Quantum circuit design for quantum walks

Oon Han Thomas Loke

    Research output: ThesisDoctoral Thesis

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    Abstract

    This thesis focuses on applying analytical and numerical techniques to the problem of designing quantum circuits for quantum walks. We develop efficient quantum circuit implementations of continuous-time quantum walks using diagonalization of the Hamiltonian. Next, for the discrete-time Szegedy quantum walk model, we provide a theoretical framework for the development of efficient quantum circuits, and apply it to a wide variety of graphs. We also investigate the optimisation of numerical techniques to the general problem of implementing a unitary matrix. Lastly, we discuss design principles for the development of efficient quantum circuit implementations of quantum walks of different types.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Award date11 May 2017
    DOIs
    Publication statusUnpublished - 2017

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    Loke, Oon Han Thomas. / Quantum circuit design for quantum walks. 2017.
    @phdthesis{c2dacf48ddf341aca084f825d3787894,
    title = "Quantum circuit design for quantum walks",
    abstract = "This thesis focuses on applying analytical and numerical techniques to the problem of designing quantum circuits for quantum walks. We develop efficient quantum circuit implementations of continuous-time quantum walks using diagonalization of the Hamiltonian. Next, for the discrete-time Szegedy quantum walk model, we provide a theoretical framework for the development of efficient quantum circuits, and apply it to a wide variety of graphs. We also investigate the optimisation of numerical techniques to the general problem of implementing a unitary matrix. Lastly, we discuss design principles for the development of efficient quantum circuit implementations of quantum walks of different types.",
    keywords = "Quantum walk, Quantum circuit, Quantum supremacy, Quantum compilation, Szegedy walk",
    author = "Loke, {Oon Han Thomas}",
    year = "2017",
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    language = "English",
    school = "The University of Western Australia",

    }

    Loke, OHT 2017, 'Quantum circuit design for quantum walks', Doctor of Philosophy, The University of Western Australia. https://doi.org/10.4225/23/5934cf1d3e3fa

    Quantum circuit design for quantum walks. / Loke, Oon Han Thomas.

    2017.

    Research output: ThesisDoctoral Thesis

    TY - THES

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    AU - Loke, Oon Han Thomas

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    Y1 - 2017

    N2 - This thesis focuses on applying analytical and numerical techniques to the problem of designing quantum circuits for quantum walks. We develop efficient quantum circuit implementations of continuous-time quantum walks using diagonalization of the Hamiltonian. Next, for the discrete-time Szegedy quantum walk model, we provide a theoretical framework for the development of efficient quantum circuits, and apply it to a wide variety of graphs. We also investigate the optimisation of numerical techniques to the general problem of implementing a unitary matrix. Lastly, we discuss design principles for the development of efficient quantum circuit implementations of quantum walks of different types.

    AB - This thesis focuses on applying analytical and numerical techniques to the problem of designing quantum circuits for quantum walks. We develop efficient quantum circuit implementations of continuous-time quantum walks using diagonalization of the Hamiltonian. Next, for the discrete-time Szegedy quantum walk model, we provide a theoretical framework for the development of efficient quantum circuits, and apply it to a wide variety of graphs. We also investigate the optimisation of numerical techniques to the general problem of implementing a unitary matrix. Lastly, we discuss design principles for the development of efficient quantum circuit implementations of quantum walks of different types.

    KW - Quantum walk

    KW - Quantum circuit

    KW - Quantum supremacy

    KW - Quantum compilation

    KW - Szegedy walk

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    DO - 10.4225/23/5934cf1d3e3fa

    M3 - Doctoral Thesis

    ER -