Control of motional states of trapped ions with quantum invariants

Quantum information processing with trapped ions is a mature field in which single and multiple qubit gates have been demonstrated with exceptionally high process fidelities. As such, there is much interest in designing architectures made up of arrays of ion traps that are able to perform general-purpose quantum computing and manufactured at large scale. These designs require that ions be shuttled throughout such an architecture as quickly as possible while avoiding decoherence of the internal motional states of the ions. Invariant-based inverse engineering has been proposed as a way to obtain such control procedures, with theoretical and experimental demonstrations. In this thesis, I will explore methods that extend the current results of invariant-based inverse engineering to allow for the precise control of motional states of trapped ions in more than one spatial dimension, which has great applicability to the problem of shuttling trapped ions through these architectures. First of all, I introduce a novel quantum invariant corresponding to that of a multidimensional motional state and show how it may be used to obtain experimental controls that realise ion shuttling around a corner, with relevant numerical examples. I then discuss how to extend this framework to the control of more than one ion at a time, with a numerical demonstration of separation of two trapped ions. Finally, I outline a method by which one may be able to characterise numerically the effect of noise and anharmonicities in trapping potentials on the motional states of trapped ions.Open Acces