Abstract

Tensor network states are ubiquitous in the investigation of quantum many-body (QMB) physics. Their advantage over other state representations is evident from their reduction in the computational complexity required to obtain various quantities of interest, namely observables. Additionally, they provide a natural platform for investigating entanglement properties within a system. In this dissertation, we develop various novel algorithms and optimizations to tensor networks for the investigation of QMB systems, including classical and quantum circuits. Specifically, we study optimizations for the two-dimensional Ising model in a transverse field, we create an algorithm for the $k$-SAT problem, and we study the entanglement properties of random unitary circuits. In addition to these applications, we reinterpret renormalization group principles from QMB physics in the context of machine learning to develop a novel algorithm for the tasks of classification and regression, and then utilize machine learning architectures for the time evolution of operators in QMB systems.

Notes

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Graduation Date

2020

Semester

Summer

Advisor

Mucciolo, Eduardo

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Physics

Degree Program

Physics

Format

application/pdf

Identifier

CFE0008224

Language

English

Release Date

August 2020

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

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