Realizing measurement-induced phase transitions in multimode circuit QED systems

Measurement-induced phase transitions (MIPTs), stemming from the competition between unitary dynamics and projective measurements, have emerged as a new frontier in non-equilibrium quantum physics. While extensively studied in qubit circuits, their realization in bosonic systems remains largely unexplored. We explore experimental implementations in a cascaded random-access memory, consisting of multimode memory tunably coupled to a buffer cavity, which in turn couples to an ancillary transmon. This design supports fast beam-splitter gates between arbitrary cavity modes via three-wave mixing, high-fidelity single-mode measurements, and tunable non-Gaussian operations. We show that MIPTs acquire a richer structure in this setting: Gaussian beam-splitter gates combined with parity measurements do not exhibit a conventional volume-area law transition, whereas adding non-Gaussian interacting gates restores qubit-like universality, but with a non-zero saturation entropy. We explore the feasibility of experimentally observing signatures of the transition through various ancilla-based order parameters.