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.

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• Open quantum systems & decoherence
• Quantum correlations, foundations & formalism
• Artificial neural networks
• Quantum many-body systems
• Machine learning