Abstract
Two schemes of implementing the Toffoli gate are proposed in an array of coupled cavities. In the first one, two classical laser fields with fixed Rabi frequency are used via quantum Zeno dynamics. While in the second scheme, the invariant-based inverse engineering is used to implement the Toffoli gate, which can drive the instantaneous eigenstates to evolve exactly under the Schrödinger equation. The strictly numerical simulations are given and the influences of cavity decay and spontaneous emission on the Toffoli gate operation are analyzed with master equation. The result shows that our schemes for the Toffoli gate are robust against the decoherence because of the short time needed.
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