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

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.