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

## TL;DR

This paper introduces fidelity-based quantum algorithms for supervised and unsupervised binary classification of quantum states, enabling classification without prior knowledge of the states by evaluating fidelities.

## Contribution

It presents novel quantum classification algorithms that utilize fidelity measures and a general scheme for fidelity evaluation, applicable to both supervised and unsupervised settings.

## Key findings

- Developed fidelity evaluation scheme for unknown quantum states
- Proposed supervised classification algorithm using training samples
- Designed unsupervised classification algorithm with quantum oracle

## 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.