Quantum Natural Gradient
This addresses the optimization challenge for variational quantum circuits, which is crucial for quantum computing applications, but it appears incremental as it adapts an existing classical method to the quantum domain.
The paper tackles the problem of optimizing variational quantum circuits by introducing a quantum generalization of Natural Gradient Descent, which interprets optimization as moving in the steepest descent direction with respect to Quantum Information Geometry, and presents an efficient algorithm for computing a block-diagonal approximation to the Fubini-Study metric tensor.
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.