Golden Ratio Unites Topological Quantum Gates and Penrose Quasicrystals — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fibonacci anyon braiding realizes quantum gates via the golden ratio, and Penrose tilings encode the same algebraic structure through inflation/deflation — a direct bridge between topological quantum computation and quasicrystalline order. | MATH: Fibonacci anyons obey fusion rule τ × τ = 1 + τ (where τ is the non-Abelian anyon). The quantum dimension of τ is φ = (1+√5)/2 ≈ 1.618. Braiding matrices for these anyons are expressed in terms of φ and its inverse φ⁻¹ = φ − 1 ≈ 0.618. Penrose tiling inflation factor is φ² = φ + 1 ≈ 2.618 (deflation factor φ⁻² ≈ 0.382). The single-qubit braiding gate compilation (arXiv:2008.03542) decomposes unitaries into sequences whose length scales with log(1/ε) and whose elementary matrices contain entries proportional to φ and φ⁻¹. The Fibonacci anyon model's Hilbert space dimension grows as Fₙ (Fibonacci numbers), whose ratio Fₙ₊₁/Fₙ → φ. | CONNECTION: Direct. The fusion space dimension of n Fibonacci anyons is the Fibonacci number Fₙ₊₁ — the
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026golden,
title = {{Golden Ratio Unites Topological Quantum Gates and Penrose Quasicrystals — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23464942},
url = {https://zenodo.org/records/23464942},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Golden Ratio Unites Topological Quantum Gates and Penrose Quasicrystals — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23464942
UR - https://zenodo.org/records/23464942
AB - FINDING: Fibonacci anyon braiding realizes quantum gates via the golden ratio, and Penrose tilings encode the same algebraic structure through inflation/deflation — a direct bridge between topological quantum computation and quasicrystalline order. | MATH: Fibonacci anyons obey fusion rule τ × τ = 1 + τ (where τ is the non-Abelian anyon). The quantum dimension of τ is φ = (1+√5)/2 ≈ 1.618. Braiding matrices for these anyons are expressed in terms of φ and its inverse φ⁻¹ = φ − 1 ≈ 0.618. Penrose tiling inflation factor is φ² = φ + 1 ≈ 2.618 (deflation factor φ⁻² ≈ 0.382). The single-qubit braiding gate compilation (arXiv:2008.03542) decomposes unitaries into sequences whose length scales with log(1/ε) and whose elementary matrices contain entries proportional to φ and φ⁻¹. The Fibonacci anyon model's Hilbert space dimension grows as Fₙ (Fibonacci numbers), whose ratio Fₙ₊₁/Fₙ → φ. | CONNECTION: Direct. The fusion space dimension of n Fibonacci anyons is the Fibonacci number Fₙ₊₁ — the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -