On quantum neural networks

Abstract

The early definition of a quantum neural network as a new field that combines the classical neurocomputing with quantum computing was rather vague and satisfactory in the 2000s. The widespread in 2020 modern definition of a quantum neural network as a model or machine learning algorithm that combines the functions of quantum computing with artificial neural networks deprives quantum neural networks of their fundamental importance. We argue that the concept of a quantum neural network should be defined in terms of its most general function as a tool for representing the amplitude of an arbitrary quantum process. Our reasoning is based on the use of the Feynman path integral formulation in quantum mechanics. This approach has been used in many works to investigate the main problem of quantum cosmology, such as the origin of the Universe. In fact, the question of whether our Universe is a quantum computer was posed by Seth Lloyd, who gave the answer is yes, but we argue that the universe can be thought of as a quantum neural network.