Date of Award

Spring 1-1-2017

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Manuel E. Lladser

Second Advisor

Harvey Segur

Third Advisor

Stephen Becker

Fourth Advisor

James Meiss

Abstract

As industry continues to inspire considerable growth in the research and development of quantum computers, it is increasingly worthwhile to familiarize oneself with the computational theory of this new and exciting field.

In this manuscript, we introduce readers to quantum computing by first developing a quantum intuition through the enlightening results of the so-called Stern-Gerlach experiment. After getting a feeling for quantum physics concepts such as superposition and measurement, and the need of linear algebra and probability to describe quantum phenomena, we move to a discussion of quantum computing. We develop a "quantum toolbox,'' the mathematical tools used to explore quantum computing, before walking through two quantum algorithms, Deutsch's and Grover's algorithms. We finally explore a real quantum computer that is available to the public and show readers how to implement these quantum algorithms on it. We also consider the effect of error due to quantum decoherence, and the limitations such errors pose on quantum algorithms.

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