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Fast, high-fidelity operations between microwave resonators are an importanttool for bosonic quantum computation and simulation with superconductingcircuits. An attractive approach for implementing these operations is to couplethese resonators via a nonlinear converter and actuate parametric processeswith RF drives. It can be challenging to make these processes simultaneouslyfast and high fidelity, since this requires introducing strong drives withoutactivating parasitic processes or introducing additional decoherence channels.We show that in addition to a careful management of drive frequencies and thespectrum of environmental noise, leveraging the inbuilt symmetries of theconverter Hamiltonian can suppress unwanted nonlinear interactions, preventingconverter-induced decoherence. We demonstrate these principles using adifferentially-driven DC-SQUID as our converter, coupled to two high-Qmicrowave cavities. Using this architecture, we engineer a highly-coherentbeamsplitter and fast ($\sim$ 100 ns) swaps between the cavities, limitedprimarily by their intrinsic single-photon loss. We characterize thisbeamsplitter in the cavities' joint single-photon subspace, and show that wecan detect and post-select photon loss events to achieve a beamsplitter gatefidelity exceeding 99.98$\%$, which to our knowledge far surpasses the currentstate of the art.

High-fidelity parametric beamsplitting with a parity-protected converter