Density Matrix Classifier

Abstract

We introduce a new type of quantum machine learning classifier based on the estimation of the Frobenius distance between density matrices. The central idea is to encode all samples in the dataset belonging to a particular class into a corresponding density matrix using the quantum feature map methodology. The same quantum feature map is used to encode every new test sample into its own corresponding density matrix. The Frobenius distances between the sample density matrix and the density matrices encoding all classes present in the training dataset are calculated. The class label is assigned by selecting the class with minimum distance. The density matrix classifier uses parameterised quantum circuits. On the Glass Identification dataset, it performed on par with, or sometimes exceeded, performance of standard classical classifiers including multi-layer perceptron, random forest, support vector machine, and logistic regression. The model is resistant to certain types of noise and is suitable for execution on NISQ computers.