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