On zeros of exponential polynomials and quantum algorithms

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 complexity of those cases. Further we consider the ratio (classical/quantum) of the complexity. Then we can observe the ratio is virtually 2 when the number of the variables is sufficiently large.