  The tunneling between the two ground states of an Ising ferromagnet is a
typical example of many-body tunneling processes between two local minima, as
they occur during quantum annealing. Performing quantum Monte Carlo (QMC)
simulations we find that the QMC tunneling rate displays the same scaling with
system size, as the rate of incoherent tunneling. The scaling in both cases is
$O(\Delta^2)$, where $\Delta$ is the tunneling splitting. An important
consequence is that QMC simulations can be used to predict the performance of a
quantum annealer for tunneling through a barrier. Furthermore, by using open
instead of periodic boundary conditions in imaginary time, equivalent to a
projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve
linear scaling in $\Delta$. We provide a physical understanding of these
results and their range of applicability based on an instanton picture.
