Applications of abelian algebraic structures in quantum computation
Name
965445128-MIT.pdf
Description
Full printable version
Size
9.51 MB
Format
Adobe PDF
Checksum (MD5)
d64004b9b1375082bf813eac3f158b23
Author(s)
Zatloukal, Kevin C. (Kevin Chaffee)
Advisor(s)
Aram W. Harrow.
Date Issued
2016
Publisher
Massachusetts Institute of Technology
Abstract
Shor's groundbreaking algorithms for integer factoring and discrete logarithm [58], along with their later generalizations 116, 35, 49, 18], demonstrated a unique ability of quantum computers to solve problems defined on abelian groups. In this thesis, we study ways in which that ability can be leveraged in order to solve problems on more complex structures such as non-abelian groups and hypergroups. This leads to new quantum algorithms for the hidden subgroup problem on nilpotent groups whose order is a product of large primes, the hidden subhypergroup problem on both strongly integral hypergroups and ultragroups, testing equivalence of group extensions, and computing the component parts of the cohomology groups of both group extensions and a generalization of simplicial complexes, amongst other problems. For each of those listed, we also show that no classical algorithm can achieve similar efficiency under standard cryptographic assumptions.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 163-168).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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