  We investigate theoretically the implementation of two-qubit gates in a
system of two coupled superconducting qubits. In particular, we analyze
two-qubit gate operations under the condition that the coupling strength is
comparable to or even larger than the anharmonicity of the qubits. By
numerically solving the time-dependent Schr\"odinger equation, we obtain the
dependence of the two-qubit gate fidelity on the system parameters in the case
of direct and indirect qubit-qubit coupling. Our numerical results can be used
to identify the "safe" parameter regime for experimentally implementing
two-qubit gates with high fidelity in these systems.
