  A remarkably simple result is derived for the minimal time $T_{\rm min}$
required to drive a general initial state to a final target state by a
Landau-Zener type Hamiltonian or, equivalently, by time-dependent laser
driving. The associated protocol is also derived. A surprise arises for some
states when the interaction strength is assumed to be bounded by a constant
$c$. Then, for large $c$, the optimal driving is of type bang-off-bang and for
increasing $c$ one recovers the unconstrained result. However, for smaller $c$
the optimal driving can suddenly switch to bang-bang type. We discuss the
notion of quantum speed limit time.
