A Bayesian analysis of classical shadows

Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In th...

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Autores principales:	Joseph M. Lukens, Kody J. H. Law, Ryan S. Bennink
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/695587a97081475592b7614e589976d5
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id	oai:doaj.org-article:695587a97081475592b7614e589976d5
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spelling	oai:doaj.org-article:695587a97081475592b7614e589976d52021-12-02T18:30:50ZA Bayesian analysis of classical shadows10.1038/s41534-021-00447-62056-6387https://doaj.org/article/695587a97081475592b7614e589976d52021-07-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00447-6https://doaj.org/toc/2056-6387Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.Joseph M. LukensKody J. H. LawRyan S. BenninkNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Joseph M. Lukens Kody J. H. Law Ryan S. Bennink A Bayesian analysis of classical shadows
description	Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.
format	article
author	Joseph M. Lukens Kody J. H. Law Ryan S. Bennink
author_facet	Joseph M. Lukens Kody J. H. Law Ryan S. Bennink
author_sort	Joseph M. Lukens
title	A Bayesian analysis of classical shadows
title_short	A Bayesian analysis of classical shadows
title_full	A Bayesian analysis of classical shadows
title_fullStr	A Bayesian analysis of classical shadows
title_full_unstemmed	A Bayesian analysis of classical shadows
title_sort	bayesian analysis of classical shadows
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/695587a97081475592b7614e589976d5
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A Bayesian analysis of classical shadows

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