Measurement-protected quantum phases

We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area law entanglement phase steady state. Our primary example is circuits respecting global Ising symmetry two competing types measurements. The diagram has an spin glass order, undergoes direct transition to paramagnetic volume entanglement, as well critical regime. Using mutual information diagnostics, we find that such transitions preserving are new universality classes. analyze generalizations higher dimensions, allow for coexistence topological without any restrictions.