# Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians

 Title Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians Publication Type Journal Article Year of Publication 2018 Authors Bringewatt, J, Dorland, W, Jordan, SP, Mink, A Journal Physical Review A Volume 97 Issue 2 Pages 022323 Date Published 2018/02/15 Abstract 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. URL https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323 DOI 10.1103/PhysRevA.97.022323