Quantum Algorithms
Welcome to Matthew Hayward's quantum algorithms page. These papers
are designed to be accessible to anyone with a technical or
engineering background. Hopefully they will serve as a primer or
tutorial for those interested in quantum computing, Shor's algorithm,
Grover's algorithm, and other quantum algorithms.
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Quantum Computing and Shor's
Algorithm this was my first foray into the world of quantum
computing, a senior thesis done at the University of Illinois with
Professor Roy Campbell. It contains a good deal of introductory
information on quantum computing in general, both theory and
motivation, as well as a discussion of Shor's algorithm.
Originally written in Spring 1999, it has since been updated. It
is available online in:
HTML,
PostScript,
PDF,
LaTeX,
tar of simulator code,
GitHub Respository
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Lower Query Bounds in the Quantum Oracle Model
My Masters Thesis in Computer Science at the University of
Illinois
with Professor
Jeff Erickson. This paper applies a result of Andris Ambainis
to produce lower bounds in the Quantum Oracle Model in a bounded
error setting for several functions and classes of functions.
Available online in:
HTML,
PostScript,
PDF,
GitHub Respository
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Quantum Computing and Grover's Algorithm
A paper written for Professor Jeff Erickson at the University of
Illinois, a semester project in CS 473, Topics on the Analysis of
Algorithms. Intended to be a complete introduction to Grover's
algorithm, an explanation of the algorithm and a summary of
various proofs relating to its correctness. Available online in:
HTML,
PostScript,
PDF,
LaTeX,
tar of figures,
GitHub Respository
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Quantum Computing, Shor's Algorithm, and Parallelism
A semester project completed for CS 433, Parallel Architecture at
the University of Illinois. This is basically a revision of the
work done above, with an emphasis on simulating quantum
parallelism with a classical parallel computer, essentially linear
speedup is attained using POSIX threads on an SGI Origin 2000.
Available online in:
HTML,
PostScript,
PDF,
LaTeX,
tar of figures,
tar of simulator code,
GitHub Respository
Matthew Hayward
Last modified: Wed Jan 14 2015