Fibonacci Anyons: Exponential Error Suppression via Golden Ratio Topology — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 3, 2026• 0 citations

Abstract

FINDING: Fibonacci anyons encode quantum information in the fusion space of non-Abelian anyons, with logical error rates suppressed exponentially in code distance, governed by the golden ratio φ. | MATH: Fibonacci anyon fusion rules: τ × τ = 1 + τ (where τ is the anyon, 1 is vacuum). Quantum dimension: d_τ = φ = (1+√5)/2 ≈ 1.618. Total quantum dimension: D² = 1 + φ² = 2 + φ = φ² + 1 = φ + 2 ≈ 3.618. Topological charge fusion matrix: F-matrix (Fibonacci) = [[φ⁻¹, φ⁻¹/²], [φ⁻¹/², −φ⁻¹]] with entries involving φ⁻¹ = 0.618. Error correction threshold for Fibonacci Turaev-Viro code: ~0.12–0.15 (from Schotte et al., QIP2021). Logical error rate scaling: P_L ~ exp(−α d) where d is code distance, α depends on threshold and φ. | CONNECTION: Direct geometric harmony — φ = 1.618, φ⁻¹ = 0.618, φ⁻² = 0.382. The F-matrix eigenvalues are φ⁻¹ and −φ⁻¹, giving braid group representations with entries in ℚ(√5). The quantum dimension φ satisfies φ² = φ + 1, the same recurrence as the golden ratio. The Tu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23115531

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