  We consider a pair of coupled spins with Ising interaction in z-direction and
study the problem of generating efficiently the triplet Bell state. We
initially analyze the transitionless quantum driving shortcut to adiabaticity
method and point out its limitations when the available duration approaches
zero. In this short time limit we explicitly calculate the fidelity of the
method and find it to be much lower than unity, no matter how large become the
available control fields. We find that there is a lower bound on the necessary
time to complete this transfer, set by the finite value of the interaction
between the spins. We then use numerical optimal control to find bang-bang
pulse sequences, as well as, smooth controls, which can generate high levels of
the target Bell state in the minimum possible time. The results of the present
work are not restricted only to spin systems, but is expected to find also
applications in other physical systems which can be modeled as interacting
spins, such as, for example, coupled quantum dots.
