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Online learning of quantum states

Author(s): Aaronson, Scott; Chen, Xinyi; Hazan, Elad; Kale, Satyen; Nayak, Ashwin

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dc.contributor.authorAaronson, Scott-
dc.contributor.authorChen, Xinyi-
dc.contributor.authorHazan, Elad-
dc.contributor.authorKale, Satyen-
dc.contributor.authorNayak, Ashwin-
dc.date.accessioned2021-10-08T19:49:37Z-
dc.date.available2021-10-08T19:49:37Z-
dc.date.issued2019en_US
dc.identifier.citationAaronson, Scott, Xinyi Chen, Elad Hazan, Satyen Kale, and Ashwin Nayak. "Online learning of quantum states." Journal of Statistical Mechanics: Theory and Experiment 2019, no. 12 (2019). doi:10.1088/1742-5468/ab3988en_US
dc.identifier.issn1742-5468-
dc.identifier.urihttps://arxiv.org/pdf/1802.09025v1.pdf-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr10z6t-
dc.description.abstractSuppose we have many copies of an unknown n-qubit state . We measure some copies of using a known two-outcome measurement E1, then other copies using a measurement E2, and so on. At each stage t, we generate a current hypothesis about the state , using the outcomes of the previous measurements. We show that it is possible to do this in a way that guarantees that , the error in our prediction for the next measurement, is at least at most times. Even in the 'non-realizable' setting—where there could be arbitrary noise in the measurement outcomes—we show how to output hypothesis states that incur at most excess loss over the best possible state on the first T measurements. These results generalize a 2007 theorem by Aaronson on the PAC-learnability of quantum states, to the online and regret-minimization settings. We give three different ways to prove our results—using convex optimization, quantum postselection, and sequential fat-shattering dimension—which have different advantages in terms of parameters and portability.en_US
dc.language.isoen_USen_US
dc.relation.ispartofJournal of Statistical Mechanics: Theory and Experimenten_US
dc.rightsAuthor's manuscripten_US
dc.titleOnline learning of quantum statesen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1088/1742-5468/ab3988-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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