  Shortcuts to adiabaticity provides a flexible method to accelerate and
improve a quantum control task beyond adiabatic criteria. Here we propose the
reverse-engineering approach to design the longitudinal coupling between a set
of qubits coupled to several field modes, for achieving a fast generation of
multi-partite quantum gates in photonic or qubit-based architecture. We show
that the enhancing generation time is at the nanosecond scale that does not
scale with the number of system components. In addition, our protocol does not
suffer noticeable detrimental effects due to the dissipative dynamics. Finally,
the possible implementation is discussed with the state-of-the-art circuit
quantum electrodynamics architecture.
