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We present two efficient methods for implementing the Fredkin gate with atomsseparately trapped in an array of three high-$Q$ coupled cavities. The firstproposal is based on the resonant dynamics, which leads to a fast resonantinteraction in a certain subspace while leaving others unchanged, and thesecond one utilizes a dispersive interaction such that the effectivelong-distance dipole-dipole interaction between two distributed target qubitsis achieved by virtually excited process. Both schemes can achieve the standardform of the Fredkin gate in a single step without any subsequent single-qubitoperation. The effects of decoherence on the performance of the gate are alsoanalyzed in virtue of master equation, and the strictly numerical simulationreveals that the average fidelity of the quantum gate is high.

One-step implementation of the genuine Fredkin gate in high-$Q$ coupled three-cavity arrays