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We investigate theoretically the implementation of two-qubit gates in asystem of two coupled superconducting qubits. In particular, we analyzetwo-qubit gate operations under the condition that the coupling strength iscomparable to or even larger than the anharmonicity of the qubits. Bynumerically solving the time-dependent Schr\"odinger equation, we obtain thedependence of the two-qubit gate fidelity on the system parameters in the caseof direct and indirect qubit-qubit coupling. Our numerical results can be usedto identify the "safe" parameter regime for experimentally implementingtwo-qubit gates with high fidelity in these systems.

Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity