  While dissipation is widely considered as being harmful for quantum
coherence, it can, when properly engineered, lead to the stabilization of
non-trivial pure quantum states. We propose a scheme for continuous generation
and stabilization of Schr\"{o}dinger cat states in a cavity using dissipation
engineering. We first generate non-classical photon states with definite parity
by means of a two-photon drive and dissipation, and then stabilize these
transient states against single-photon decay. The single-photon stabilization
is autonomous, and is implemented through a second engineered bath, which
exploits the photon number dependent frequency-splitting due to Kerr
interactions in the strongly dispersive regime of circuit QED. Starting with
the Hamiltonian of the baths plus cavity, we derive an effective model of only
the cavity photon states along with analytic expressions for relevant physical
quantities, such as the stabilization rate. The deterministic generation of
such cat states is one of the key ingredients in performing universal quantum
computation.
