A new quantum approach to binary classification

PLoS One. 2019 May 9;14(5):e0216224. doi: 10.1371/journal.pone.0216224. eCollection 2019.

Abstract

This paper proposes a new quantum-like method for the binary classification applied to classical datasets. Inspired by the quantum Helstrom measurement, this innovative approach has enabled us to define a new classifier, called Helstrom Quantum Centroid (HQC). This binary classifier (inspired by the concept of distinguishability between quantum states) acts on density matrices-called density patterns-that are the quantum encoding of classical patterns of a dataset. In this paper we compare the performance of HQC with respect to twelve standard (linear and non-linear) classifiers over fourteen different datasets. The experimental results show that HQC outperforms the other classifiers when compared to the Balanced Accuracy and other statistical measures. Finally, we show that the performance of our classifier is positively correlated to the increase in the number of "quantum copies" of a pattern and the resulting tensor product thereof.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Databases, Factual*
  • Electronic Data Processing*
  • Models, Theoretical*

Grants and funding

This work is supported by i) the Sardinia Region Project “Time-logical evolution of correlated microscopic systems”, CRP 55, LR 7/8/2007 (G. Sergioli as principal investigator); ii) “Strategies and Technologies for Scientific Education and Dissemination” (number F71I17000330002) founded by Fondazione Sardegna (G. Sergioli as principal investigator); iii) by the Horizon 2020 program of the European Commission: SYSMICS project, number: 689176, MSCA-RISE-2015 and iv) Fondazione Banco di Sardegna project “Science and its Logics”, Cagliari, number: F72F16003220002 (H. Freytes and R. Giuntini as members).