  It has been recently demonstrated that a singlet-triplet spin qubit in
semiconductor double quantum dots can be controlled by changing the height of
the potential barrier between the two dots ("barrier control"), which has led
to a considerable reduction of charge noises as compared to the traditional
tilt control method. In this paper we show, through a
molecular-orbital-theoretic calculation of double quantum dots influenced by a
charged impurity, that the relative charge noise for a system under the barrier
control not only is smaller than that for the tilt control, but actually
decreases as a function of an increasing exchange interaction. This is
understood as a combined consequence of the greatly suppressed detuning noise
when the two dots are symmetrically operated, as well as an enhancement of the
inter-dot hopping energy of an electron when the barrier is lowered which in
turn reduces the relative charge noise at large exchange interaction values. We
have also studied the response of the qubit to charged impurities at different
locations, and found that the improvement of barrier control is least for
impurities equidistant from the two dots due to the small detuning noise they
cause, but is otherwise significant along other directions.
