Fig. 3: Simulation of a σ_z-gate in a loop MSH structure.

a–d Spatial plot of the zero-energy N_neq during consecutive times in the gate operation. e Majorana world lines, as obtained from a projection of the zero-energy N_neq onto the dashed yellow line in (a). f Fidelity of the odd parity many-body wave function and geometric phase as a function of time. g Time- and energy-dependent N_neq at a site in the MSH network (see yellow arrow in (a)). For all results (T_R, ΔT_R) = (500, 100)τ_e. h, i Same as (f, g) but for a 10 times faster gate operation with (T_R, ΔT_R) = (50, 10)τ_e. Parameters are (μ, α, Δ, JS) = (−3.993, 0.9, 2.4, 5.2)t_e, and Γ = 0.01t_e. Total system size for all results is 441 sites with dimensions (21a₀ × 21a₀).