  Adiabatic quantum computation employs a slow change of a time-dependent
control function (or functions) to interpolate between an initial and final
Hamiltonian, which helps to keep the system in the instantaneous ground state.
When the evolution time is finite, the degree of adiabaticity (quantified in
this work as the average ground-state population during evolution) depends on
the particulars of a dynamic trajectory associated with a given set of control
functions. We use quantum optimal control theory with a composite objective
functional to numerically search for controls that achieve the target final
state with a high fidelity while simultaneously maximizing the degree of
adiabaticity. Exploring properties of optimal adiabatic trajectories in model
systems elucidates the dynamic mechanisms that suppress unwanted excitations
from the ground state. Specifically, we discover that the use of multiple
control functions makes it possible to access a rich set of dynamic
trajectories, some of which attain a significantly improved performance (in
terms of both fidelity and adiabaticity) through the increase of the energy gap
during most of the evolution time.
