Simulated quantum annealing is a Monte-Carlo algorithm, running on a classical computer, which samples the equilibrium thermal state of a quantum annealing Hamiltonian. Elizabeth Crosson
, with Aram Harrow, showed that simulated quantum annealing sometimes successfully accounts for the effects of quantum tunneling in a quantum annealer, exhibiting an exponential advantage over classical simulated annealing in which quantum tunneling is not faithfully described . This work supports the growing consensus that quantum annealers are unlikely to achieve exponential speedups over classical computing solely by the use of quantum tunneling.
2. E. Crosson and A. W. Harrow, Simulated quantum annealing can be exponentially faster than classical simulated annealing, http://arxiv.org/abs/1601.03030