  Significant effort in applied quantum computing has been devoted to the
problem of ground state energy estimation for molecules and materials. Yet, for
many applications of practical value, additional properties of the ground state
must be estimated. These include Green's functions used to compute electron
transport in materials and the one-particle reduced density matrices used to
compute electric dipoles of molecules. In this paper, we propose a
quantum-classical hybrid algorithm to efficiently estimate such ground state
properties with high accuracy using low-depth quantum circuits. We provide an
analysis of various costs (circuit repetitions, maximal evolution time, and
expected total runtime) as a function of target accuracy, spectral gap, and
initial ground state overlap. This algorithm suggests a concrete approach to
using early fault tolerant quantum computers for carrying out industry-relevant
molecular and materials calculations.
