  We formulate a time-optimal approach to adiabatic quantum computation (AQC).
A corresponding natural Riemannian metric is also derived, through which AQC
can be understood as the problem of finding a geodesic on the manifold of
control parameters. This geometrization of AQC is demonstrated through two
examples, where we show that it leads to improved performance of AQC, and sheds
light on the roles of entanglement and curvature of the control manifold in
algorithmic performance.
