Research ArticlePHYSICS

Easing the Monte Carlo sign problem

See allHide authors and affiliations

Science Advances  14 Aug 2020:
Vol. 6, no. 33, eabb8341
DOI: 10.1126/sciadv.abb8341


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.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

View Full Text

Stay Connected to Science Advances