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 interactions of the superconducting circuit with the cavity modes to implement multimode bosonic quantum circuits interspersed with local measurements (such as parity or the photon number operator). This allows for interesting hybrid dynamics and the possibility of studying measurement-induced entanglement phase transitions (MIPT) in a multi-qudit system in the presence of conserved quantities. We will present theoretical results showing signatures of MIPT in this system in various ancilla based order parameters. We will also explore the feasibility of observing this transition in experiments featuring a 3D circuit QED device where a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) interfaces a multimode cavity to a separate few-mode buffer cavity, in turn integrated with a separate transmon ancilla. This system allows for the implementation of fast beam-splitter gates between any pair of cavity modes via 3-wave mixing, as well as high-fidelity measurements on individual modes using the transmon ancilla.