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 intercon-necting 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.

Automated summary

The design of quantum perceptrons and neural network architectures is central to the field of quantum machine learning. This study establishes a connection between (1 + 1)D quantum cellular automata and quantum neural networks (QNNs), allowing for the construction of structured QNNs that can be connected to continuous-time Lindblad dynamics. An example case analysis reveals a change in critical behavior when quantum effects are varied, demonstrating the potential impact on information processing in large-scale QNNs.