Discrete Quantum Theories and Computing

Most quantum computing models are based on the continuum of real numbers, while classical digital computers faithfully realize only discrete computational models. Analog computers appear to be an option, but in reality are far weaker than would be needed for computational models requiring real numbers. One approach to resolving this conflict is to find consistent mathematical ways to limit measurement precision to computable contexts that do not require incomputable real numbers. Our goal is to build a more philosophically consistent models by investigating discrete quantum comput- ing using finite number systems, and, alternatively, by incorporating finite precision measurement using intervals into quantum theory. We begin by replacing the continuum of complex numbers by discrete finite fields in quantum theory. The simplest theory, defined over unrestricted finite fields, is so weak that it cannot ex- press Deutsch’s algorithm, but, paradoxically, is also so powerful that it can be used to solve the UNIQUE-SAT problem, which is as hard as a general NP-complete problem. (See the thesis for full Abstract)

Grantor dc:publisher

[Bloomington, Ind.] : Indiana University

Year dc:date.issued

2019

Author dc:creator

• Tai, Yu-Tsung

Advisors dc:contributor.advisor

• Sabry, Amr A.
• Thurston, Dylan Paul
• Ortiz, Gerardo

• quantum computing
• finite fields
• quantum probability

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2022/23178

OAI identifier oai:identifier

oai:scholarworks.iu.edu:2022/23178