Unbiased expectation values from diffusion quantum Monte Carlo simulations with a fixed number of walkers

We append forward walking to a diffusion Monte Carlo algorithm which maintains a fixed number of walkers. This removes the importance sampling bias of expectation values of operators which do not commute with the Hamiltonian. We demonstrate the effectiveness of this approach by employing three importance sampling functions for the hydrogen atom ground state, two very crude. We estimate moments of the electron-nuclear distance, static polarizabilities, and high-order hyperpolarizabilites up to the fourth power in the electric field, where no use is made of the finite field approximation. The results agree with the analytical values, with a statistical error which increases substantially with decreasing overlap of the guiding function with the exact wave function.