The sign problem, non-stoquasticity and everything in between*

The quantum Monte Carlo sign problem has been rightfully recognized as one of the grand challenges of computational physics. This problem encapsulates our inability to develop a proper understanding of many important quantum many-body phenomena in physics, chemistry and well beyond. Despite its centrality, the circumstances under which the sign 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 talk, I will attempt to elucidate the circumstances under which the sign problem emerges and clear up some of the confusion surrounding this intricate computational phenomenon. Making use of the recently introduced off-diagonal series expansion quantum Monte Carlo technique, I will discuss a sufficient and necessary condition for the simulability of quantum many-body Hamiltonians and provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models.