Date of Award

2023

Document Type

Thesis (Ph.D.)

Department or Program

Physics and Astronomy

First Advisor

James D. Whitfield

Abstract

The study of the properties of quantum mechanical systems of many particles occupies a central role in condensed matter physics, high-energy physics, and quantum chemistry. In recent decades, developments in quantum information theory have suggested that quantum computers could become an especially useful tool for studying such quantum systems.

In this thesis, we address the additional challenges for quantum simulations posed by particles which are fermionic in nature, namely those caused by the nonlocal fermionic statistics. In particular, we study the encodings of fermionic degrees of freedom into the qubits of a quantum computer. We focus on finding a scheme which minimizes the resources required to execute a simulation and investigate the ability to mitigate errors in noisy near-term quantum simulation experiments. We finally present an algebraic theory of such encodings which clarifies their mathematical structure and facilitates devising algorithms for generating new encodings.

We then turn to the study of a specific class of tensor network algorithms well-suited to studying ground state properties of critical many-body systems, called the multiscale entanglement renormalization ansatz. In particular, we investigate an instance of this tensor network structure that takes the form of an isometric quantum circuit that can be naturally executed on a quantum computer. We study the accuracy scaling with the required computational resources. We also uncover new emergent structures that provide new insights into the entanglement renormalization and can be leveraged to accelerate numerical computations.

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