Using (1+1)D quantum cellular automata for exploring collective effects in large scale quantum neural networks

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 such models process information. Here, we establish a connection between (1+1)D quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through successive applications of local quantum gates, and quantum neural networks (QNNs), which process information by feeding it through perceptrons interconnecting adjacent layers. Exploiting this link, we construct a class of QNNs that are highly structured - aiding both interpretability and helping to avoid trainability issues in machine learning tasks - yet can be connected rigorously to continuous-time Lindblad dynamics. We further analyze the universal properties of an example case, identifying a change of critical behavior when quantum effects are varied, showing their potential impact on the collective dynamical behavior underlying information processing in large-scale QNNs.