Optimization stability in excited state-specific variational Monte Carlo

TL;DR

This paper studies the stability of optimization algorithms in excited state-specific variational Monte Carlo, highlighting the importance of adaptive step control and hybrid methods for improved performance and reliable excitation energy calculations.

Contribution

It introduces a hybrid optimization approach combining the linear method with accelerated descent, enhancing stability and efficiency in wave function optimization.

Findings

Adaptive step control is essential for stability.

Hybrid optimization improves convergence and stability.

Variance minimization yields accurate excitation energies.

Abstract

We investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance. As a verification of variance minimization's practical utility, we report an excitation energy in the cyanine dye that is in good agreement with both benchmark quantum chemistry values and results obtained from state-averaged energy-based variational Monte Carlo.