Improving approximate vacuum prepared by the adiabatic quantum computation

According to the quantum adiabatic theorem, we can in principle obtain a true vacuum of a quantum system starting from a trivial vacuum of a simple Hamiltonian. In actual adiabatic digital quantum simulation with finite time length and non-infinitesimal time steps, we can only obtain an approximate vacuum that is supposed to be a superposition of a true vacuum and excited states. We propose a procedure to improve the approximate vacuum.