# Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo

## TL;DR

This paper introduces preconditioning and perturbative estimators in FCIQMC, significantly enhancing efficiency and accuracy by reducing noise and enabling larger time steps, demonstrated on benzene.

## Contribution

It presents a novel combination of preconditioning with perturbative estimators in FCIQMC, improving efficiency and accuracy over previous methods.

## Key findings

- Reduced statistical noise in perturbative corrections
- Allowed larger time steps without errors
- Achieved more accurate results for benzene

## Abstract

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.