Topological Quantum Computing: Non-Abelian Anyons, Braiding, and Majorana Qubits — E8 Intelligence Research

FINDING: Topological quantum computing uses anyons with non-Abelian braiding statistics for fault-tolerant qubits, with Microsoft's Majorana 1 chip claiming topological qubit realization. | MATH: Braiding group \( B_n \) generators satisfy \( \sigma_i \sigma_{i+1} \sigma_i = \sigma_{i+1} \sigma_i \sigma_{i+1} \); anyon fusion rules \( a \times b = \sum_c N_{ab}^c c \); Fibonacci anyon quantum dimension \( d = \phi = (1+\sqrt{5})/2 \approx 1.618 \); Majorana zero modes obey \( \gamma_i^\dagger = \gamma_i, \{\gamma_i, \gamma_j\} = 2\delta_{ij} \). | CONNECTION: Fibonacci anyon dimension \( d = 1.618 \) is the golden ratio; braid group representations relate to Temperley-Lieb algebras with parameter \( \tau = 1/d^2 = 0.382 \); anyon fusion rules mirror SU(2)_k modular tensor categories with \( q = e^{2\pi i/(k+2)} \), linking to root systems \( A_n, D_n, E_6, E_7, E_8 \). | DEPTH: 8 — Directly ties golden ratio, modular tensor categories, and non-Abelian statistics to fault-tolerant quant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com