Measurement-Induced Phase Transitions in Quantum Circuits

This thesis is devoted to the study of quantum dynamics interspersed with quantum measurements. Focusing on a one-dimensional “hybrid” quantum circuit model consisting of random unitary gates and local projective measurements, we provide extensive evidence for a stable “weakly measured phase” that exhibits volume law entanglement entropy, and a novel continuous quantum dynamical phase transition between the weakly measured phase and a strongly measured “quantum Zeno phase” that exhibits area law entanglement entropy. We further study consequences of conformal symmetry at the critical point, as well as properties of the weakly measured phase. In the latter case, we develop an effective domain wall theory which correctly accounts for an unusual subvolume powerlaw correction to the entanglement entropy, and draw close connections between the domain wall theory and an emergent quantum error correcting code. In the last Chapter, we discuss an experimental protocol that can avoid the so- called “postselection problem” and allow scalable experimental observations of such transitions on near term quantum processors.