



01752nas a2200169   4500008004100000245007800041210006900119260001500188300001100203490000700214520121000221100002201431700002101453700002401474700001501498856006901513       2018                        eng d00aDiffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians0 aDiffusion Monte Carlo Versus Adiabatic Computation for Local Ham  c2018/02/15  a0223230 v973 a<p><span style="font-family: &quot;Lucida Grande&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.</span></p>1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P.1 aMink, Alan  uhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323