  Decoherence due to charge noise is one of the central challenges in using
spin qubits in semiconductor quantum dots as a platform for quantum information
processing. Recently, it has been experimentally demonstrated in both Si and
GaAs singlet-triplet qubits that the effects of charge noise can be suppressed
if qubit operations are implemented using symmetric barrier control instead of
the standard tilt control. Here, we investigate the key issue of whether the
benefits of barrier control persist over the entire set of single-qubit gates
by performing randomized benchmarking simulations. We find the surprising
result that the improvement afforded by barrier control depends sensitively on
the amount of spin noise: for the minimal nuclear spin noise levels present in
Si, the coherence time improves by more than two orders of magnitude whereas in
GaAs, by contrast the coherence time is essentially the same for barrier and
tilt control. However, we establish that barrier control becomes beneficial if
qubit operations are performed using a new family of composite pulses that
reduce gate times by up to 90%. With these optimized pulses, barrier control is
the best way to achieve high-fidelity quantum gates in singlet-triplet qubits.
