Measurement-induced phase transitions in deterministic non-local quantum circuits*

Measurement-induced Phase Transitions (MPTs) are a novel class of dynamical phase transitions driven by a competition between quantum information scrambling and measurements. So far, MPTs have been studied extensively in random circuits in 1+1D and to a lesser extent in random all-to-all models. But is randomness a necessary ingredient for this phase transition? Here we show that the answer is no: the same effect can be observed even in deterministic hybrid quantum circuits whose 2-qubit gates are arranged according to a fixed, non-local coupling graph. Specifically, we numerically study hybrid Clifford quantum circuits on the Bethe lattice and a family of non-local sparse graphs, and demonstrate the presence of percolation, entanglement, and purification transitions in these models. We show that the choice of non-local couplings in the network can substantially increase the critical measurement rate.