On quantum neural networks

TL;DR

This paper redefines quantum neural networks as general tools for representing quantum process amplitudes, emphasizing their fundamental role in quantum mechanics and cosmology, beyond just machine learning applications.

Contribution

It proposes a new, more fundamental definition of quantum neural networks based on the Feynman path integral formulation, linking them to quantum processes and cosmology.

Findings

Quantum neural networks can be viewed as tools for representing quantum process amplitudes.

The universe itself can be conceptualized as a quantum neural network.

This perspective connects quantum computing, neural networks, and cosmology.

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.