  We theoretically propose an alternative method to realize a deterministic
SWAP gate using shortcuts to adiabatic passage based on the approach of Lewis-
Riesenfeld invariants in cavity quantum electronic dynamics (QED). By combining
Lewis-Riesenfeld invariants with quantum Zeno dynamics, the SWAP gate can be
achieved deterministically. The strict numerical results show that our scheme
is a fast and robust approach to achieve SWAP gate.
