In particular our current implementation of the FCI algorithm, requires an element-wise search which scales N 2 (N being the number of CI states), because it must search every determinant pair to discover its connectivity. If the set of determinants can be generated systematically instead of searched, then the connectivity is automatically known. This algorithm scales pseudolinearly O ∼ N 1 . Note this still does not help the O ∼ N 3 diagonalization costs, with exponentiate with exponential N → exp (N ).