Directed percolation in nonunitary quantum cellular automata

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