Directed percolation in nonunitary quantum cellular automata

Ramil Nigmatullin,Gavin K. Brennen,Elisabeth Wagner

doi:10.1103/physrevresearch.3.043167

Ramil Nigmatullin, Gavin K. Brennen + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.3.043167

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Abstract

Probabilistic cellular automata (CA) provide a classic framework for studying nonequilibrium statistical physics on lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate the process of directed percolation and the critical dynamics of the nonequilibrium phase transition between absorbing and percolating phases. In this work, we construct a nonunitary quantum CA that generalizes the Domany-Kinzel CA and study the resulting dynamical evolution using numerical simulations using the tensor network infinite time-evolving block decimation (iTEBD) algorithm. We demonstrate that the system undergoes the absorbing/percolating phase transition and that the addition of the Hamiltonian generates coherences, which are a distinct feature of quantum dynamics. A proposal for the implementation of the model with Rydberg array is put forward, which does not require local addressing of individual sites.

Highlights

In recent years there have been great advances in the development of quantum simulation platforms
The 3-cell rule of such nonunitary QCA is the CP map generated by the open nonunitary quantum dynamics specified by the choice of the local Lindblad jump operators and the Hamiltonian
We have considered the dynamics of the model in the large τ limit, which corresponds to discrete block-partitioned nonunitary QCA, and the small τ limit, which corresponds to continuous nonunitary QCA

Summary

Introduction

In recent years there have been great advances in the development of quantum simulation platforms These include ultracold atoms, ions, superconducting qubits, and photonic systems. One of the most recent advances has been the development of a quantum simulator based on arrays of ultracold Rydberg atoms [1]. In the domain of nonequilibrium physics, one promising application of Rydberg arrays is in the exploration of nonequilibrium phase transitions (NEPTs), the study of which is challenging due to the requirement of large system sizes and the long-time evolution needed to reach steady states.

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