Absorbing State Phase Transition with Clifford Circuits

Abstract

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.

Entanglement and Absorbing State Transitions in (d+1)-Dimensional Stabilizer Circuits

“…This idea has been successful for monitored free fermions and certain models of quantum chaos [33,34], but the introduction of feedback does not necessarily imply that MIT is observable on the level of average state. For instance, when a feedback mechanism introduces an absorbing state to the system, i.e., a state that is a fixed point of the dynamics, the resulting absorbing phase transition (APT) and MIT are generally distinct [35][36][37][38]. Nevertheless, for carefully chosen feedback operations [39], fluctuations of the order parameter of APT and the entanglement entropy can be coupled.…”