A computer-implemented method including a momentum refreshment process and a conservative dynamics process, wherein the refreshment process including carrying out an operation of mixing the collective momentum vector with a noise vector and carrying out an acceptance/rejection (acceptance and rejection) operation; the dynamics process including applying a multiple time stepping conservative dynamics operation to a current state, in which calculations corresponding to more slowly varying energy parts undergo an averaging procedure and are carried out at a larger time step than calculations corresponding to more quickly varying energy parts; and carrying out an acceptance/rejection operation based on an approximation of the system energy expressed using shadow Hamiltonians and include accepting a current state or returning a replacement state.