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

Gillman, Edward; Carollo, Federico; Lesanovsky, Igor

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