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In this work we perform real time simulations for the dynamics of braiding apair of Majorana zero modes (MZMs) through a quantum dot in a minimal setup ofpure 1D realization. We reveal the strong nonadiabatic effect when the dotenergy level approaches to zero in order to achieve a geometric phase $\pi/4$which is required for a full exchange between the MZMs. Rather than thestrategies of nonuniformly manipulating the system according to adiabaticcondition and shortcuts-to-adiabaticity, we propose and illustrate a morefeasible scheme to suppress the nonadiabatic transition, meanwhile which allowsfor a full exchange between the Majorana modes.

Dynamics simulation of braiding two Majorana-zero-modes via a quantum dot