Rapid initial state preparation for the quantum simulation of strongly correlated molecules

Studies on quantum algorithms for ground state energy estimation often assume perfect ground state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here we address that problem in two ways: by faster preparation of matrix product state (MPS) approximations, and more efficient filtering of the prepared state to find the ground state energy. We show how to achieve unitary synthesis with a Toffoli complexity about 7x lower than that in prior work, and use that to derive a more efficient MPS preparation method. For filtering we use the theory of window functions to avoid large phase errors and minimize the complexity. Finally, we estimate the total resources to perform ground state energy estimation of Fe-S cluster systems, including the FeMo cofactor by estimating the overlap of different MPS initial states with potential ground-states of the FeMo cofactor using an extrapolation procedure. With a modest MPS bond dimension of 4000, our procedure produces an estimate of ~0.9 overlap squared with a candidate ground-state of the FeMo cofactor, producing a total resource estimate of 7x10^10 Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that used perfect ground state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system.