Quantum machine learning beyond kernel methods

Nature Communications, vol. 14, pp. 517

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.

Authors 6

1. Sofiène Jerbi corresponding

   Universität Innsbruck

   Affiliation as printed

   Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria. sofiene.jerbi@uibk.ac.at

   Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria

2. Lukas J. Fiderer

   Universität Innsbruck

   Affiliation as printed

   Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria

3. Hendrik Poulsen Nautrup

   Universität Innsbruck

   Affiliation as printed

   Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria

4. Jonas M. Kübler

   Max Planck Institute for Intelligent Systems

   Affiliation as printed

   Max Planck Institute for Intelligent Systems, Tübingen, Germany

5. Hans J. Briegel

   Universität Innsbruck

   Affiliation as printed

   Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria

6. Vedran Dunjko Aachen

   Leiden University

   Affiliation as printed

   Leiden University, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands