Quantum walk via open systems

Jeremy Philip Jacques Rodriguez

    Research output: ThesisDoctoral Thesis

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    Abstract

    In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 11 Jan 2016

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    proteins
    theses
    titanium oxides
    excitons
    electrodes
    molecules
    electrons

    Cite this

    Rodriguez, J. P. J. (2016). Quantum walk via open systems.
    Rodriguez, Jeremy Philip Jacques. / Quantum walk via open systems. 2016.
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    title = "Quantum walk via open systems",
    abstract = "In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.",
    keywords = "Quantum walk, Open system, Electron transport, Directed walks, Discord, Entanglement, Multiple walkers",
    author = "Rodriguez, {Jeremy Philip Jacques}",
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    Rodriguez, JPJ 2016, 'Quantum walk via open systems', Doctor of Philosophy.

    Quantum walk via open systems. / Rodriguez, Jeremy Philip Jacques.

    2016.

    Research output: ThesisDoctoral Thesis

    TY - THES

    T1 - Quantum walk via open systems

    AU - Rodriguez, Jeremy Philip Jacques

    PY - 2016/1/11

    Y1 - 2016/1/11

    N2 - In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.

    AB - In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.

    KW - Quantum walk

    KW - Open system

    KW - Electron transport

    KW - Directed walks

    KW - Discord

    KW - Entanglement

    KW - Multiple walkers

    M3 - Doctoral Thesis

    ER -

    Rodriguez JPJ. Quantum walk via open systems. 2016.