  We explore to what extent path-integral quantum Monte Carlo methods can
efficiently simulate the tunneling behavior of quantum adiabatic optimization
algorithms. Specifically we look at symmetric cost functions defined over n
bits with a single potential barrier that a successful optimization algorithm
will have to tunnel through. The height and width of this barrier depend on n,
and by tuning these dependencies, we can make the optimization algorithm
succeed or fail in polynomial time. In this article we compare the strength of
quantum adiabatic tunneling with that of path-integral quantum Monte Carlo
methods. We find numerical evidence that quantum Monte Carlo algorithms will
succeed in the same regimes where quantum adiabatic optimization succeeds.
