Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices

Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work [J. Arguello-Luengo et al., Nature (London) 574, 215 (2019)], ultracold fermionic atoms have been proposed for this purpose by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these results in several ways. First, we numerically benchmark the working conditions of the analog simulator and find less demanding experimental setups where chemistry-like behavior in three dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite-size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behavior of two-electron atoms (He) and molecules (HeH+) beyond the example considered in the original work.