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
If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
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; DP0023578
URL
https://purls.library.ucf.edu/go/DP0023578
Language
English
Release Date
August 2020
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Reyes, Justin, "Tensor Network States: Optimizations and Applications in Quantum Many-Body Physics and Machine Learning" (2020). Electronic Theses and Dissertations, 2020-. 275.
https://stars.library.ucf.edu/etd2020/275