  A quantum generalization of Natural Gradient Descent is presented as part of
a general-purpose optimization framework for variational quantum circuits. The
optimization dynamics is interpreted as moving in the steepest descent
direction with respect to the Quantum Information Geometry, corresponding to
the real part of the Quantum Geometric Tensor (QGT), also known as the
Fubini-Study metric tensor. An efficient algorithm is presented for computing a
block-diagonal approximation to the Fubini-Study metric tensor for parametrized
quantum circuits, which may be of independent interest.
