  Computation of the Green's function is crucial to study the properties of
quantum many-body systems such as strongly correlated systems. Although the
high-precision calculation of the Green's function is a notoriously challenging
task on classical computers, the development of quantum computers may enable us
to compute the Green's function with high accuracy even for
classically-intractable large-scale systems. Here, we propose an efficient
method to compute the real-time Green's function based on the local variational
quantum compilation (LVQC) algorithm, which simulates the time evolution of a
large-scale quantum system using a low-depth quantum circuit constructed
through optimization on a smaller-size subsystem. Our method requires shallow
quantum circuits to calculate the Green's function and can be utilized on both
near-term noisy intermediate-scale and long-term fault-tolerant quantum
computers depending on the computational resources we have. We perform a
numerical simulation of the Green's function for the one- and two-dimensional
Fermi-Hubbard model up to $4\times4$ sites lattice (32 qubits) and demonstrate
the validity of our protocol compared to a standard method based on the Trotter
decomposition. We finally present a detailed estimation of the gate count for
the large-scale Fermi-Hubbard model, which also illustrates the advantage of
our method over the Trotter decomposition.
