Fibonacci Anyons: Universal Quantum Computation via Golden Ratio Braiding — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fibonacci anyons carry quantum dimension φ = (1+√5)/2 ≈ 1.618, enabling universal topological quantum computation via braiding alone; recent Quantinuum experiment claims first non-abelian anyon braiding gate. | MATH: Quantum dimension of Fibonacci anyon: d = φ = 2cos(π/5) = (1+√5)/2 ≈ 1.618; satisfies d² = d + 1. Fusion rule: τ ⊗ τ = 1 ⊕ τ (where τ is the anyon). Braid matrices generate a dense subset of SU(2) — specifically, the Yang-Baxter R-matrix eigenvalues are {e^{±4πi/5}, e^{±2πi/5}} — yielding universal gates. Ising anyons: d = √2, fusion τ⊗τ = 1 ⊕ ψ (non-universal, only Clifford gates). | CONNECTION: φ = 2cos(π/5) ties directly to pentagonal symmetry (crystallographic point group 5, root system of H₂ — the icosahedral/dodecahedral symmetry group). The golden ratio appears as the quantum dimension because the Fibonacci fusion category is the simplest non-abelian category with a self-dual object whose fusion matrix has spectral radius φ. The braid group B₃ maps onto the
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Fibonacci Anyons Realize Universal Topological Quantum Computation via Golden Ratio Braiding — E8 Intelligence Research
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- E8 Fibonacci Anyon Time-Crystal for Universal Topological Quantum Computation — E8 Intelligence Research
- Fibonacci Anyons: Golden Ratio Quantum Dimension Enables Universal Topological Computation — E8 Intelligence Research
BibTeX
@misc{caldin2026fibonacci,
title = {{Fibonacci Anyons: Universal Quantum Computation via Golden Ratio Braiding — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447087},
url = {https://zenodo.org/records/23447087},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fibonacci Anyons: Universal Quantum Computation via Golden Ratio Braiding — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447087
UR - https://zenodo.org/records/23447087
AB - FINDING: Fibonacci anyons carry quantum dimension φ = (1+√5)/2 ≈ 1.618, enabling universal topological quantum computation via braiding alone; recent Quantinuum experiment claims first non-abelian anyon braiding gate. | MATH: Quantum dimension of Fibonacci anyon: d = φ = 2cos(π/5) = (1+√5)/2 ≈ 1.618; satisfies d² = d + 1. Fusion rule: τ ⊗ τ = 1 ⊕ τ (where τ is the anyon). Braid matrices generate a dense subset of SU(2) — specifically, the Yang-Baxter R-matrix eigenvalues are {e^{±4πi/5}, e^{±2πi/5}} — yielding universal gates. Ising anyons: d = √2, fusion τ⊗τ = 1 ⊕ ψ (non-universal, only Clifford gates). | CONNECTION: φ = 2cos(π/5) ties directly to pentagonal symmetry (crystallographic point group 5, root system of H₂ — the icosahedral/dodecahedral symmetry group). The golden ratio appears as the quantum dimension because the Fibonacci fusion category is the simplest non-abelian category with a self-dual object whose fusion matrix has spectral radius φ. The braid group B₃ maps onto the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -