  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 flips and one-qubit NOT gates
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 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 fidelities for the bit
flip and marginal improvement for the NOT gate.
