  We investigate the use of programmable optical lattices for quantum
simulation of Hubbard models, determining analytic expressions for the hopping
and Hubbard U, finding that they are suitable for emulating strongly correlated
systems with arbitrary structures, including those with multiple site basis and
impurities. Programmable potentials are highly flexible, with the ability to
control the depth and shape of individual sites in the optical lattice
dynamically. Quantum simulators of Hubbard models with (1) arbitrary basis are
required to represent many real materials of contemporary interest, (2) broken
translational symmetry are needed to study impurity physics, and (3) dynamical
lattices are needed to investigate strong correlation out of equilibrium. We
derive analytic expressions for Hubbard Hamiltonians in programmable potential
systems. We find experimental parameters for quantum simulation of Hubbard
models with arbitrary basis, concluding that programmable optical lattices are
suitable for this purpose. We discuss how programmable optical lattices can be
used for quantum simulation of dynamical multi-band Hubbard models that
represent complicated compounds, impurities, and non-equilibrium physics.
