  Nonselective quantum measurements, i.e., measurements without reading the
results, are often considered as a resource for manipulating quantum systems.
In this work, we investigate optimal acceleration of the Landau-Zener (LZ)
transitions by non-selective quantum measurements. We use the measurements of a
population of a diabatic state of the LZ system at certain time instants as
control and find the optimal time instants which maximize the LZ transition. We
find surprising nonmonotonic behavior of the maximal transition probability
with increase of the coupling parameter when the number of measurements is
large. This transition probability gives an optimal approximation to the
fundamental quantum Zeno effect (which corresponds to continuous measurements)
by a fixed number of discrete measurements. The difficulty for the analysis is
that the transition probability as a function of time instants has a huge
number of local maxima. We resolve this problem both analytically by asymptotic
analysis and numerically by the development of efficient algorithms mainly
based on the dynamic programming. The proposed numerical methods can be
applied, besides this problem, to a wide class of measurement-based optimal
control problems.
