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We theoretically present an effective method to realize NiSWAP, N(sqrt(iSWAP)), NSWAP, N(sqrt(SWAP)) and NTQ-NOT gates based on the qubit-qubit interaction in a circuit QED using N+1 transmon qubits driven by a strong microwave field. In this system, the interaction between the qubits and the resonator field can be achieved by turning the gate voltage and the external flux. The operation time is independent of the number of qubits involved in the scheme, and the gates operations are insensitive to the initial state of the resonator. These quantum logic gates can be realized in a time (nanosecond-scale) much smaller than decoherence time (microsecond-scale), and it is more immune to the 1/f charge noise and has longer dephasing time due to the favorable properties of the transmon qubits in the circuit QED. Numerical simulation under the influence of the gates operations shows that the scheme can be implemented with high fidelity. We also propose a detailed procedure and experimentally analyze its feasibility. Moreover, the scheme might be experimentally achieved efficiently within current state-of-the-art technology.

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