  Quantum tomography is the main method used to assess the quality of quantum
information processing devices, but its complexity presents a major obstacle
for the characterization of even moderately large systems. The number of
experimental settings required to extract complete information about a device
grows exponentially with its size, and so does the running time for processing
the data generated by these experiments. Part of the problem is that tomography
generates much more information than is usually sought. Taking a more targeted
approach, we develop schemes that enable (i) estimating the fidelity of an
experiment to a theoretical ideal description, (ii) learning which description
within a reduced subset best matches the experimental data. Both these
approaches yield a significant reduction in resources compared to tomography.
In particular, we demonstrate that fidelity can be estimated from a number of
simple experimental settings that is independent of the system size, removing
an important roadblock for the experimental study of larger quantum information
processing units.
