Physics & Astronomy ETDs

Publication Date

Spring 5-13-2023

Abstract

We present a rigorous analysis of the rapid convergence of techniques based on Markov chains for the simulation of thermal quantum systems. We show that a classical computing algorithm called path integral Monte Carlo is capable of simulating thermal states of transverse field Ising models above a threshold temperature by demonstrating the existence of a rapidly mixing Markov chain. We then turn to quantum computing algorithms and show that an idealized version of quantum Metropolis sampling can efficiently simulate systems that satisfy the eigenstate thermalization hypothesis. In a related result, we find a class of stoquastic frustration free Hamiltonians that always have ground states that are coherent Gibbs states in the stoquastic basis.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

Tameem Albash

Second Committee Member

Elizabeth Crosson

Third Committee Member

Ivan Deutsch

Fourth Committee Member

Milad Marvian

Language

English

Keywords

Quantum Information Physics Complexity Computer Science

Document Type

Dissertation

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