A quantum procedure for estimating information gain in Boolean classification task

Abstract

A substantial portion of global quantum computing research has been conducted using quantum mechanics, which recently has been applied to quantum computers. However, the design of a quantum algorithm requires a comprehensive understanding of quantum mechanics and physical procedures. This work presents a quantum procedure for estimating information gain. It is aimed at making quantum computing accessible to those without preliminary knowledge of quantum mechanics. The procedure can be a basis for building data mining processes according to measures from information theory using quantum computers. The main advantage of this procedure is the use of amplitude encoding and the inner product of two quantum states to calculate the conditional entropy between two vectors. The method was implemented using the IBM simulator and tested over a dataset of six features and a Boolean target variable. The results showed a correlation of 0.942 between the ranks achieved by the classical and quantum computations with a significance of p < 0.005.