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.
@article{arxiv.1108.3442,
title = {Quantum-control approach to realizing a Toffoli gate in circuit QED},
author = {Vladimir M. Stojanovic and A. Fedorov and A. Wallraff and C. Bruder},
journal= {arXiv preprint arXiv:1108.3442},
year = {2012}
}