  We theoretically investigate the motional excitation of a single ion caused
by spring-constant and position uctuations of a harmonic trap during trap
shuttling processes. A detailed study of the sensitivity on noise for several
transport protocols and noise spectra is provided. The effect of slow
spring-constant drifts is also analyzed. Trap trajectories that minimize the
excitation are designed combining invariant-based inverse engineering,
perturbation theory, and optimal control.
