  We introduce and demonstrate experimentally: (1) a framework called "gate set
tomography" (GST) for self-consistently characterizing an entire set of quantum
logic gates on a black-box quantum device; (2) an explicit closed-form protocol
for linear-inversion gate set tomography (LGST), whose reliability is
independent of pathologies such as local maxima of the likelihood; and (3) a
simple protocol for objectively scoring the accuracy of a tomographic estimate
without reference to target gates, based on how well it predicts a set of
testing experiments. We use gate set tomography to characterize a set of
Clifford-generating gates on a single trapped-ion qubit, and compare the
performance of (i) standard process tomography; (ii) linear gate set
tomography; and (iii) maximum likelihood gate set tomography.
