Discrete Dirac Dynamics: a quantum walk-based framework in discrete spacetime

Gareth Jay

doi:10.26182/mrmr-0v98

Discrete Dirac Dynamics: a quantum walk-based framework in discrete spacetime

Gareth Jay

Research output: Thesis › Doctoral Thesis

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Abstract

In this thesis a study of a special type of quantum cellular automata called Dirac quantum walks (DQWs) is presented. At the continuous limit, these DQWs coincide with the Dirac equation. A new systematic method to build DQWs, with particular focus on non-square or cube shaped grids, is constructed and is put to test on several examples of increasing difficulty. Ultimately, a quantum walk simulating the Dirac equation on a spatial polar grid is constructed with a discrete analogue to the conservation of angular momentum. Cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Wang, Jingbo, Supervisor Debbasch, Fabrice, Supervisor, External person Grasso, Darren, Supervisor McArthur, Ian, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	8 Jul 2021
DOIs	https://doi.org/10.26182/mrmr-0v98
Publication status	Unpublished - 2021

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10.26182/mrmr-0v98

THESIS - DOCTOR OF PHILOSOPHY - JAY, Gareth Michael - 2021
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Cite this

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AB - In this thesis a study of a special type of quantum cellular automata called Dirac quantum walks (DQWs) is presented. At the continuous limit, these DQWs coincide with the Dirac equation. A new systematic method to build DQWs, with particular focus on non-square or cube shaped grids, is constructed and is put to test on several examples of increasing difficulty. Ultimately, a quantum walk simulating the Dirac equation on a spatial polar grid is constructed with a discrete analogue to the conservation of angular momentum. Cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated.

KW - Dirac

KW - Quantum Walk

KW - Quantum Field Theory

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Discrete Dirac Dynamics: a quantum walk-based framework in discrete spacetime

Abstract

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