Quantum machine learning beyond kernel methods

Sofiene Jerbi (), Lukas J. Fiderer, Hendrik Poulsen Nautrup, Jonas M. Kübler, Hans J. Briegel and Vedran Dunjko
Additional contact information
Sofiene Jerbi: University of Innsbruck
Lukas J. Fiderer: University of Innsbruck
Hendrik Poulsen Nautrup: University of Innsbruck
Jonas M. Kübler: Max Planck Institute for Intelligent Systems
Hans J. Briegel: University of Innsbruck
Vedran Dunjko: Leiden University

Nature Communications, 2023, vol. 14, issue 1, 1-8

Abstract: Abstract Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.nature.com/articles/s41467-023-36159-y Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-36159-y

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-023-36159-y

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().