Toward extracting scattering phase shift from integrated correlation functions on quantum computers

Based on an established relation that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral, we propose to extract the infinite volume scattering phase shifts through quantum simulation of the integrated correlation functions of trapped two-particle systems on quantum computers. The integrated correlation function can be computed by an ancilla-based algorithm. The proposal is demonstrated with a simple contact interaction fermion model.