Control of motional states of trapped ions with quantum invariants
File(s)
Author(s)
Simsek, Selwyn
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2022-03
Date Awarded
2022-07
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Mintert, Florian
Sponsor
Engineering and Physical Sciences Research Council (Great Britain)
Grant Number
EP/L016524/1
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)