Microwave swap gates with a Kerr-cat ancilla*

Quantum computation requires coherent highly controllable gates with low error rates. A long-standing target is an exponential-swap gate which requires an ancilla qubit to entangle two microwave fields. A transmon ancilla has been previously used (Gao et al. Nature 566, 509 (2019)); it introduces a back propagation of ancilla errors into the fields. We propose a new way of doing a controlled beam splitter with a SNAIL-based Kerr cat that is transparent to the dominant error channel. We show that one can implement a beam splitter with a phase that depends on the state of the ancilla cat using suitable driving fields. Encoding quantum information into coherent states of the Kerr cat biases its decoherence towards phase flips, allowing significantly improved performance compared to the transmon setup. With this controlled beam splitter, it is possible to implement controlled-swap and further exponential-swap gates for microwave fields, which allows further applications such as swap tests or quantum random access memory protocols.