Abstract: Green’s functions play a central role in describing excited state electronic structures in quantum chemistry and materials science. At the heart of Green’s function computation is the solution of a linear system of size , where is the number of spin-orbitals in the quantum system. We will discuss how to use quantum linear system solvers to compute Green’s functions, and how to accelerate such computations using a new quantum primitive called the fast inversion, as well as preconditioning techniques.