Efficient Toffoli Gate in Circuit Quantum Electrodynamics*

The fidelity of quantum gates in circuit quantum electrodynamics is typically limited by qubit decoherence.  As such, significant improvements can be realized by shortening gate duration [1, 2]. The three-qubit Toffoli gate, also called the controlled-controlled NOT, is an important operation in basic quantum error correction.  We report a scheme for a Toffoli gate that exploits interactions with non-computational excited states of transmon qubits which can be executed faster than an equivalent construction using one- and two-qubit gates.  The application of this gate to efficient measurement-free quantum error correction will be discussed. \\[4pt] [1] DiCarlo, et al. Nature 467, 574 (2010). \\[0pt] [2] Chow, et al. Phys. Rev. Lett. 102, 090502 (2009).