  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 unprecedented 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.
