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• W3136115687 abstract "We investigate a systematic statistical bias found in full configuration quantum Monte Carlo (FCIQMC) that originates from controlling a walker population with a fluctuating shift parameter and can become large in bosonic systems. FCIQMC is a powerful statistical method for obtaining information about the ground state of a sparse and abstract matrix. We show that the shift estimator has the nice property of providing an upper bound for the exact ground state energy and all projected energy estimators, while a variational estimator is still an upper bound to the exact energy with substantially reduced bias. A scalar model of the general FCIQMC population dynamics leads to an exactly solvable Ito stochastic differential equation. It provides further insights into the nature of the bias and gives accurate analytical predictions for delayed cross-covariance and auto-covariance functions of the shift energy estimator and the walker number. The model provides a toe-hold on finding a cure for the population control bias. We provide evidence for non-universal power-law scaling of the population control bias with walker number in the Bose-Hubbard model for various estimators of the ground state energy based on the shift or on projected energies. For the specific case of the non-interacting Bose-Hubbard Hamiltonian we obtain a full analytical prediction for the bias of the shift energy estimator." @default.
• W3136115687 created "2021-03-29" @default.
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• W3136115687 date "2021-03-13" @default.
• W3136115687 modified "2023-09-27" @default.
• W3136115687 title "Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo" @default.
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