  We introduce a new gate that transfers an arbitrary state of a qubit into a
superposition of two quasi-orthogonal coherent states of a cavity mode, with
opposite phases. This qcMAP gate is based on conditional qubit and cavity
operations exploiting the energy level dispersive shifts, in the regime where
they are much stronger than the cavity and qubit linewidths. The generation of
multi-component superpositions of quasi-orthogonal coherent states, non-local
entangled states of two resonators and multi-qubit GHZ states can be
efficiently achieved by this gate.
