Generalization of some hidden subgroup algorithms for input sets of arbitrary size

Damla Poslu; A. C. Cem Say

doi:10.1117/12.665806

12 May 2006 Generalization of some hidden subgroup algorithms for input sets of arbitrary size

Damla Poslu, A. C. Cem Say

Proceedings Volume 6244, Quantum Information and Computation IV; 624415 (2006) https://doi.org/10.1117/12.665806
Event: Defense and Security Symposium, 2006, Orlando (Kissimmee), Florida, United States

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.

Citation Download Citation

Damla Poslu and A. C. Cem Say "Generalization of some hidden subgroup algorithms for input sets of arbitrary size", Proc. SPIE 6244, Quantum Information and Computation IV, 624415 (12 May 2006); https://doi.org/10.1117/12.665806

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KEYWORDS

Superposition

Quantum communications

Quantum computing

Algorithm development

Computer engineering

Error analysis

Quantum information

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