Sign learning kink-based (SiLK) quantum Monte Carlo for molecular systems

TL;DR

The SiLK quantum Monte Carlo method improves the calculation of molecular ground state energies by reducing the sign problem through a learning stage, showing high accuracy across multiple molecules.

Contribution

Introduction of the SiLK QMC method that optimizes Slater determinants to mitigate the sign problem in molecular simulations.

Findings

Accurately computes ground state energies for H₂O, N₂, and F₂.

Reduces or eliminates the minus sign problem in QMC.

Compared favorably to other quantum chemical methods.

Abstract

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H$_{2}$O, N$_2$, and F$_2$ molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.