High-fidelity one-qubit operations under random telegraph noise

We address the problem of implementing high-fidelity one-qubit operations subject to time-dependent noise in the qubit energy splitting. We show with explicit numerical results that high-fidelity bit flip operations may be generated by imposing bounded control fields. For noise correlation times shorter than the time for a pi pulse, the time-optimal pi pulse itself yields the highest fidelity. For very long correlation times, fidelity loss is approximately due to systematic error, which is efficiently tackled by compensation for off resonance with a pulse sequence (CORPSE). For intermediate ranges of the noise correlation time, we find that short CORPSE, which is less accurate than CORPSE in correcting systematic errors, yields higher fidelities. Numerical optimization of the pulse sequences using gradient ascent pulse engineering results in noticeable improvement of the fidelity for a bit flip operation on the computational basis states and a small but still positive fidelity enhancement for the NOT gate.