RT Journal Article
SR Electronic
T1 Easing the Monte Carlo sign problem
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP eabb8341
DO 10.1126/sciadv.abb8341
VO 6
IS 33
A1 Hangleiter, Dominik
A1 Roth, Ingo
A1 Nagaj, Daniel
A1 Eisert, Jens
YR 2020
UL http://advances.sciencemag.org/content/6/33/eabb8341.abstract
AB 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.