Physics & Astronomy ETDs

Publication Date

Summer 7-26-2019

Abstract

The simulation of quantum physical systems is expected to be an important application for quantum computers. The work presented in this dissertation aims to improve the resource requirements of quantum computers for solving simulation problems, by providing both novel quantum algorithms and improved implementations of existing ones. I present three main results that cover diverse aspects of simulation including equilibrium physics, the preparation of useful quantum states, and simulations based on classical stochastic processes. The results rely on established quantum algorithms and other recent techniques which I review. My first original contribution is a new quantum algorithm to sample from the thermal Gibbs state of quantum Hamiltonians. The complexity of this algorithm has an exponentially improved dependence on precision compared to an earlier quantum algorithm, and also provides polynomial improvements in other parameters. My second contribution is an improved algorithm to implement reflections about the eigenstates of unitary operators and Hamiltonians, an operation that can be used to prepare ground states of many-body Hamiltonians by quantum amplitude amplification. The improved algorithm for implementing reflections significantly reduces the number of ancilla qubits required over earlier implementations. The improvement relies in part on a novel quantum algorithm for efficiently preparing states with Gaussian-like amplitudes, which may have broad applications. I also prove a lower bound for implementing reflections, which shows that our algorithm is almost optimal. My third and final contribution regards quantum algorithms for classical stochastic processes, which are of importance in statistical physics. I present a quantum algorithm that estimates the average running time of a stochastic process, and provides a quadratic speed-up over a comparable classical algorithm.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

Rolando Somma

Second Committee Member

Ivan Deutsch

Third Committee Member

Andrew Landahl

Fourth Committee Member

Akimasa Miyake

Project Sponsors

Google Research Award, Laboratory Directed Research and Development Program at Los Alamos National Laboratory

Language

English

Keywords

quantum computation, quantum algorithms, quantum simulations

Document Type

Dissertation

Download

Share

COinS