Eur. Phys. J. Plus (2021) 136: 280
https://doi.org/10.1140/epjp/s13360-021-01232-2

Regular Article

Fidelity-based supervised and unsupervised learning for binary classification of quantum states

¹ Department of Physics, Sharif University of Technology, 14588, Tehran, Iran
² School of Physics, Institute for Research in Fundamental Sciences (IPM), 19538, Tehran, Iran

^b rezakhani@sharif.edu

Received: 5 November 2020
Accepted: 13 February 2021
Published online: 2 March 2021

Abstract

Here, we develop two quantum-computational schemes for supervised and unsupervised classification tasks in a quantum world by employing the quantum information-geometric tools of quantum fidelity and quantum search algorithm. Presuming that pure states of a set of given quantum systems (or objects) belong to one of two known classes, the objective here is to decide to which of these classes each system belongs—without knowing its state. The supervised binary classification algorithm is based on having a training sample of quantum systems whose class memberships are already known. The unsupervised binary classification algorithm, however, uses a quantum oracle which knows the class membership of the states of the computational basis. Both algorithms require the ability to evaluate the fidelity between states of the quantum systems with unknown states, for which here we also develop a general scheme.