# Classification Problem in a Quantum Framework

## TL;DR

This paper develops a quantum version of the Nearest Mean Classifier, introduces a new encoding method for n-dimensional data, and explores how feature rescaling affects its performance through experimental comparisons.

## Contribution

It presents a new encoding scheme for quantum classifiers and analyzes the impact of feature rescaling, enhancing the quantum classification framework.

## Key findings

- Quantum NMC performance varies with feature rescaling.
- New encoding improves quantum classifier flexibility.
- Experimental results compare classical and quantum classifiers.

## Abstract

The aim of this paper is to provide a quantum counterpart of the well known minimum-distance classifier named Nearest Mean Classifier (NMC). In particular, we refer to the following previous works: i) in Sergioli et al. 2016, we have introduced a detailed quantum version of the NMC, named Quantum Nearest Mean Classifier (QNMC), for two-dimensional problems and we have proposed a generalization to abitrary dimensions; ii) in Sergioli et al. 2017, the n-dimensional problem was analyzed in detail and a particular encoding for arbitrary n-feature vectors into density operators has been presented. In this paper, we introduce a new promizing encoding of arbitrary n-dimensional patterns into density operators, starting from the two-feature encoding provided in the first work. Further, unlike the NMC, the QNMC shows to be not invariant by rescaling the features of each pattern. This property allows us to introduce a free parameter whose variation provides, in some case, an improvement of the QNMC performance. We show experimental results where: i) the NMC and QNMC performances are compared on different datasets; ii) the effects of the non-invariance under uniform rescaling for the QNMC are investigated.