Simple scheme for implementing the Grover search algorithm with superconducting qubits

This work concerns a three-qubit processor implemented as three transmon-type superconducting qubits capacitively coupled to a superconducting resonator driven by a microwave field. Based on an effective Hamiltonian of this system, we propose a scheme to realize an X-rotation gate for three qubits requiring only a single-step operation. During the gate operation, the cavity photon-number is canceled due to the strong microwave field. It does not require the cavity to be initially in the vacuum state and the scheme is insensitive to cavity decay. We also present an effective scheme to implement Grover's search algorithm based on this quantum gate and a phase oracle. Using numerical simulation and analysis, we show that the proposed schemes allow for efficiently finding the target state with a high fidelity. The potential application of these proposals with current QED circuit technology is also discussed.