Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo

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.

15 pages, 7 figures

References in corpus (7)

• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• Excited states using semistochastic heat-bath configuration interaction
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• Minimising biases in Full Configuration Interaction Quantum Monte Carlo
• Diagrammatic Coupled Cluster Monte Carlo