  Quantum state tomography is an indispensable but costly part of many quantum
experiments. Typically, it requires measurements to be carried in a number of
different settings on a fixed experimental setup. The collected data is often
informationally overcomplete, with the amount of information redundancy
depending on the particular set of measurement settings chosen. This raises a
question about how should one optimally take data so that the number of
measurement settings necessary can be reduced. Here, we cast this problem in
terms of integer programming. For a given experimental setup, standard integer
programming algorithms allow us to find the minimum set of readout operations
that can realize a target tomographic task. We apply the method to certain
basic and practical state tomographic problems in nuclear magnetic resonance
experimental systems. The results show that, considerably less readout
operations can be found using our technique than it was by using the previous
greedy search strategy. Therefore, our method could be helpful for simplifying
measurement schemes so as to minimize the experimental effort.
