TY - JOUR
T1 - Easing the Monte Carlo sign problem
JF - Science Advances
JO - Sci Adv
DO - 10.1126/sciadv.abb8341
VL - 6
IS - 33
SP - eabb8341
AU - Hangleiter, Dominik
AU - Roth, Ingo
AU - Nagaj, Daniel
AU - Eisert, Jens
Y1 - 2020/08/01
UR - http://advances.sciencemag.org/content/6/33/eabb8341.abstract
N2 - Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems. However, in many interesting situations, QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the runtime of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that—as we demonstrate analytically and numerically—at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is generally an NP-complete task for nearest-neighbor Hamiltonians and simple basis choices by a reduction to the MAXCUT-problem.
ER -