Composite pulses for robust universal control of singlet-triplet qubits

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. Here, we report 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, as 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 cancelling errors up to the sixth order in gradient fluctuations, and for large gradients, carry out arbitrary rotations while cancelling the leading order error.