Quantum algorithms in combinatorial group theory.
Item
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Title
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Quantum algorithms in combinatorial group theory.
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Identifier
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AAI3287108
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identifier
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3287108
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Creator
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Bonanome, Marianna Cecilia.
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Contributor
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Adviser: Mark Hillery
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Date
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2007
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Physics, Theory
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Abstract
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We discuss three applications of quantum algorithms to determining properties of group automorphisms. The first two make use of modifications of the Grover search algorithm. The first finds which of a set of automorphisms maps one particular element of a group into another. This has relevance to the conjugacy problem for groups and for the solution of Whitehead's problem for free groups. The second finds the fixed point(s) of an automorphism. It can be generalized to find orbits of a specified size for automorphisms. The last uses the Bernstein-Vazarani algorithm to determine an unknown homomorphism from Zp-1 to Aut( Zp) where p is prime.
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Type
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dissertation
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Source
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PQT Legacy Restricted.xlsx
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degree
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Ph.D.