Fast coherent swaps between high-Q bosonic modes with a parity-protected coupler

Superconducting resonators with long lifetimes and a highly biased noise channel have shown promise for CVQC in the last decade, with demonstrations of universal single-mode control and error correction beyond break-even. For scaling up this architecture, fast, clean, and tunable multi-cavity operations that do not spoil their lifetime and noise bias are highly desirable. In the past, this has been difficult because the source of non-linearity that enables such operations also introduces spurious processes that lead to heating and dephasing, limiting the operation's fidelity. We show that applying a selectively differential pump to a DC-SQUID gives us a coupling mechanism that is parity-protected, only allowing processes that couple an even number of pump photons to an even number of mode quanta. This circumvents the previously mentioned difficulties, letting us implement a highly coherent beamsplitter between two cavities limited only by their single-photon loss.