Improved diffusion Monte Carlo for bosonic systems using time-step extrapolation "on the fly"

A diffusion Monte Carlo algorithm employing "on the fly" extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.