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Extending the Promise of the Deutsch–Jozsa–Høyer Algorithm for Finite Groups

Published online by Cambridge University Press:  01 February 2010

Michael Batty ,
Andrew J. Duncan  and
Samuel L. Braunstein
Michael Batty
Affiliation:
Department of Mathematics, School of Mathematics and Statistics, Merz Court, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom, Michael.Batty@ncl.ac.uk, http://www.mas.ncl.ac.uk/~nmb45/
Andrew J. Duncan
Affiliation:
Department of Mathematics, School of Mathematics and Statistics, Merz Court, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom, A.Duncan@ncl.ac.uk, http://www.mas.ncl.ac.uk/~najd2/
Samuel L. Braunstein
Affiliation:
Department of Computer Science, University of York, York, YO10 5DD, United Kingdom. schmuel@cs.york.ac.uk, http://www-users.cs.york.ac.uk/~schmuel/

Abstract

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Høyer has given a generalisation of the Deutsch–Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes between functions which are either perfectly balanced (m-to-one) or constant, with certainty, and using a single quantum query. Here, we show that this algorithm (which we call the Deutsch–Jozsa–Høyer algorithm) can in fact deal with a broader range of promises, which we define in terms of the irreducible representations of G.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 40 - 63
Copyright
Copyright © London Mathematical Society 2006

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