Quantum Natural Gradient

James Stokes; Josh Izaac; Nathan Killoran; Giuseppe Carleo

doi:10.22331/q-2020-05-25-269

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

Published:	2020-05-25, volume 4, page 269
Eprint:	arXiv:1909.02108v3
Doi:	https://doi.org/10.22331/q-2020-05-25-269
Citation:	Quantum 4, 269 (2020).

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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.

► BibTeX data

@article{Stokes2020quantumnatural,
  doi = {10.22331/q-2020-05-25-269},
  url = {https://doi.org/10.22331/q-2020-05-25-269},
  title = {Quantum {N}atural {G}radient},
  author = {Stokes, James and Izaac, Josh and Killoran, Nathan and Carleo, Giuseppe},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {269},
  month = may,
  year = {2020}
}

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Quantum Natural Gradient

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