  We propose the use of preconditioning in FCIQMC which, in combination with
perturbative estimators, greatly increases the efficiency of the algorithm. The
use of preconditioning allows a time step close to unity to be used (without
time-step errors), provided that multiple spawning attempts are made per
walker. We show that this approach substantially reduces statistical noise on
perturbative corrections to initiator error, which improve the accuracy of
FCIQMC but which can suffer from significant noise in the original scheme.
Therefore, the use of preconditioning and perturbatively-corrected estimators
in combination leads to a significantly more efficient algorithm. In addition,
a simpler approach to sampling variational and perturbative estimators in
FCIQMC is presented, which also allows the variance of the energy to be
calculated. These developments are investigated and applied to benzene
(30e,108o), an example where accurate treatment is not possible with the
original method.
