  Population control is an essential component of any projector Monte Carlo
algorithm. This control mechanism usually introduces a bias in the sampled
quantities that is inversely proportional to the population size. In this
paper, we investigate the population control bias in the full configuration
interaction quantum Monte Carlo method. We identify the precise origin of this
bias and quantify it in general. We show that it has different effects on
different estimators and that the shift estimator is particularly susceptible.
We derive a re-weighting technique, similar to the one used in diffusion Monte
Carlo, for correcting this bias and apply it to the shift estimator. We also
show that by using importance sampling, the bias can be reduced substantially.
We demonstrate the necessity and the effectiveness of applying these techniques
for sign-problem-free systems where this bias is especially notable.
Specifically, we show results for large one-dimensional Hubbard models and the
two-dimensional Heisenberg model, where corrected FCIQMC results are comparable
to the other high-accuracy results.
