Investigating non-equilibrium phase transition with 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 transitions between absorbing and percolating phases. In this talk, we construct a non-unitary Quantum Cellular Automaton that generalises the Domany-Kinzel cellular automaton into the quantum domain 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.

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Dr Nigmatullin is an EQUS Research Fellow in Macquarie University. 

He earned his PhD in controlled quantum dynamics in Imperial College London in 2013. 

Dr Nigmatullin research focuses on statistical physics and many-body dynamics of ultracold atomic systems with applications to quantum computing, simulations and sensing. In January 2020, he joined Macquarie University, where his research focuses on theory of quantum cellular automata.