  We study the propagation and amplification of a microwave field in a
four-level cascade quantum system which is realized in a superconducting phase
quantum circuit. It is shown that by increasing the microwave pump tones
feeding the system, the normal dispersion switches to the anomalous and the
gain-assisted superluminal microwave propagation is obtained in this system.
Moreover, it is demonstrated that the stimulated microwave field is generated
via four-wave mixing without any inversion population in the energy levels of
the system (amplification without inversion) and the group velocity of the
generated pulse can be controlled by the external oscillating magnetic fluxes.
We also show that in some special set of parameters, the absorption-free
superluminal generated microwave propagation is obtained in superconducting
phase quantum circuit system.
