Topological Quantum Computing: Braid Groups and Majorana 1 Milestone — E8 Intelligence Research

FINDING: Topological quantum computing leverages non-Abelian anyons and braid group representations for inherently fault-tolerant quantum gates, with Microsoft's Majorana 1 chip as a physical milestone. | MATH: Braid group \(B_n\) generators \(σ_i\) satisfy \(σ_iσᵢ₊₁σ_i = σᵢ₊₁σ_iσᵢ₊₁\) and \(σ_iσ_j = σ_jσ_i\) for \(|i-j|≥ 2\). Non-Abelian anyons carry unitary representations \(U(σ_i)\) with \(U(σ_i)^2 ≠ I\) (unlike fermions/bosons). Majorana zero modes obey \(γ_i^ = γ_i\), \(\{γ_i,γ_j\} = 2δᵢⱼ\), and a pair encodes a qubit via parity \(iγ_1γ_2 = ± 1\). Topological protection arises from the gap \(Δ E ~ e-L/ξ\) (exponential suppression with wire length \(L\) vs coherence length \(ξ\)). Fibonacci anyons (from SU(2)\(_3\) Chern-Simons theory) have quantum dimension \(φ = (1+√5)/2 ≈ 1.618\), giving dense braiding — universal quantum co Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com