  Cat-state qubits (qubits encoded with cat states) have recently drawn
intensive attention due to their enhanced life times with quantum error
correction. We here propose a method to implement a universal controlled-phase
gate of two cat-state qubits, via two microwave resonators coupled to a
superconducting transmon qutrit. During the gate operation, the qutrit remains
in the ground state; thus decoherence from the qutrit is greatly suppressed.
This proposal requires only two basic operations and neither classical pulse
nor measurement is needed; therefore the gate realization is simple. Numerical
simulations show that high-fidelity implementation of this gate is feasible
with current circuit QED technology. The proposal is quite general and can be
applied to implement the proposed gate with two microwave resonators or two
optical cavities coupled to a single three-level natural or artificial atom.
