  Generalized cat states represent arbitrary superpositions of coherent states,
which are of great importance in various quantum information processing
protocols. Here we demonstrate a versatile approach to creating generalized
itinerant cat states in the microwave domain, by reflecting coherent state
photons from a microwave cavity containing a superconducting qubit. We show
that, with a coherent control of the qubit state, a full control over the
coherent state superposition can be realized. The prepared cat states are
verified through quantum state tomography of the qubit state dependent
reflection photon field. We further quantify quantum coherence in the prepared
cat states based on the resource theory, revealing a good experimental control
on the coherent state superpositions. The photon number statistic and the
squeezing properties are also analyzed. Remarkably, fourth-order squeezing is
observed in the experimental states. Those results open up new possibilities of
applying generalized cat states for the purpose of quantum information
processing.
