Minimising biases in full configuration interaction quantum Monte Carlo

Area of Science:

• Quantum Chemistry
• Computational Physics
• Stochastic Methods

Background:

• Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a powerful quantum chemistry method.
• Understanding the underlying mathematical structure of FCIQMC is crucial for algorithm development.
• Population control is a key aspect of Monte Carlo methods in quantum mechanics.

Purpose of the Study:

• To establish FCIQMC as a Markov chain and analyze its properties.
• To quantify the population control bias inherent in the FCIQMC algorithm.
• To propose methods for mitigating bias in FCIQMC simulations.

Main Methods:

• Formulating FCIQMC as a Markov chain.
• Constructing the Markov matrix for a two-determinant system.
• Computing the stationary distribution to analyze population dynamics.
• Investigating bias effects on the neon atom using simulation parameters.

Main Results:

• FCIQMC is demonstrated to be a Markov chain.
• A population control bias was identified even in simple two-determinant systems.
• Simulation parameters influencing bias were quantified for the neon atom.
• A reweighting scheme, effective for Diffusion Monte Carlo, was shown to remove FCIQMC bias.

Conclusions:

• The Markov chain formulation provides insights into FCIQMC dynamics.
• Population control bias is an inherent feature of FCIQMC that requires mitigation.
• Optimized simulation parameters and post-processing reweighting can improve FCIQMC accuracy.