Investigating the linear structure of Boolean functions based on Simon's period-finding quantum algorithm

TL;DR

This paper introduces a quantum algorithm based on Simon's period-finding method to efficiently determine the linear structure of Boolean functions, addressing a problem thought to lack efficient classical solutions.

Contribution

It extends Simon's quantum algorithm to develop an efficient method for identifying the linear structure of Boolean functions, a task previously considered classically intractable.

Findings

The proposed quantum algorithm successfully determines the linear structure of Boolean functions.

It demonstrates a potential quantum advantage over classical methods.

The algorithm operates efficiently, suggesting practical quantum applications in Boolean function analysis.

Abstract

It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to determine the linear structure of Boolean function.