A Quantum Algorithm for Testing Junta Variables and Learning Boolean Functions via Entanglement Measure

TL;DR

This paper introduces a quantum algorithm that efficiently tests whether variables in a Boolean function are juntas by leveraging entanglement measurement, advancing quantum learning techniques.

Contribution

It presents a novel quantum method using entanglement measures to identify junta variables in Boolean functions, improving testing efficiency.

Findings

The algorithm effectively identifies junta variables using entanglement measures.

Application to learning Boolean functions demonstrates improved categorization.

Quantum entanglement measurement enables faster testing compared to classical methods.

Abstract

Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm creates entanglement between the variable under test and an auxiliary qubit, where the entanglement is measured using concurrence measure to decide if the variable is junta. The paper shows applications to the proposed algorithm in learning and categorization of Boolean functions.