Controlled-squeeze gate in superconducting quantum circuits

We present a method to prepare nonclassical states of the electromagnetic field in a microwave resonator. It is based on a controlled gate that applies a squeezing operation on a SQUID-terminated resonator conditioned on the state of a dispersively coupled qubit. This controlled-squeeze gate, when combined with Gaussian operations on the resonator, is universal. We explore the use of this tool to map an arbitrary qubit state into a superposition of squeezed states. In particular, we target a bosonic code with well-defined superparity which makes photon losses detectable by nondemolition parity measurements. We analyze the possibility of implementing this using state-of-the-art circuit QED tools and conclude that it is within reach of current technologies.