Modular Tensor Categories as Algebraic Framework for Topological Quantum Computation — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Modular tensor categories (MTCs) provide the algebraic backbone for topological quantum computation, with S and T matrices encoding anyon braiding and fusion rules. | MATH: MTC data: fusion rules Nkij, S-matrix (modular transformation τ → −1/τ), T-matrix (diagonal, θa = e2π i ha topological spins), satisfying S2 = C (charge conjugation), (ST)3 = e2π i c/8 S2 (where c is the chiral central charge). The entries of S and T lie in a cyclotomic field ℚ(ζN), ζN = e2π i/N. For the Fibonacci anyon MTC: S = 1/(√(ϕ+2)) 1 & ϕ ϕ & −1, T = diag(1, e4π i/5), where ϕ = (1+√5)/2. | CONNECTION: **Direct hit**: The Fibonacci MTC's S-matrix contains ϕ = 1.618 and ϕ+2 = ϕ2+1 = 3.618, whose inverse square root yields 1/√(3.618) ≈ 0.5257. The golden ratio appears intrinsically.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Reversible Computation as Algebraic Symmetry: A Group-Theoretic Structure — E8 Intelligence Research
- E8 Fibonacci Anyon Time-Crystal for Universal Topological Quantum Computation — E8 Intelligence Research
- Golden Ratio Confirmed as Physical Constant in 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
BibTeX
@misc{caldin2026modular,
title = {{Modular Tensor Categories as Algebraic Framework for Topological Quantum Computation — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587332},
url = {https://zenodo.org/records/23587332},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Modular Tensor Categories as Algebraic Framework for Topological Quantum Computation — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587332
UR - https://zenodo.org/records/23587332
AB - FINDING: Modular tensor categories (MTCs) provide the algebraic backbone for topological quantum computation, with S and T matrices encoding anyon braiding and fusion rules. | MATH: MTC data: fusion rules N^k_ij, S-matrix (modular transformation τ → −1/τ), T-matrix (diagonal, θ_a = e^2π i h_a topological spins), satisfying S^2 = C (charge conjugation), (ST)^3 = e^2π i c/8 S^2 (where c is the chiral central charge). The entries of S and T lie in a cyclotomic field ℚ(ζ_N), ζ_N = e^2π i/N. For the Fibonacci anyon MTC: S = 1/(√(ϕ+2)) 1 & ϕ ϕ & −1, T = diag(1, e^4π i/5), where ϕ = (1+√5)/2. | CONNECTION: **Direct hit**: The Fibonacci MTC's S-matrix contains ϕ = 1.618 and ϕ+2 = ϕ^2+1 = 3.618, whose inverse square root yields 1/√(3.618) ≈ 0.5257. The golden ratio appears intrinsically. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -