  We design fast trajectories of a trap to transport two ions using a
shortcut-to-adiabaticity technique based on invariants. The effects of
anharmonicity are analyzed first perturbatively, with an approximate, single
relative-motion mode, description. Then we use classical calculations and full
quantum calculations. This allows to identify discrete transport times that
minimize excitation in the presence of anharmonicity. An even better strategy
to suppress the effects of anharmonicity in a continuous range of transport
times is to modify the trajectory using an effective trap frequency shifted
with respect to the actual frequency by the coupling between relative and
center of mass motions.
