  We propose an alternative scheme of shortcuts to quantum phase gate in a much
shorter time based on the approach of Lewis-Riesenfeld invariants in cavity
quantum electronic dynamics (QED) systems. This scheme can be used to perform
one-qubit phase gate, two-qubit controlled phase gate and also multiqubit
controlled phase gate. The strict numerical simulation for some quantum gates
are given, and demonstrate that the total operation time of our scheme is
shorter than previous schemes and very robustness against decoherence.
