The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three superconduct
ing transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubit, the number of elementary gates needed for the implementation of the Toffoli gate, as well as the total gate time can be reduced significantly in comparison to theoretical proposals using two-level systems only. We characterize the performance of the gate by full process tomography and Monte Carlo process certification. The gate fidelity is found to be $68.5pm0.5$%.
A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit whose gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We
show full spectroscopy of the qubit-resonator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency $ u_{osc}$ we find the strongest qubit-resonator coupling ($g/hsim0.1 u_{rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible.
