Quantum Natural Gradient

James Stokes, Josh Izaac, Nathan Killoran, Giuseppe Carleo
9/4/2019
quant-phcs.LGstat.ML

Official code: PennyLaneAI/demos (679 stars, Apache-2.0, PyTorch, last commit 2026-10-21).

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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Cite this paper

@article{stokes2019quantum,
  title  = {Quantum Natural Gradient},
  author = {James Stokes and Josh Izaac and Nathan Killoran and Giuseppe Carleo},
  year   = {2019},
  eprint = {1909.02108},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1909.02108}
}

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