  The role of quantum fluctuations in modifying the critical behavior of
non-equilibrium phase transitions is a fundamental but unsolved question. In
this study, we examine the absorbing state phase transition of a 1D chain of
qubits undergoing a contact process that involves both coherent and classical
dynamics. We adopt a discrete-time quantum model with states that can be
described in the stabilizer formalism, and therefore allows for an efficient
simulation of large system sizes. The extracted critical exponents indicate
that the absorbing state phase transition of this Clifford circuit model
belongs to the directed percolation universality class. This suggests that the
inclusion of quantum fluctuations does not necessarily alter the critical
behavior of non-equilibrium phase transitions of purely classical systems.
Finally, we extend our analysis to a non-Clifford circuit model, where a
tentative scaling analysis in small systems reveals critical exponents that are
also consistent with the directed percolation universality class.
