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

• Published in: European physical journal plus Vol. 136; no. 3; p. 280
• Main Authors: Shahi, F., Rezakhani, A. T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021; Springer Nature B.V
• Subjects: Accuracy; Algorithms; Applied and Technical Physics; Approximation; Atomic; Classification; Complex Systems; Condensed Matter Physics; Eigenvalues; Euclidean space; Expected values; Focus Point on Classical and Quantum Information Geometry; Hilbert space; Machine learning; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Quantum computing; Quantum phenomena; Regular Article; Search algorithms; Support vector machines; Theoretical; Unsupervised learning
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01232-2

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.