Quantum Monte Carlo simulations are emerging as a useful tool to understand the behavior of quantum annealing devices [1, 2] and to shed light on the potential superiority of adiabatic quantum computers compared to classical optimization methods . We investigate the efficiency of projective QMC methods based on the Diffusion Monte Carlo algorithm in solving double-well and multi-well optimization problems, and we compare the DMC algorithm with Path Integral Monte Carlo simulations as well as with the real-time and the imaginary-time dynamics . Furthermore, we implement a DMC algorithm for Quantum Ising models and we show that the DMC tunneling dynamics has the scaling behavior of incoherent quantum tunneling, even in models where PIMC simulations display a pathological slowdown .
 G. E. Santoro, R. Martonak, E. Tosatti, and R. Car, Science 295, 2427 (2002).
 S. V. Isakov, G. Mazzola, V. N. Smelyanskiy, Z. Jiang, S. Boixo, H. Neven, and M. Troyer,
Phys. Rev. Lett. 117, 180402 (2016).
 V. S. Denchev, S. Boixo, S. V. Isakov, N. Ding, R. Bab- bush, V. Smelyanskiy, J. Martinis,
and H. Neven, Phys. Rev. X 6, 031015 (2016).
 E. M. Inack and S. Pilati, Phys. Rev. E 92, 053304 (2015).
 E. Andriyash and M. H. Amin, arXiv:1703.09277v1 (2017).