Quantum Information Processing

, Volume 9, Issue 3, pp 419–427 | Cite as

On zeros of exponential polynomials and quantum algorithms

Article

Abstract

We calculate the zeros of an exponential polynomial of some variables by a classical algorithm and quantum algorithms which are based on the method of van Dam and Shparlinski, they treated the case of two variables, and compare with the time complexity of those cases. Further we consider the ratio (classical/quantum) of the exponent in the time complexity. Then we can observe the ratio is virtually 2 when the number of the variables is sufficiently large.

Keywords

Quantum computing Exponential congruence Discrete logarithm Character sum 

PACS

02.10.De 03.67.Lx 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Interdisciplinary Graduate School of Science and EngineeringKinki UniversityHigashi-Osaka, OsakaJapan

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