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Directed percolation in non-unitary quantum cellular automata

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.