Non-Abelian Anyons: Theoretical Promise, Experimental Gap — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Anyon braiding provides non-abelian statistics for topologically protected quantum computation, but the search results are mostly pedagogical videos and one unrelated ATLAS squark paper — no primary experimental data or new mathematical result is presented. | MATH: Anyons obey fractional statistics: braiding operator B acts on degenerate ground-state manifold with unitary representation ρ(B), where ρ(B1)ρ(B2) ≠ ρ(B2)ρ(B1) for non-abelian anyons. Exchange phase θ generalizes Fermi (θ=π) and Bose (θ=0) to θ = 2π s with s fractional (e.g., s=1/3, 1/5). Fibonacci anyon fusion rules: τ × τ = 1 + τ, with quantum dimension dτ = φ = (1+√5)/2 ≈ 1.618. | CONNECTION: **Strong.** The Fibonacci anyon quantum dimension is exactly the golden ratio φ = 1.618. Braid group Bn representations relate to Temperley–Lieb algebra with l
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026nonabelian,
title = {{Non-Abelian Anyons: Theoretical Promise, Experimental Gap — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490715},
url = {https://zenodo.org/records/23490715},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Abelian Anyons: Theoretical Promise, Experimental Gap — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490715
UR - https://zenodo.org/records/23490715
AB - FINDING: Anyon braiding provides non-abelian statistics for topologically protected quantum computation, but the search results are mostly pedagogical videos and one unrelated ATLAS squark paper — no primary experimental data or new mathematical result is presented. | MATH: Anyons obey fractional statistics: braiding operator B acts on degenerate ground-state manifold with unitary representation ρ(B), where ρ(B_1)ρ(B_2) ≠ ρ(B_2)ρ(B_1) for non-abelian anyons. Exchange phase θ generalizes Fermi (θ=π) and Bose (θ=0) to θ = 2π s with s fractional (e.g., s=1/3, 1/5). Fibonacci anyon fusion rules: τ × τ = 1 + τ, with quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618. | CONNECTION: **Strong.** The Fibonacci anyon quantum dimension is exactly the golden ratio φ = 1.618. Braid group B_n representations relate to Temperley–Lieb algebra with l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -