Abstract: Trapped ions are one of the most promising platforms for quantum information processing. Single and entangling qubit gates have been recently implemented in the lab to extremely high fidelities. Proposals exist for the construction of a quantum computer in which a large number of trapped ions are coherently manipulated and shuttled throughout a large microfabricated structure, which necessitates the accurate motional control of trapped ions. Performing ion shuttling as fast as possible without exciting the motional mode of the ion once it reaches its destination is an important goal that will facilitate the implementation of these proposals.

In this talk, we present recent work relating to the control of the motional states of trapped ions in three dimensions, in which we introduce a novel quantum invariant. The role of quantum invariants in quantum control will be explained, together with a statement of these recent results, and numerical applications to ion shuttling will be presented and discussed.