  It was recently shown that, for solving NP-complete problems, adiabatic paths
always exist without finite-order perturbative crossings between local and
global minima, which could lead to anticrossings with exponentially small
energy gaps if present. However, it was not shown whether such a path could be
found easily. Here, we give a simple construction that deterministically
eliminates all such anticrossings in polynomial time, space, and energy, for
any Ising models with polynomial final gap. Thus, in order for adiabatic
quantum optimization to require exponential time to solve any NP-complete
problem, some quality other than this type of anticrossing must be unavoidable
and necessitate exponentially long runtimes.
