Precise ultra fast single qubit control using optimal control pulses

Ultra fast and accurate quantum operations are required in many modern scientific areas - for instance quantum information, quantum metrology and magnetometry. However the accuracy is limited if the Rabi frequency is comparable with the transition frequency due to the breakdown of the rotating wave approximation (RWA). Here we report the experimental implementation of a method based on optimal control theory, which does not suffer these restrictions. We realised the most commonly used quantum gates - the Hadamard (π/2 pulse) and NOT (πpulse) gates with fidelities $F^exp_π/2=0.9472pm0.01$ and $F^exp_π=0.993pm0.016$, in an excellent agreement with the theoretical predictions $F^theory_π/2=0.9545$ and $F^theory_π=0.9986$. Moreover, we demonstrate magnetic resonance experiments both in the rotating and lab frames and we can deliberately "switch" between these two frames. Since our technique is general, it could find a wide application in magnetic resonance, quantum computing, quantum optics and broadband magnetometry.