Fast generation of quantum logic gate with Rydberg superatoms

Quantum logic gate is a basic resource in quantum computing. Here, we propose a scheme to generate a CNOT gate and a Toffoli gate with Rydberg superatoms. In the current scheme, the collective states of superatom become the coding carrier of quantum information. Integrating quantum Zeno dynamics with transitionless quantum driving, the present scheme can be implemented rapidly by selecting the appropriate parameters of the laser pulses. Furthermore, the precise numerical simulation demonstrate that the scheme possesses a high fidelity and exhibits insensitivity to atomic spontaneous emission as well as cavity decay.