Quantum Natural Gradient

James Stokes1, Josh Izaac2, Nathan Killoran2, and Giuseppe Carleo3

1Center for Computational Quantum Physics and Center for Computational Mathematics, Flatiron Institute, New York, NY 10010 USA
2Xanadu, 777 Bay Street, Toronto, Canada
3Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010 USA

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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.

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