Golden Ratio Confirmed as Physical Constant in Topological Quantum Computation — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fibonacci anyons — whose braiding statistics are governed by the golden ratio — have been experimentally realized (Quantinuum) and theoretically compiled into universal single-qubit gates, confirming the golden ratio as a physical constant of topological quantum computation. | MATH: Fibonacci anyon quantum dimension d = ϕ = (1+√5)/2 ≈ 1.618; fusion rule τ × τ = 1 + τ (non-Abelian); braid matrices satisfy σi2 ≠ 1 but Yang-Baxter σi σi+1 σi = σi+1 σi σi+1; single-qubit gate compilation uses F-matrix with entries involving ϕ−1 = ϕ − 1 ≈ 0.618 and ϕ−1/2. The Ising anyon has d = √2, but Fibonacci is universal for topological QC while Ising is not (without magic state distillation). | CONNECTION: Direct geometric harmony — the golden ratio ϕ appears as the quantum dimension, and its inverse ϕ−1 = 0.618
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- The Golden Ratio as a Universal Structural Constant in Physics, Audio, and Computation — E8 Intelligence Research
- E8 Fibonacci Anyon Time-Crystal for Universal Topological Quantum Computation — E8 Intelligence Research
- Fibonacci Anyons Realize Universal Topological Quantum Computation via Golden Ratio Braiding — E8 Intelligence Research
- Fibonacci Anyons: Universal Topological Quantum Computation via Braiding — E8 Intelligence Research
- Fibonacci Anyons: Golden Ratio Quantum Dimension Enables Universal Topological Computation — E8 Intelligence Research
BibTeX
@misc{caldin2026golden,
title = {{Golden Ratio Confirmed as Physical Constant in Topological Quantum Computation — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447152},
url = {https://zenodo.org/records/23447152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Golden Ratio Confirmed as Physical Constant in Topological Quantum Computation — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447152
UR - https://zenodo.org/records/23447152
AB - FINDING: Fibonacci anyons — whose braiding statistics are governed by the golden ratio — have been experimentally realized (Quantinuum) and theoretically compiled into universal single-qubit gates, confirming the golden ratio as a physical constant of topological quantum computation. | MATH: Fibonacci anyon quantum dimension d = ϕ = (1+√5)/2 ≈ 1.618; fusion rule τ × τ = 1 + τ (non-Abelian); braid matrices satisfy σ_i^2 ≠ 1 but Yang-Baxter σ_i σ_i+1 σ_i = σ_i+1 σ_i σ_i+1; single-qubit gate compilation uses F-matrix with entries involving ϕ^−1 = ϕ − 1 ≈ 0.618 and ϕ^−1/2. The Ising anyon has d = √2, but Fibonacci is universal for topological QC while Ising is not (without magic state distillation). | CONNECTION: Direct geometric harmony — the golden ratio ϕ appears as the quantum dimension, and its inverse ϕ^−1 = 0.618 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -