We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a
Markov Chain in its present form. We construct the Markov matrix of FCIQMC for
a two determinant system and hence compute the stationary distribution. These
solutions are used to quantify the dependence of the population dynamics on the
parameters defining the Markov chain. Despite the simplicity of a system with
only two determinants, it still reveals a population control bias inherent to
the FCIQMC algorithm. We investigate the effect of simulation parameters on the
population control bias for the neon atom and suggest simulation setups to in
general minimise the bias. We show a reweighting scheme to remove the bias
caused by population control commonly used in Diffusion Monte Carlo [J. Chem.
Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing
step.Comment: Supplementary material available as 'Ancillary Files
