A Quantum Algorithm for Testing Juntas in Boolean Functions

TL;DR

This paper introduces a quantum algorithm that efficiently tests whether a variable in a Boolean function is a junta or far from being one, using amplitude amplification with fewer queries than classical methods.

Contribution

It presents a novel quantum algorithm capable of testing junta variables in general Boolean functions with improved query complexity.

Findings

Uses $ ilde{O}( oot 2 )$ queries for testing

Works on Boolean functions of general form

Employs amplitude amplification with a constructed black-box

Abstract

Given a Boolean function $f$ provided as a black-box with $n$ variables, this paper will propose a quantum algorithm for testing if a certain variable is junta or $\epsilon$-far from being junta. The proposed algorithm constructs another black-box using two copies of the provided black-box. The constructed black-box is used with the partial diffusion operator in an amplitude amplification technique to test whether the variable being tested is junta or not, using $\mathcal{O}(\sqrt{2^n})$ queries to the constructed black-box. The proposed algorithm considers a Boolean function of general form, contrary to relevant algorithms proposed by others.