  Determining the properties of molecules and materials is one of the premier
applications of quantum computing. A major question in the field is: how might
we use imperfect near-term quantum computers to solve problems of practical
value? We propose a quantum algorithm to estimate the properties of molecules
using near-term quantum devices. The method is a recursive variational series
estimation method, where we expand an operator of interest in terms of
Chebyshev polynomials and evaluate each term in the expansion using a
variational quantum algorithm. We test our method by computing the one-particle
Green's function in the energy domain and the autocorrelation function in the
time domain.
