Abstract
In the past decade, Matrix Product State (MPS) algorithms have emerged as an efficient method of modeling some many-body quantum spin systems. Since spin system Hamiltonians can be considered constraint satisfaction problems (CSPs), it follows that MPS should provide a versatile framework for studying a variety of general CSPs. In this thesis, we apply MPS to two types of CSP. First, use MPS to simulate adiabatic quantum computation (AQC), where the target Hamiltonians are instances of a fully connected, random Ising spin glass. Results of the simulations help shed light on why AQC fails for some optimization problems. We then present the novel application of a modified MPS algorithm to classical Boolean satisfiability problems, specifically k-SAT and max k-SAT. By construction, the algorithm also counts solutions to a given Boolean formula (\#-SAT). For easy satisfiable instances, the method is more expensive than other existing algorithms; however, for hard and unsatisfiable instances, the method succeeds in finding satisfying assignments where other algorithms fail to converge.
Notes
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Graduation Date
2017
Semester
Fall
Advisor
Mucciolo, Eduardo
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Physics
Degree Program
Physics
Format
application/pdf
Identifier
CFE0006902
URL
http://purl.fcla.edu/fcla/etd/CFE0006902
Language
English
Release Date
December 2017
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Pelton, Sabine, "Solving Constraint Satisfaction Problems with Matrix Product States" (2017). Electronic Theses and Dissertations. 5712.
https://stars.library.ucf.edu/etd/5712