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

TL;DR

This paper investigates how asynchronism introduced by non-commuting quantum gates affects the nonequilibrium phase transitions in (1+1)D quantum cellular automata, revealing an abrupt asynchronism transition that alters phase transition behavior.

Contribution

It demonstrates how non-commuting gates induce an asynchronism transition, significantly impacting the phase transition dynamics in quantum cellular automata.

Findings

Asynchronism causes a qualitative change in phase transition behavior.

Quantum effects can lead to abrupt changes in non-equilibrium dynamics.

The model exhibits a transition in the directed percolation universality class.

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.