Continuous-time quantum walks: simulation and application

Joshua Izaac

    Research output: Thesis › Doctoral Thesis

    Abstract

    Quantum walks are a fundamental tool in the study of quantum information, bridging the gap between quantum computation and modelling complex systems. In this thesis, we present a software package for simulation of multiparticle continuous-time quantum walks (CTQWs) using high performance computation, and detail a method of systematic dimensionalty reduction for fermionic CTQWs. We then consider CTQW applications; proving that the single particle CTQW is unsuited for determining graph isomorphism, and proposing a CTQW-based network centrality algorithm. This algorithm is utilized in the first successful physical quantum centrality implementation. Finally, we extend our centrality algorithm to PT-symmetric directed graphs.
    LanguageEnglish
    QualificationDoctorate
    Awarding Institution
    • The University of Western Australia
    Award date1 Aug 2017
    DOIs
    Publication statusUnpublished - 2017

    Fingerprint

    simulation
    isomorphism
    theses
    quantum computation
    complex systems
    computer programs

    Cite this

    Izaac, Joshua. / Continuous-time quantum walks: simulation and application. 2017.
    @phdthesis{2f9e307533074e56bf28f82a17953c1f,
    title = "Continuous-time quantum walks: simulation and application",
    abstract = "Quantum walks are a fundamental tool in the study of quantum information, bridging the gap between quantum computation and modelling complex systems. In this thesis, we present a software package for simulation of multiparticle continuous-time quantum walks (CTQWs) using high performance computation, and detail a method of systematic dimensionalty reduction for fermionic CTQWs. We then consider CTQW applications; proving that the single particle CTQW is unsuited for determining graph isomorphism, and proposing a CTQW-based network centrality algorithm. This algorithm is utilized in the first successful physical quantum centrality implementation. Finally, we extend our centrality algorithm to PT-symmetric directed graphs.",
    keywords = "Quantum information, Quantum computation, Algorithm, simulation, Fermions, NETWORK CENTRALITY, Graph isomorphism, PT-symmetry",
    author = "Joshua Izaac",
    year = "2017",
    doi = "10.4225/23/59a4c65736bdc",
    language = "English",
    school = "The University of Western Australia",

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    Izaac, J 2017, 'Continuous-time quantum walks: simulation and application', Doctorate, The University of Western Australia. https://doi.org/10.4225/23/59a4c65736bdc

    Continuous-time quantum walks: simulation and application. / Izaac, Joshua.

    2017.

    Research output: Thesis › Doctoral Thesis

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    N2 - Quantum walks are a fundamental tool in the study of quantum information, bridging the gap between quantum computation and modelling complex systems. In this thesis, we present a software package for simulation of multiparticle continuous-time quantum walks (CTQWs) using high performance computation, and detail a method of systematic dimensionalty reduction for fermionic CTQWs. We then consider CTQW applications; proving that the single particle CTQW is unsuited for determining graph isomorphism, and proposing a CTQW-based network centrality algorithm. This algorithm is utilized in the first successful physical quantum centrality implementation. Finally, we extend our centrality algorithm to PT-symmetric directed graphs.

    AB - Quantum walks are a fundamental tool in the study of quantum information, bridging the gap between quantum computation and modelling complex systems. In this thesis, we present a software package for simulation of multiparticle continuous-time quantum walks (CTQWs) using high performance computation, and detail a method of systematic dimensionalty reduction for fermionic CTQWs. We then consider CTQW applications; proving that the single particle CTQW is unsuited for determining graph isomorphism, and proposing a CTQW-based network centrality algorithm. This algorithm is utilized in the first successful physical quantum centrality implementation. Finally, we extend our centrality algorithm to PT-symmetric directed graphs.

    KW - Quantum information

    KW - Quantum computation

    KW - Algorithm

    KW - simulation

    KW - Fermions

    KW - NETWORK CENTRALITY

    KW - Graph isomorphism

    KW - PT-symmetry

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    M3 - Doctoral Thesis

    ER -

    Izaac J. Continuous-time quantum walks: simulation and application. 2017. https://doi.org/10.4225/23/59a4c65736bdc

    Access to Document

    • THESIS - DOCTOR OF PHILOSOPHY - IZAAC Joshua Abe - 2017

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