Continuous-time quantum walks: simulation and application

Joshua Izaac

doi:10.4225/23/59a4c65736bdc

Continuous-time quantum walks: simulation and application

Joshua Izaac

Research output: Thesis › Doctoral Thesis

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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.

Original language	English
Qualification	Doctorate
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Wang, Jingbo, Supervisor Pan, Jie, Supervisor
Award date	1 Aug 2017
DOIs	https://doi.org/10.4225/23/59a4c65736bdc
Publication status	Unpublished - 2017

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THESIS - DOCTOR OF PHILOSOPHY - IZAAC Joshua Abe - 2017
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Cite this

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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.",

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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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DO - 10.4225/23/59a4c65736bdc

M3 - Doctoral Thesis

ER -

Continuous-time quantum walks: simulation and application

Abstract

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