Elucidating the interplay between non-stoquasticity and the sign problem

TL;DR

This paper investigates the conditions under which the quantum sign problem appears and explores its relationship with non-stoquastic Hamiltonians, using off-diagonal series expansion quantum Monte Carlo methods to analyze key examples.

Contribution

It clarifies the circumstances leading to the sign problem and its connection to non-stoquasticity, providing detailed analysis through a novel Monte Carlo approach.

Findings

Identifies specific conditions causing the sign problem.

Clarifies the relationship between non-stoquasticity and the sign problem.

Demonstrates the effectiveness of off-diagonal series expansion in analysis.

Abstract

The sign problem is a key challenge in computational physics, encapsulating our inability to properly understand many important quantum many-body phenomena in physics, chemistry and the material sciences. Despite its centrality, the circumstances under which the problem arises or can be resolved as well as its interplay with the related notion of `non-stoquasticity' are often not very well understood. In this study, we make an attempt to elucidate the circumstances under which the sign problem emerges and to clear up some of the confusion surrounding this intricate computational phenomenon. To that aim, we make use of the recently introduced off-diagonal series expansion quantum Monte Carlo scheme with which we analyze in detail a number of examples that capture the essence of our results.