Cautious optimism for deep parameterized quantum circuits

arXiv (Cornell University)

Abstract

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

Authors 8

1. Marie Kempkes Aachen

   Leiden University · Volkswagen Group (Germany) · University of Applied Sciences Leiden · Volkswagen Group (United States)

   Affiliation as printed

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

   Volkswagen Group Innovation , Berliner Ring 2 , 38440 Wolfsburg , Germany

2. Elies Gil-Fuster

   Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute · Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , 14195 Berlin , Germany

   Fraunhofer Heinrich Hertz Institute , 10587 Berlin , Germany

3. Carlos Bravo-Prieto

   Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , 14195 Berlin , Germany

4. Aroosa Ijaz

   University of Waterloo · Vector Institute

   Affiliation as printed

   Department of Physics and Astronomy , University of Waterloo , ON N2L 3G1 , Canada

   Vector Institute , Toronto , ON M5G 0C6 , Canada

5. Alissa Wilms

   Ludwigsburg University of Education · Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , 14195 Berlin , Germany

   Porsche Digital GmbH , 71636 Ludwigsburg , Germany

6. Jens Eisert

   Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , 14195 Berlin , Germany

7. Evert van Nieuwenburg Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

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

8. Vedran Dunjko Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

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