IQIM Postdoctoral and Graduate Student Seminar

Abstract: We will present a framework of quantum algorithms for estimating properties of general matrix functions, with applications to estimating ground state energies, Green's functions, and measurement distributions of time-evolved states. Our methods exhibit commutator scaling in matrix parameters similar to that found for algorithms using product formulae, near-optimal circuit depths in all other parameters, and use at most a single ancillary qubit. Operationally, our central primitive consists of classically postprocessing data from randomly chosen circuits, which allows a tradeoff of reduced quantum circuit depth for more circuit samples. Mathematically, this corresponds to an approximation of a Richardson extrapolation. Beyond asymptotic statements, we will argue our methods could show promise as a theory-informed heuristic, and we will present some numerical experiments supporting this idea.

Following the talk, lunch will be provided on the lawn outside East Bridge.