  In the framework of the hybrid quantum-classical variational cluster approach
(VCA) to strongly correlated fermion systems one of the goals of a quantum
subroutine is to find single-particle correlation functions of lattice fermions
in polynomial time. Previous works suggested to use variants of the Hadamard
test for this purpose. However, it requires an implementation of controlled
unitaries specifying the full dynamics of the simulated model. In this work, we
propose a new quantum algorithm, which uses an analog of the Kubo formula
within linear response theory adapted to a quantum circuit simulating the
Hubbard model. It allows to access the Green's function of a cluster directly
and thereby circumvents the usage of the Hadamard test. We find a drastic
reduction in gate count of two-qubits gates and limitations on hardware design
as compared to previous approaches.
