Realizing measurement-induced phase transitions in multimode circuit QED systems

Multimode microwave cavities with ultra-low losses have been combined with superconducting circuits to realize a novel platform for quantum information processing and quantum simulations with bosons. This platform leverages the nonlinear coupling between the superconducting circuits and cavity modes to implement multimode bosonic quantum circuits comprised of unitary gates interlaced with local midcircuit measurements. The competing dynamics of entangling unitary gates and disentangling measurements allow the opportunity to experimentally study measurement-induced entanglement phase transitions (MIPT) in a multimode bosonic system. We will explore the feasibility of observing this transition in experimental hardware featuring a 3D circuit QED device where a tuneable coupler, such as a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL), interfaces a multimode cavity to a separate measurement cavity, which in turn is integrated with a separate transmon ancilla. Unique aspects of the MIPT in this setting will be discussed.