Minimising biases in Full Configuration Interaction Quantum Monte Carlo

Abstract

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.

arXiv commentSupplementary material available as 'Ancillary Files'

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• The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications
• Exciting determinants in Quantum Monte Carlo: Loading the dice with fast, low memory weights
• A study of the dense Uniform Electron Gas with high orders of Coupled Cluster
• Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo
• Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
• Improved walker population control for full configuration interaction quantum Monte Carlo
• Large Scale Parallelization in Stochastic Coupled Cluster
• Understanding and Improving the Efficiency of Full Configuration Interaction Quantum Monte Carlo
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity
• Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo
• A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems
• Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration
• Improved Fast Randomized Iteration Approach to Full Configuration Interaction