Online learning of quantum states
Author(s): Aaronson, Scott; Chen, Xinyi; Hazan, Elad; Kale, Satyen; Nayak, Ashwin
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Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Aaronson, Scott | - |
dc.contributor.author | Chen, Xinyi | - |
dc.contributor.author | Hazan, Elad | - |
dc.contributor.author | Kale, Satyen | - |
dc.contributor.author | Nayak, Ashwin | - |
dc.date.accessioned | 2021-10-08T19:49:37Z | - |
dc.date.available | 2021-10-08T19:49:37Z | - |
dc.date.issued | 2019 | en_US |
dc.identifier.citation | Aaronson, 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/ab3988 | en_US |
dc.identifier.issn | 1742-5468 | - |
dc.identifier.uri | https://arxiv.org/pdf/1802.09025v1.pdf | - |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/pr10z6t | - |
dc.description.abstract | Suppose 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.iso | en_US | en_US |
dc.relation.ispartof | Journal of Statistical Mechanics: Theory and Experiment | en_US |
dc.rights | Author's manuscript | en_US |
dc.title | Online learning of quantum states | en_US |
dc.type | Journal Article | en_US |
dc.identifier.doi | 10.1088/1742-5468/ab3988 | - |
pu.type.symplectic | http://www.symplectic.co.uk/publications/atom-terms/1.0/journal-article | en_US |
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OnlineLearningQuantum.pdf | 241.49 kB | Adobe PDF | View/Download |
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