Controlled beam splitter gate transparent to dominant ancilla errors

In hybrid circuit quantum electrodynamics (QED) architectures containing both ancilla qubits and bosonic modes, a controlled beam splitter (cBS) gate is a powerful resource. It can be used to create (up to a controlled-parity operation) an ancilla-controlled SWAP gate acting on two bosonic modes. This is the essential element required to execute the 'swap test' for purity, prepare quantum non-Gaussian entanglement and directly measure nonlinear functionals of quantum states. It also constitutes an important gate for hybrid discrete/continuous-variable quantum computation. We propose a new realization of a hybrid cSWAP utilizing 'Kerr-cat' qubits-anharmonic oscillators subject to strong two-photon driving. The Kerr-cat is used to generate a controlled-phase beam splitter operation. When combined with an ordinary beam splitter one obtains a cBS and from this a cSWAP. The strongly biased error channel for the Kerr-cat has phase flips which dominate over bit flips. This yields important benefits for the cSWAP gate which becomes non-destructive and transparent to the dominate error. Our proposal is straightforward to implement and, based on currently existing experimental parameters, should achieve cBS gates with high fidelities comparable to current ordinary beam-splitter operations available in circuit QED.