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

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.

5 pages, 3 figures. Supplemental material of 3 pages

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• 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
• Nonequilibrium phases and quantum correlations in synthetic transport models