Implementation of a Toffoli Gate with Superconducting Circuits

The Toffoli gate is an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the implementation of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator [1]. Following Ralph \emph{et~al.}~[2] we used the third energy level of the transmon qubit to significantly reduce the number of elementary gates needed to implemente the Toffoli gate in comparison to approaches using two-level systems only. A similar scheme to realize a Toffoli-class gate has independently been devised on a system of three logical qubits encoded in the states of two qubits and a resonator [3]. Our gate fidelity evaluated by both full process tomography and Monte Carlo process certification is $68.5\pm0.5$\%. The results reinforce the potential of macroscopic superconducting qubits for implementation of complex quantum operations and point at the possibility to implement quantum error correction schemes~[4]. \newline [1] A. Fedorov \emph{et~al.}, arXiv:1108.3966. \newline [2] T.~C.~Ralph, K.~J.~Resch, A.~Gilchrist, Phys. Rev. A \textbf{75}, 022313 (2007).\newline [3] M. Mariantoni, \emph{et~al.} Science \textbf{334}, 61 (2011).\newline [4] M.~D. Reed, \emph{et~al.}, arXiv:1109.4948.