Precise programmable quantum simulations with optical lattices

We present an efficient approach to precisely simulate tight binding models with optical lattices, based on programmable digital-micromirror-device (DMD) techniques. Our approach consists of a subroutine of Wegner-flow enabled precise extraction of a tight-binding model for a given optical potential, and a reverse engineering step of adjusting the potential for a targeting model, for both of which we develop classical algorithms to achieve high precision and high efficiency. With renormalization of Wannier functions and high band effects systematically calibrated in our protocol, we show the tight-binding models with programmable onsite energies and tunnelings can be precisely simulated with optical lattices integrated with the DMD techniques. With numerical simulation, we demonstrate that our approach would facilitate quantum simulation of localization physics with adequate programmability and atom-based boson sampling for illustration of quantum computational advantage. We expect this approach would pave a way towards large-scale and precise programmable quantum simulations based on optical lattices.