dc.contributor.author
Caro, Matthias C.
dc.contributor.author
Huang, Hsin-Yuan
dc.contributor.author
Cerezo, M.
dc.contributor.author
Sharma, Kunal
dc.contributor.author
Sornborger, Andrew
dc.contributor.author
Cincio, Lukasz
dc.contributor.author
Coles, Patrick J.
dc.date.accessioned
2023-04-28T10:16:41Z
dc.date.available
2023-04-28T10:16:41Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/39135
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-38852
dc.description.abstract
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as T/N−−−−√. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to K/N−−−−√. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.
en
dc.format.extent
11 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
quantum machine learning
en
dc.subject
quantum circuits
other
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::539 Moderne Physik
dc.title
Generalization in quantum machine learning from few training data
dc.type
Wissenschaftlicher Artikel
dc.identifier.sepid
92905
dcterms.bibliographicCitation.articlenumber
4919
dcterms.bibliographicCitation.doi
10.1038/s41467-022-32550-3
dcterms.bibliographicCitation.journaltitle
Nature Communications
dcterms.bibliographicCitation.number
1
dcterms.bibliographicCitation.originalpublishername
Nature Publishing Group UK
dcterms.bibliographicCitation.originalpublisherplace
[London]
dcterms.bibliographicCitation.volume
13 (2022)
dcterms.bibliographicCitation.url
https://www.nature.com/articles/s41467-022-32550-3
refubium.affiliation
Physik
refubium.affiliation.other
Institut für Theoretische Physik
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refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
2041-1723