In principle, Equation 6 can be solved deterministically. However, the evaluation of the large number of Hamiltonian matrix element and the operation count bound to the CI update and the storage of the updated CI vector, makes this equation prohibitive to solve deterministically, in practical cases where large active spaces are utilized. In FCIQMC the imaginary-time evolution of the CI wave function is represented via the propagation of signed stochastic walkers across the configurational space. At each time-step, ∆τ , the propagation process is divided in four steps: excitation generation, spawning, annihilation and death.