Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

TL;DR

This paper introduces an efficient algorithm leveraging adjoint algorithmic differentiation to compute forces in quantum Monte Carlo simulations, enabling accurate calculation of thermodynamic properties with computational effort comparable to energy calculations.

Contribution

The paper presents a novel application of adjoint algorithmic differentiation to quantum Monte Carlo for force computation, improving efficiency and feasibility for thermodynamic property calculations.

Findings

Force calculation efficiency comparable to energy computation

Successful application to water molecule systems

Potential for finite-temperature thermodynamic property analysis

Abstract

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.