Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks

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 in which such models process information. Here, we approach this question by establishing a connection between $(1+1)D$ quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through the successive application of local quantum gates, and recurrent quantum neural networks, which process information by feeding it through perceptrons interconnecting adjacent layers. This relation allows the processing of information in quantum neural networks to be studied in terms of the properties of their equivalent cellular automaton dynamics. We exploit this by constructing a class of quantum gates (perceptrons) that allow for the introduction of quantum effects, such as those associated with a coherent Hamiltonian evolution, and establish a rigorous link to continuous-time Lindblad dynamics. We further analyse the universal properties of a specific quantum cellular automaton, and identify a change of critical behavior when quantum effects are varied, demonstrating that they can indeed affect the collective dynamical behavior underlying the processing of information in large-scale neural networks.

main text: 6 pages, 3 figures; supplemental materials: 10 pages, 4 figures; additional files: 3 data files, 1 example script for data loading

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Cited by in corpus (8)

• Triviality of quantum trajectories close to a directed percolation transition
• Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• A perturbative approach to the solution of the Thirring quantum cellular automaton
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Entanglement transition in a cluster spin chain coupled with free spins