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Proceedings Paper

Generalization of some hidden subgroup algorithms for input sets of arbitrary size
Author(s): Damla Poslu; A. C. Cem Say
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Paper Abstract

We consider the problem of generalizing some quantum algorithms so that they will work on input domains whose cardinalities are not necessarily powers of two. When analyzing the algorithms we assume that generating superpositions of arbitrary subsets of basis states whose cardinalities are not necessarily powers of two perfectly is possible. We have taken Ballhysa's model as a template and have extended it to Chi, Kim and Lee's generalizations of the Deutsch-Jozsa algorithm and to Simon's algorithm. With perfectly equal superpositions of input sets of arbitrary size, Chi, Kim and Lee's generalized Deutsch-Jozsa algorithms, both for evenly-distributed and evenly-balanced functions, worked with one-sided error property. For Simon's algorithm the success probability of the generalized algorithm is the same as that of the original for input sets of arbitrary cardinalities with equiprobable superpositions, since the property that the measured strings are all those which have dot product zero with the string we search, for the case where the function is 2-to-1, is not lost.

Paper Details

Date Published: 12 May 2006
PDF: 7 pages
Proc. SPIE 6244, Quantum Information and Computation IV, 624415 (12 May 2006); doi: 10.1117/12.665806
Show Author Affiliations
Damla Poslu, Boğaziçi Univ. (Turkey)
A. C. Cem Say, Boğaziçi Univ. (Turkey)

Published in SPIE Proceedings Vol. 6244:
Quantum Information and Computation IV
Eric J. Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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