Conversely, FCIQMC is a method that benefits from sparsity in the wave function, and unpopulated determinants do not occupy memory and are rarely selected at the spawning step. Hence, invariant GAS constraints do not improve the course of the dynamics, nor do they reduce the corresponding computational costs (spawning process and storage). On the contrary, non-invariant GAS constraints would effectively reduce the CI space that walkers are allowed to propagate to. Consequently, these GAS constraints can effectively reduce the computational costs for FCIQMC.