Non-Abelian Majorana Modes Enable Topologically Protected Quantum Gates — E8 Intelligence Research

FINDING: Majorana zero modes (MZMs) in topological superconductors obey non-Abelian braid statistics, with exponential suppression of coupling between spatially separated modes enabling topologically protected quantum gates. | MATH: The Kitaev chain Hamiltonian \( H = -t∑ c^_i cᵢ₊₁ + Δ∑ c_i cᵢ₊₁ + h.c. - μ∑ c^_i c_i \) yields unpaired Majorana operators \( γ_1, γ_2 \) with \( γ_i^ = γ_i \), \( \{γ_i,γ_j\} = 2δᵢⱼ \). Braiding exchanges \( γ_i → γ_j \) via unitary \( Uᵢⱼ = exp(π/4γ_iγ_j) \), giving non-Abelian representation of the braid group \( B_n \) (e.g., \( U₁₂U₂₃ ≠ U₂₃U₁₂ \)). Splitting energy \( Δ E ∝ e-L/ξ \) where \( ξ = v_F/Δ \) is the coherence length — exponential suppression with wire length \( L \). | CONNECTION: The braid group \( B_n \) is generated by transpositions \( σ_i \) satisfying \( σ_i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com