Topological Protection and Non-Abelian Braiding of Majorana Zero Modes — E8 Intelligence Research

FINDING: Majorana zero modes (MZMs) realize non-Abelian braid statistics via the Ising anyon model, with topological protection scaling exponentially in wire length. | MATH: Braid group \( B_n \) generators \( σ_i \) act on a 2D degenerate ground space (for \( 2n \) MZMs) via \( γ_i → γ_j = U^ γ_i U \), where \( U = exp(π/4γ_iγ_j) \). The non-Abelian exchange yields \( σ_i^2 = -1 \) (fermion parity flip), and the topological gap \( Δₜₒₚ ∝ e-L/ξ \) (exponential suppression of splitting with wire length \( L \), coherence length \( ξ \)). Kitaev chain Hamiltonian: \( H = -μ∑ c_i^ c_i - t∑(cᵢ₊₁^ c_i + { h.c.}) + Δ∑(cᵢ₊₁^ c_i^ + { h.c.}) \), with MZM operators \( γ_1 = c_1 + c_1^ \), \( γ_2 = -i(c_N - c_N^) \) at \( μ=0, t=Δ \). | CONNECTION: The braid group \( B_n \) is the fundamental group of configuration space of \( n \) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com