi/5}) governs the braiding phases. φ = 1.618, 1/φ = 0.618, φ² = 2.618 all appe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23830518

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