  We study the realization of a Toffoli gate with superconducting qubits in a
circuit-QED setup using quantum-control methods. Starting with optimized
piecewise-constant control fields acting on all qubits and typical strengths of
XY-type coupling between the qubits, we demonstrate that the optimal gate
fidelities are affected only slightly by a "low-pass" filtering of these fields
with the typical cutoff frequencies of microwave driving. Restricting ourselves
to the range of control-field amplitudes for which the leakage to the
non-computational states of a physical qubit is heavily suppressed, we
theoretically predict that in the absence of decoherence and leakage, within 75
ns a Toffoli gate can be realized with intrinsic fidelities higher than 90%,
while fidelities above 99% can be reached in about 140 ns.
