Directed percolation in non-unitary quantum cellular automata

Abstract

Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on a 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 non-equilibrium phase transition betweeen absorbing and percolating phases. In this work, we construct a non-unitary Quantum Cellular Automaton that generalises the Domany-Kinzel cellular automaton and study the resulting dynamical evolution using the numerical simulations using the tensor network iTEBD algorithm. We demonstrate the system undergoes the absorbing/percolating phase transition and the addition of the Hamiltonian generates coherences, which are a distinct feature of the 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.

arXiv comment10 pages, 6 figures

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Cited by in corpus (12)

• Characterizing a non-equilibrium phase transition on a quantum computer
• Reaction-limited quantum reaction-diffusion dynamics
• Quantum reaction-limited reaction-diffusion dynamics of annihilation processes
• Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks
• Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically-constrained open many-body system with two absorbing states
• Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata
• Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Information Flow in Non-Unitary Quantum Cellular Automata
• Density Classification with Non-Unitary Quantum Cellular Automata
• IPS/Zeta Correspondence for the Domany-Kinzel model
• Nonequilibrium dark space phase transition