Quantum system characterization with limited resources

The construction and operation of large-scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from device to device. We review strategies for obtaining such knowledge from minimal initial resources and in an efficient manner, and apply these to the problem of characterization of a qubit embedded into a larger state manifold, made tractable by exploiting prior structural knowledge. We also investigate adaptive sampling for estimation of multiple parameters.