Adiabatic Optimization versus Diffusion Monte Carlo

Published

October 13, 2016

Author(s)

Stephen P. Jordan, Michael Jarret, Brad Lackey

Abstract

Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Sub-Stochastic Monte Carlo. In fact, our simulations are good classical optimization heuristics in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k = 2,3,4.

Citation

Physical Review A

Volume

94

Pub Type

Journals

Keywords

quantum computing, optimization, adiabatic, Monte Carlo

Citation

Jordan, S. , Jarret, M. and Lackey, B. (2016), Adiabatic Optimization versus Diffusion Monte Carlo, Physical Review A (Accessed October 15, 2025)