Cat states of the microwave field stored in high-Q resonators show great promise for robust encoding and manipulation of quantum information. Here we propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. We show that this preparation is robust against single-photon loss. We moreover find that it is possible to remove undesirable phase evolution induced by a Kerr nonlinearity using a two-photon drive of appropriate amplitude and phase. Finally, we present a universal set of quantum logical gates that can be performed on the engineered eigenspace of the two-photon driven Kerr-nonlinear resonator.
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