Fig. 4: Simulation of a σ_x-gate in a double-loop MSH structure.

a Schematic picture of the σ_x-gate in an MSH system, consisting of two intersecting loops of magnetic adatoms, and two pairs of MZMs. b Effect of the σ_x-gate on the even and odd parity many-body wave functions. c–h Spatial plot of the zero-energy N_neq at successive times during the gate process. i Majorana world lines of MZMs α - δ (see (a)), as obtained from a projection of the zero-energy N_neq onto the axis depicted by the dashed yellow line in (c). Whenever two Majorana world lines cross, the one in front is indicated by a thick line. The inset shows the corresponding (simplified) braiding diagram of the gate process. Success and failure probabilities within the (j) even parity sector with μ = −3.5t_e, ΔT_R = 0.2T_R, and (k) odd parity sector for μ = −3.45805t_e, ΔT_R = 0.1T_R. For all other panels, parameters are (μ, α, Δ, JS) = (-3.5, 0.9, 2.4, 5.2)t_e, (T_R, ΔT_R) = (100, 20)τ_e, and Γ = 0.01t_e.