Quantum simulation of many-body non-equilibrium dynamics in tilted Fermi-Hubbard models*

Identifying applications of state-of-the art quantum computers and quantum simulators within their limitations is a problem of contemporary interest. Problems in quantum many-body physics often lie at the intersection of computational hardness and physical pertinence. Here we show that a quantum simulator can be used to develop new, efficient classical algorithms to study the dynamics of many-body systems. We first consider a localized 1D Fermi-Hubbard system where the exact techniques of computing the time dynamics are inefficient, and develop an efficient  approximate theory. Our approximate theory does not have an error estimate and therefore, we use a quantum simulator to benchmark its performance in terms of accuracy of its outcome. We use the approximate theory to further study the interacting features of localized systems [1]. Moreover, we extend this approximation to the 2D Fermi-Hubbard model, where the reach of existing numerical techniques is very limited. We show that our method, together with sequence extrapolation techniques can be used to study some 2D Fermi-Hubbard models.