Optimum and efficient sampling for variational quantum Monte Carlo.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Statistical mechanics

Background:

• Quantum Monte Carlo (QMC) methods, specifically variational quantum Monte Carlo (VQMC), are used for ab initio calculations of many-body systems.
• Conventional VQMC implementations often rely on samples distributed according to the trial wave function's probability density and assume the validity of the central limit theorem.

Purpose of the Study:

• To analyze random error in estimation and optimization within VQMC.
• To develop novel sampling strategies with improved computational and statistical properties.
• To enhance the theoretical foundation of parameter optimization in VQMC.

Main Methods:

• Derivation of a rigorous lower bound for random error in VQMC.
• Development and presentation of an efficient sampling strategy.
• Analysis of error types in parameter optimization, replacing heavy-tailed errors with Normal random errors.

Main Results:

• A new sampling strategy significantly increases computational efficiency.
• A rigorous lower limit to random error is established.
• Infinite variance heavy-tailed random errors in optimum parameters are replaced with Normal random errors, improving theoretical robustness.

Conclusions:

• The developed methods offer enhanced computational and statistical properties for VQMC.
• The new approach strengthens the theoretical basis for optimization in quantum mechanical calculations.
• The method shows promise, with applications to first-row systems yielding comparable or improved results over previous methods.