Preconditioning and Perturbative Estimators 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 method for electronic structure calculations.
• Traditional FCIQMC can suffer from significant statistical noise, particularly in perturbative corrections.
• Accurate treatment of larger systems remains computationally challenging.

Purpose of the Study:

• To enhance the efficiency and accuracy of the FCIQMC algorithm.
• To reduce statistical noise in perturbative corrections to initiator error.
• To enable accurate calculations for systems intractable with the original FCIQMC method.

Main Methods:

• Implementation of preconditioning within the FCIQMC framework.
• Combination of preconditioning with perturbative estimators.
• Development of a simplified sampling approach for variational and perturbative estimators.
• Application to the benzene molecule (30 electrons, 108 orbitals).

Main Results:

• Preconditioning allows for time steps close to unity, significantly increasing computational efficiency.
• The combined approach substantially reduces statistical noise on perturbative corrections.
• Improved accuracy is achieved for the initiator error.
• A simpler sampling method allows for variance calculation.
• Accurate treatment of the benzene system was demonstrated.

Conclusions:

• The combination of preconditioning and perturbatively corrected estimators offers a significantly more efficient and accurate FCIQMC algorithm.
• The developed methods overcome limitations of the original FCIQMC scheme, enabling the study of larger, more complex molecular systems.
• This work advances the applicability of FCIQMC for high-accuracy electronic structure calculations.