  Precise qubit manipulation is fundamental to quantum computing, yet
experimental systems generally have stray coupling between the qubit and the
environment, which hinders the necessary high-precision control. We report here
the first theoretical progress in correcting an important class of errors
stemming from fluctuations in the magnetic field gradient, in the context of
the singlet-triplet spin qubit in a semiconductor double quantum dot. These
errors are not amenable to correction via control techniques developed in other
contexts, since here the experimenter has precise control only over the
rotation rate about the z-axis of the Bloch sphere, and this rate is
furthermore restricted to be positive and bounded. Despite these strong
constraints, we construct simple electrical pulse sequences that, for small
gradients, carry out z-axis rotations while canceling errors up to the sixth
order in gradient fluctuations, and for large gradients, carry out arbitrary
rotations while canceling the leading order error.
