Taking advantage of low-level hardware instructions, 152 we are able, given two arbitrary determinants |I and |J , to nd with a minimal cost the excitation operator T such that |J = T |I . is is a necessary step to obtain the (i, j, k, l) indices of the two-electron integral(s) involved in the Hamiltonian matrix element between |I and |J . en, fetching the values of the integrals can be done quickly using the hash table presented in Sec. III A.