Quantum Natural Gradient

TL;DR

This paper introduces Quantum Natural Gradient, a method that optimizes variational quantum circuits by leveraging Quantum Information Geometry, leading to potentially more efficient convergence in quantum algorithms.

Contribution

It presents a quantum generalization of Natural Gradient Descent and an efficient algorithm for approximating the Quantum Geometric Tensor in variational quantum circuits.

Findings

Provides a new optimization framework for quantum circuits

Introduces an efficient block-diagonal approximation algorithm

Enhances convergence properties of variational quantum algorithms

Abstract

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.