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

Abstract

Here we develop two quantum-computational models for supervised and unsupervised classification tasks in quantum world. Presuming that the 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 memberships 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.