Adiabatic fusion and nucleation of Majorana bound states

A semiconductor nanowire with strong spin-orbit coupling and induced superconductivity can host Majorana bound states. Using them in topological quantum computation usually requires braiding them as well as nucleating and fusing pairs of Majorana fermions. In all these processes, the time evolution should be adiabatic in order to prevent any qubit errors triggered by transitions above the bandgap. In this study, we investigate the maximum speed for remaining in the adiabatic limit during these manipulations. In particular, we derive the criteria for nucleation and fusion of Majorana bound states to remain adiabatic. To obtain our results, we use the density-matrix renormalization group and exact diagonalization as numerical techniques and compare those to analytical results from perturbation theory.