Efficient state preparation for the quantum simulation of molecules in first quantization

In this talk, we present improvements to state preparation algorithms for the first-quantized simulation of electronic structure. We show that the cost of preparing physically meaningful initial states, either for ground state energy estimation or for dynamical simulation, can be exponentially reduced when compared with the naive linear scaling in the basis set size. We address the preparation of both Hartree-Fock and post-Hartree-Fock states derived from efficient classical calculations, and provide a general prescription that allows for a variety of work on second-quantized simulations in a typical Gaussian basis set to be used to construct initial states for first-quantized simulations in a plane wave basis. The main improvements come from leveraging tensor network methods, but we also use modern compilation techniques designed to reduce the number of non-Clifford gates required for our state preparation scheme.