  We study the dynamics of Majorana zero modes that are shuttled via local
tuning of the electrochemical potential in a superconducting wire. By
performing time-dependent simulations of microscopic lattice models, we show
that diabatic corrections associated with the moving Majorana modes are
quantitatively captured by a simple Landau-Zener description. We further
simulate a Rabi-oscillation protocol in a specific qubit design with four
Majorana zero modes in a single wire and quantify constraints on the timescales
for performing qubit operations in this setup. Our simulations utilize a
Majorana representation of the system, which greatly simplifies simulations of
superconductors at the mean-field level.
