  We investigate the fundamental limits in precision allowed by quantum
mechanics from Landau-Zener transitions, concerning Hamiltonian parameters.
While the Landau-Zener transition probabilities depend sensitively on the
system parameters, much more precision may be obtained using the acquired
phase, quantified by the quantum Fisher information. This information scales
with a power of the elapsed time for the quantum case, whereas it is
time-independent if the transition probabilities alone are used. We add
coherent control to the system, and increase the permitted maximum precision in
this time-dependent quantum system. The case of multiple passes before
measurement, "Landau-Zener-Stueckelberg interferometry", is considered, and we
demonstrate that proper quantum control can cause the quantum Fisher
information about the oscillation frequency to scale as $T^4$, where $T$ is the
elapsed time.
