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Computing the full QFIM for a model with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>parameters, however, is computationally expensive and generally requires<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>d<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>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.<\/jats:p>","DOI":"10.22331\/q-2021-10-20-567","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T12:57:08Z","timestamp":1634734628000},"page":"567","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":86,"title":["Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information"],"prefix":"10.22331","volume":"5","author":[{"given":"Julien","family":"Gacon","sequence":"first","affiliation":[{"name":"IBM Quantum, IBM Research \u2013 Zurich, CH-8803 R\u00fcschlikon, Switzerland"},{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christa","family":"Zoufal","sequence":"additional","affiliation":[{"name":"IBM Quantum, IBM Research \u2013 Zurich, CH-8803 R\u00fcschlikon, Switzerland"},{"name":"Institute for Theoretical Physics, ETH Zurich, CH-8092 Z\u00fcrich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Carleo","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Woerner","sequence":"additional","affiliation":[{"name":"IBM Quantum, IBM Research \u2013 Zurich, CH-8803 R\u00fcschlikon, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2021,10,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Al\u00e1n Aspuru-Guzik, Anthony D. 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