On exponential polynomials and quantum computing

TL;DR

This paper compares classical and quantum algorithms for finding zeros of exponential polynomials in three variables, extending previous two-variable methods and analyzing the efficiency gains of quantum approaches.

Contribution

It extends the quantum algorithm for exponential polynomial zeros from two to three variables and analyzes the complexity ratio between classical and quantum methods.

Findings

Quantum algorithms show decreased complexity ratios compared to classical algorithms.

The method of van Dam and Shparlinski is adapted for three-variable cases.

Quantum algorithms potentially offer efficiency improvements over classical ones.

Abstract

We calculate the zeros of an exponential polynomial of three 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 compare the case of van Dam and Shparlinski with our case by considering the ratio (classical/quantum) of the time complexity. Then we can observe the ratio decreases.