A hybrid quantum circuit is constructed by using both local unitary gates and non-unitary single qubit projective measurement gates. We find a quantum phase transition through tuning the measurement strength with the order parameter as the entanglement entropy density. We explore the steady state in Clifford circuit model by performing large scale simulation.
We further investigate the quantum dynamics at the critical point and study the emergent conformal symmetry in this hybrid quantum circuit by performing data collapse for both entanglement entropy and mutual information.
We find emergent criticality in non-unitary random free fermion dynamics and we show that the dynamics the correlation function arises out of a simple non-linear master equation.
