The quantum perspective of machine learning: a review

Abstract

Machine learning combined with quantum technologies has given rise to a new scientific field called quantum machine learning (QML). QML implements quantum superiority due to a higher capacity for representing data in quantum states, compared to classical binary coding, and the use of quantum parallelism. An important incentive for the development of QML is the progress in quantum computing and technologies of nanoprocessors in which quantum effects become an integral part of their functioning. QML allows one to directly operate with quantum data during their measurement and in the processes of controlling quantum systems. The review considers the general statistical method on which traditional machine learning is based. It is characterized by the use of the maximum likelihood principle and the Bayesian approach to assessing big data. The requirement to increase performance and reduce energy consumption leads to a quantum formulation of the machine learning problem based on the statistical theory of quantum measurements, which is a generalization of the classical statistical approach. A distinctive feature of quantum systems is their description based on probability amplitudes, which leads to interference phenomena absent in classical probabilistic models. The most general way to represent quantum states is given by the density matrix method. The process of measuring a quantum state is statistical, i.e. it requires measuring a quantum ensemble. As a result of a separate measurement, the quantum system abruptly transitions to a new state. To build machine learning systems, the concept of the distance between quantum data for pure and mixed states is introduced and the probability of their distinction is determined. The principles of constructing linear and nonlinear QML models and their main varieties are discussed. The prospects of reservoir and extreme quantum machine learning, in which the mixing of amplitudes introduced into the system is performed through the use of random Hamiltonians, are shown. The opportunities of physical implementation of QML are discussed. An approach to constructing a quantum extreme learning machine by forming a spectral response of an ensemble of quantum dots to a time-modulated input external signal is proposed. The formulated basic concepts and principles of QML, as well as the method for implementing a quantum reservoir with time coding of a signal based on an optical response, provide a basis for the development of new quantum models and devices based on modern achievements of quantum technologies and nanooptics.he article.