  The "Lewis-Riesenfeld phases" which plays a crucial role in constructing
shortcuts to adiabaticity may be a resource for the implementation of quantum
phase gates. By combining "Lewis-Riesenfeld invariant" with "quantum Zeno
dynamics", we propose an effective scheme of rapidly implementing $\pi$ phase
gates via constructing shortcuts to adiabatic passage in a
two-distant-atom-cavity system. The influence of various decoherence processes
such as spontaneous emission and photon loss on the fidelity is discussed. It
is noted that this scheme is insensitive to both two error sources.
Additionally, a creation of N-atom cluster states is put forward as a typical
example of the applications of the fast and noise-resistant phase gates. The
study results show that the shortcuts idea is not only applicable in other
logic gates with different systems, but also propagable for many quantum
information tasks.
