On the natural gradient for variational quantum eigensolver

TL;DR

This paper investigates the application of the natural gradient optimization method to the variational quantum eigensolver, demonstrating how it leverages geometric information to enhance the efficiency of finding ground states.

Contribution

It provides case studies illustrating the benefits of natural gradient methods in variational quantum algorithms, highlighting improvements over standard gradient approaches.

Findings

Natural gradient exploits geometric structure for better optimization.

Case studies show improved convergence with natural gradient.

Enhanced understanding of optimization dynamics in quantum algorithms.

Abstract

The variational quantum eigensolver is a hybrid algorithm composed of quantum state driving and classical parameter optimization, for finding the ground state of a given Hamiltonian. The natural gradient method is an optimization method taking into account the geometric structure of the parameter space. Very recently, Stokes et al. developed the general method for employing the natural gradient for the variational quantum eigensolver. This paper gives some simple case-studies of this optimization method, to see in detail how the natural gradient optimizer makes use of the geometric property to change and improve the ordinary gradient method.