Fibonacci Anyons: Universal Topological Quantum Computation via Braiding — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fibonacci anyons encode quantum information via braiding, with quantum dimension φ = (1+√5)/2 ≈ 1.618, enabling universal topological quantum computation; recent Quantinuum hardware demonstrates non-Abelian anyon braiding gates. | MATH: Fibonacci anyon fusion rule: τ ⊗ τ = 1 ⊕ τ (single non-trivial particle type τ); quantum dimension d_τ satisfies d_τ² = d_τ + 1 → d_τ = φ = (1+√5)/2 ≈ 1.6180339887; related constants: 1/φ = φ−1 = 0.6180339887, φ² = φ+1 = 2.6180339887, φ⁻² = 2−φ = 0.3819660113; braid group representations yield unitary matrices with entries in ℚ(√5); single-qubit gate compilation (arXiv:2008.03542) uses Fibonacci anyon braid words approximating Clifford+T-like gates to precision ε with O(log(1/ε)) overhead. | CONNECTION: The quantum dimension φ is the golden ratio itself — the same constant governing pentagonal symmetry (diagonal/edge ratio of regular pentagon), 5-fold crystallographic (forbidden in periodic lattices but allowed in quasicrystals), and the Fibona
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026fibonacci,
title = {{Fibonacci Anyons: Universal Topological Quantum Computation via Braiding — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447148},
url = {https://zenodo.org/records/23447148},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fibonacci Anyons: Universal Topological Quantum Computation via Braiding — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447148
UR - https://zenodo.org/records/23447148
AB - FINDING: Fibonacci anyons encode quantum information via braiding, with quantum dimension φ = (1+√5)/2 ≈ 1.618, enabling universal topological quantum computation; recent Quantinuum hardware demonstrates non-Abelian anyon braiding gates. | MATH: Fibonacci anyon fusion rule: τ ⊗ τ = 1 ⊕ τ (single non-trivial particle type τ); quantum dimension d_τ satisfies d_τ² = d_τ + 1 → d_τ = φ = (1+√5)/2 ≈ 1.6180339887; related constants: 1/φ = φ−1 = 0.6180339887, φ² = φ+1 = 2.6180339887, φ⁻² = 2−φ = 0.3819660113; braid group representations yield unitary matrices with entries in ℚ(√5); single-qubit gate compilation (arXiv:2008.03542) uses Fibonacci anyon braid words approximating Clifford+T-like gates to precision ε with O(log(1/ε)) overhead. | CONNECTION: The quantum dimension φ is the golden ratio itself — the same constant governing pentagonal symmetry (diagonal/edge ratio of regular pentagon), 5-fold crystallographic (forbidden in periodic lattices but allowed in quasicrystals), and the Fibona Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -