Classification Problem in a Quantum Framework

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 [20] 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 arbitrary dimensions; ii) in [19] 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 promising encoding of arbitrary n-dimensional patterns into density operators, starting from the two-feature encoding provided in [20]. 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.