  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.
