  In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes
slowly from zero to one with finite rate, a transition to excited states
inevitably occurs and this induces an intrinsic computational error. We show
that this computational error depends not only on the total computation time
$T$ but also on the time derivatives of the adiabatic parameter $s(t)$ at the
beginning and the end of evolution. Previous work (Phys. Rev. A \textbf{82},
052305) also suggested this result. With six typical paths, we systematically
demonstrate how to optimally design an adiabatic path to reduce the
computational errors. Our method has a clear physical picture and also explains
the pattern of computational error. In this paper we focus on quantum adiabatic
search algorithm although our results are general.
