Towards universal quantum computation in continuous-variable systems

In this thesis we explore the possibility of creating continuousvariable quantum systems that are capable of supporting universal quantum computation. We begin by examining the measurement-based model, which employs sequences of measurements on highly entangled resource states, known as a cluster st...

Full description

Bibliographic Details
Main Author: Milne, Darran F.
Other Authors: Korolkova, Natalia
Published: University of St Andrews 2012
Subjects:
Online Access:http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.558142
id ndltd-bl.uk-oai-ethos.bl.uk-558142
record_format oai_dc
spelling ndltd-bl.uk-oai-ethos.bl.uk-5581422015-03-20T03:24:35ZTowards universal quantum computation in continuous-variable systemsMilne, Darran F.Korolkova, Natalia2012In this thesis we explore the possibility of creating continuousvariable quantum systems that are capable of supporting universal quantum computation. We begin by examining the measurement-based model, which employs sequences of measurements on highly entangled resource states, known as a cluster states. We suggest a method for the construction of Gaussian cluster states based on ensembles of atoms and quantum non-demolition interactions. We then go on to expand our model to allow for the inclusion of light modes as part of the cluster. This yields a new class of states, the composite cluster states. This leads us to propose a new architecture for the measurement-based model that uses these composite clusters to increase resource e ciency and reduce computational errors. The second part of this thesis concerns topological quantum computation. In states exhibiting topological degrees of freedom, quantum information can be stored as a non-local property of the physical system and manipulated by braiding quasiparticles known as anyons. Here we show how these ideas can be extended to continuous variables. We establish a continuous variable analogue of the Kitaev toric code, show that excitations correspond to continuous versions of Abelian anyons and investigate their behaviour under the condition of nite squeezing of the resource state. Finally, we expand our continuous variable topological model to include non-abelian excitations by constructing superpositions of CV toric code anyons. We derive the fusion and braiding behaviour of these non-abelian excitations and nd that they correspond to a CV analog of Ising anyons. Using these resources, we go on to suggest a computational scheme that encodes qubits within the fusion spaces of the CV Ising anyons and derive one- and two-qubit quantum gates operations that are implemented in a topological manner.006.3University of St Andrewshttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.558142http://hdl.handle.net/10023/3210Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
topic 006.3
spellingShingle 006.3
Milne, Darran F.
Towards universal quantum computation in continuous-variable systems
description In this thesis we explore the possibility of creating continuousvariable quantum systems that are capable of supporting universal quantum computation. We begin by examining the measurement-based model, which employs sequences of measurements on highly entangled resource states, known as a cluster states. We suggest a method for the construction of Gaussian cluster states based on ensembles of atoms and quantum non-demolition interactions. We then go on to expand our model to allow for the inclusion of light modes as part of the cluster. This yields a new class of states, the composite cluster states. This leads us to propose a new architecture for the measurement-based model that uses these composite clusters to increase resource e ciency and reduce computational errors. The second part of this thesis concerns topological quantum computation. In states exhibiting topological degrees of freedom, quantum information can be stored as a non-local property of the physical system and manipulated by braiding quasiparticles known as anyons. Here we show how these ideas can be extended to continuous variables. We establish a continuous variable analogue of the Kitaev toric code, show that excitations correspond to continuous versions of Abelian anyons and investigate their behaviour under the condition of nite squeezing of the resource state. Finally, we expand our continuous variable topological model to include non-abelian excitations by constructing superpositions of CV toric code anyons. We derive the fusion and braiding behaviour of these non-abelian excitations and nd that they correspond to a CV analog of Ising anyons. Using these resources, we go on to suggest a computational scheme that encodes qubits within the fusion spaces of the CV Ising anyons and derive one- and two-qubit quantum gates operations that are implemented in a topological manner.
author2 Korolkova, Natalia
author_facet Korolkova, Natalia
Milne, Darran F.
author Milne, Darran F.
author_sort Milne, Darran F.
title Towards universal quantum computation in continuous-variable systems
title_short Towards universal quantum computation in continuous-variable systems
title_full Towards universal quantum computation in continuous-variable systems
title_fullStr Towards universal quantum computation in continuous-variable systems
title_full_unstemmed Towards universal quantum computation in continuous-variable systems
title_sort towards universal quantum computation in continuous-variable systems
publisher University of St Andrews
publishDate 2012
url http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.558142
work_keys_str_mv AT milnedarranf towardsuniversalquantumcomputationincontinuousvariablesystems
_version_ 1716780919889592320