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Using quantum systems to efficiently solve quantum chemistry problems is oneof the long-sought applications of near-future quantum technologies. In arecent work, ultra-cold fermionic atoms have been proposed for these purposesby showing us how to simulate in an analog way the quantum chemistryHamiltonian projected in a lattice basis set. Here, we continue exploring thispath and go beyond these first results in several ways. First, we numericallybenchmark the working conditions of the analog simulator, and find lessdemanding experimental setups where chemistry-like behaviour inthree-dimensions can still be observed. We also provide a deeper understandingof the errors of the simulation appearing due to discretization and finite sizeeffects and provide a way to mitigate them. Finally, we benchmark the simulatorcharacterizing the behaviour of two-electron atoms (He) and molecules (HeH$^+$)beyond the example considered in the original work.

Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices