Elementary quantum gates between long-distance qubits mediated by a resonator

We propose a scheme to realize Controlled-NOT, Controlled-V, Controlled- $$V^{\dag }$$ gate based on the indirect coupling of two qubits which are coupled to a common resonator. Based on the state-of-the-art controllability of longitudinal and transverse coupling between a qubit and a resonator, we let the control qubit couple to the resonator longitudinally and the target qubit couple to the resonator transversely. One can get the fidelity of these gates (as well as the synthesized Toffoli gate) over 99% within effective gate timescales. The proposed gate scheme is possible for the experimental setups where the effective qubit–resonator coupling strength is far bigger than the cavity decay rate and the dephasing rate of the qubits and applicable to quantum circuit synthesizing and long-distance qubit interaction.

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