On zeros of exponential polynomials and quantum algorithms

TL;DR

This paper compares classical and quantum algorithms for finding zeros of exponential polynomials with multiple variables, revealing that quantum algorithms nearly halve the complexity as the number of variables grows large.

Contribution

It extends previous work on two-variable cases to multiple variables and analyzes the complexity ratio between classical and quantum methods.

Findings

Quantum algorithms nearly double efficiency for large-variable cases

Classical and quantum complexities are compared across variable counts

The complexity ratio approaches 2 as variables increase

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.