Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Julien Gacon; Christa Zoufal; Giuseppe Carleo; Stefan Woerner

doi:10.22331/q-2021-10-20-567

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Julien Gacon^1,2, Christa Zoufal^1,3, Giuseppe Carleo², and Stefan Woerner¹

¹IBM Quantum, IBM Research – Zurich, CH-8803 Rüschlikon, Switzerland
²Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
³Institute for Theoretical Physics, ETH Zurich, CH-8092 Zürich, Switzerland

Published:	2021-10-20, volume 5, page 567
Eprint:	arXiv:2103.09232v2
Doi:	https://doi.org/10.22331/q-2021-10-20-567
Citation:	Quantum 5, 567 (2021).

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Abstract

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

► BibTeX data

@article{Gacon2021simultaneous,
  doi = {10.22331/q-2021-10-20-567},
  url = {https://doi.org/10.22331/q-2021-10-20-567},
  title = {Simultaneous {P}erturbation {S}tochastic {A}pproximation of the {Q}uantum {F}isher {I}nformation},
  author = {Gacon, Julien and Zoufal, Christa and Carleo, Giuseppe and Woerner, Stefan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {567},
  month = oct,
  year = {2021}
}

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