Measurement-Induced Phase Transitions in Long-range Quantum Circuits

Hybrid quantum circuits, in which random unitary gates are interspersed with projective measurements, can exhibit a phase transition between volume- and area-law scaling of steady-state entanglement entropy, owing to the competition between information scrambling and measurements. Long-range interactions can scramble information parametrically faster than short-range interactions, suggesting they may qualitatively modify the transition. In this talk, we study 1D long-range hybrid quantum circuits where each unitary is a random two-qubit Clifford gate with range sampled from a 1/r^α power law distribution. We find that the presence of long-range interactions changes the universality of the transition: for α>3, the critical exponents agree with studies of nearest-neighbor hybrid circuits, while for α<3 the critical exponents change continuously with α. In particular, we find the dynamical exponent z<1 for α<3, indicating the transition cannot be described by conformal field theory. Moreover, for α<2 the area-law scaling crosses over to a sub-volume law scaling in which entanglement entropy grows with system size, even under high measurement rates. Our work is especially relevant for hybrid quantum circuits realized in experimental systems with inherently long-range interactions.