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arXiv · 2201.01557

Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata

Edward Gillman·Federico Carollo·Igor Lesanovsky
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Abstract

Probabilistic cellular automata provide a simple framework for the exploration of classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state along a fictitious discrete time dimension via the sequential application of quantum gates. The resulting $(1+1)$-dimensional space-time structure makes these automata special cases of feed-forward quantum neural networks. Here we show how asynchronism -- introduced via non-commuting gates -- impacts on the collective nonequilibrium behavior of quantum cellular automata. We illustrate this through a simple model, whose synchronous version implements a contact process and features a nonequilibrium phase transition in the directed percolation universality class. Non-commuting quantum gates lead to an "asynchronism transition", i.e. a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed. Our results show how quantum effects may lead to abrupt changes of non-equilibrium dynamics, which may be relevant for understanding the role of quantum correlations in neural networks.

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Edward Gillman, Federico Carollo, Igor Lesanovsky. 2022-01-05. Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata. https://doi.org/10.1103/physreve.106.l032103

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