  Quantitative descriptions of strongly correlated materials pose a
considerable challenge in condensed matter physics and chemistry. A promising
approach to address this problem is quantum embedding methods. In particular,
the dynamical mean-field theory (DMFT) maps the original system to an effective
quantum impurity model comprising correlated orbitals embedded in an electron
bath. The biggest bottleneck in DMFT calculations is numerically solving the
quantum impurity model, i.e., computing Green's function. Past studies have
proposed theoretical methods to compute Green's function of a quantum impurity
model in polynomial time using a quantum computer. So far, however, efficient
methods for computing the imaginary-time Green's functions have not been
established despite the advantages of the imaginary-time formulation. We
propose a quantum-classical hybrid algorithm for computing imaginary-time
Green's functions on quantum devices with limited hardware resources by
applying the variational quantum simulation. Using a quantum circuit simulator,
we verified this algorithm by computing Green's functions for a dimer model as
well as a four-site impurity model obtained by DMFT calculations of the
single-band Hubbard model, although our method can be applied to general
imaginary-time correlation functions.
