  We present an information geometric characterization of quantum driving
schemes specified by su(2;C) time-dependent Hamiltonians in terms of both
complexity and efficiency concepts. By employing a minimum action principle,
the optimum path connecting initial and final states on the manifold in
finite-time is the geodesic path between the two states. In particular, the
total entropy production that occurs during the transfer is minimized along
these optimum paths. For each optimum path that emerges from the given quantum
driving scheme, we evaluate the so-called information geometric complexity
(IGC) and our newly proposed measure of entropic efficiency constructed in
terms of the constant entropy production rates that specify the entropy
minimizing paths being compared. From our analytical estimates of complexity
and efficiency, we provide a relative ranking among the driving schemes being
investigated. Finally, we conclude by commenting on the fact that an higher
entropic speed in quantum transfer processes seems to necessarily go along with
a lower entropic efficiency together with a higher information geometric
complexity.
