Simulating Chemistry with Fermionic Optical Superlattices

Abstract: We show that quantum number preserving Ans\"{a}tze for variational optimization in quantum chemistry find an elegant mapping to ultracold fermions in optical superlattices. Using native Hubbard dynamics, trial ground states of molecular Hamiltonians can be prepared and their molecular energies measured in the lattice. The scheme requires local control over interactions and chemical potentials and global control over tunneling dynamics, but foregoes the need for optical tweezers, shuttling operations, or long-range interactions. We describe a complete compilation pipeline from the molecular Hamiltonian to the sequence of lattice operations, thus providing a concrete link between quantum simulation and chemistry. Our work enables the application of recent quantum algorithmic techniques, such as Double Factorization and quantum Tailored Coupled Cluster, to present-day fermionic optical lattice systems with significant improvements in the required number of experimental repetitions. We provide detailed quantum resource estimates for small non-trivial hardware experiments.