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.
Gillman, E., Carollo, F., & Lesanovsky, I. (2023). Using (1+1)D quantum cellular automata for exploring collective effects in large-scale quantum neural networks. Physical Review E, 107(2), Article L022102. https://doi.org/10.1103/physreve.107.l022102