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

Gillman, Edward; Carollo, Federico; Lesanovsky, Igor

Authors

Federico Carollo



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 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.

Citation

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

Journal Article Type Article
Acceptance Date Jan 13, 2023
Online Publication Date Feb 22, 2023
Publication Date Feb 1, 2023
Deposit Date Mar 1, 2023
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 107
Issue 2
Article Number L022102
DOI https://doi.org/10.1103/PhysRevE.107.L022102
Keywords Open quantum systems; Decoherence; Quantum theory; Artificial neural networks; Quantum many-body systems; Machine learning
Public URL https://nottingham-repository.worktribe.com/output/17665383