Overcoming the charge noise is key to the realization of scalable quantum computation using spin qubits. It has been recently demonstrated that the effects of charge noise can be suppressed if operations of a singlet-triplet qubit are implemented using barrier control instead of the traditional tilt control. We have found, however, that for certain gates involving extensive x-rotations, barrier control offers little or no improvement when the nuclear noise is significant. Nevertheless, we introduce a new set of composite pulses that reduce gate times by up to 90%. Using these optimized pulses, the barrier control shows great advantages in randomized benchmarking simulations, with the coherence time extended by about two orders of magnitude for experimentally relevant noises . We have also performed microscopic calculations of a singlet-triplet qubit under the influence of an impurity. We have found that, the relative charge noise (charge noise divided by the exchange interaction), while generally believed to increase with increasing exchange interaction, actually decreases when the barrier control is implemented . Moreover, we show that the exchange interaction of a singlet-triplet spin qubit confined in double quantum dots, when being controlled by the barrier method, is insensitive to a charged impurity lying along certain directions away from the center of the double-dot system. These directions differ from the polar axis of the double dots by the “magic angle”, 54.7 degrees, a value previously found in atomic physics and nuclear magnetic resonance .
 C. Zhang, R.E. Throckmorton, X.-C. Yang, X. Wang, E. Barnes, S. Das Sarma, Phys. Rev. Lett. 118, 216802 (2017).
 X.-C. Yang, X. Wang, Phys. Rev. A 96, 012318 (2017).
 X.-C. Yang, X. Wang, arXiv:1707.07929.