Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks

TL;DR

This paper establishes a connection between 1+1D quantum cellular automata and quantum neural networks, showing how quantum effects influence collective dynamics and information processing in large-scale quantum neural systems.

Contribution

It introduces a framework linking quantum cellular automata to quantum neural networks, enabling analysis of quantum effects on neural dynamics and identifying critical behavior changes.

Findings

Quantum effects can alter the collective dynamics of quantum neural networks.

A class of quantum gates (perceptrons) introduces quantum effects into neural models.

Critical behavior changes with quantum effects, affecting information processing.

Abstract

Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way in which such models process information. Here, we approach this question by establishing a connection between $(1+1)D$ quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through the successive application of local quantum gates, and recurrent quantum neural networks, which process information by feeding it through perceptrons interconnecting adjacent layers. This relation allows the processing of information in quantum neural networks to be studied in terms of the properties of their equivalent cellular automaton dynamics. We exploit this by constructing a class of quantum gates (perceptrons) that allow for the introduction of quantum effects, such as those associated with a coherent Hamiltonian evolution, and establish a rigorous link to continuous-time Lindblad dynamics. We further analyse the universal properties of a specific quantum cellular automaton, and identify a change of critical behavior when quantum effects are varied, demonstrating that they can indeed affect the collective dynamical behavior underlying the processing of information in large-scale neural networks.