  A recurring challenge in quantum science and technology is the precise
control of their underlying dynamics that lead to the desired quantum
operations, often described by a set of quantum gates. These gates can be
subject to application-specific errors, leading to a dependence of their
controls on the chosen circuit, the quality measure and the gate-set itself. A
natural solution would be to apply quantum optimal control in an
application-oriented fashion. In turn, this requires the definition of a
meaningful measure of the contextual gate-set performance. Therefore, we
explore and compare the applicability of quantum process tomography, linear
inversion gate-set tomography, randomized linear gate-set tomography, and
randomized benchmarking as measures for closed-loop quantum optimal control
experiments, using a macroscopic ensemble of nitrogen-vacancy centers in
diamond as a test-bed. Our work demonstrates the relative trade-offs between
those measures and how to significantly enhance the gate-set performance,
leading to an improvement across all investigated methods.
