Does provable absence of barren plateaus imply classical simulability?

Creators: Cerezo, M.¹; Larocca, Martin¹; García-Martín, Diego¹; Diaz, N. L.^{1, 2}; Braccia, Paolo¹; Fontana, Enrico³; Rudolph, Manuel S.⁴; Bermejo, Pablo^{1, 5}; Ijaz, Aroosa^{1, 6, 7}; Thanasilp, Supanut^{4, 8}; Anschuetz, Eric R.⁹; Holmes, Zoë⁴

1. Los Alamos National Laboratory
2. National University of La Plata
3. University of Strathclyde
4. École Polytechnique Fédérale de Lausanne
5. Donostia International Physics Center
6. University of Waterloo
7. Vector Institute
8. Chulalongkorn University
9. California Institute of Technology

Abstract

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We collect evidence-on a case-by-case basis-that many commonly used models whose loss landscapes avoid barren plateaus can also admit classical simulation, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing that quantum computers can be essential for collecting data, our analysis sheds doubt on the information processing capabilities of many parametrized quantum circuits with provably barren plateau-free landscapes. We end by discussing the (many) caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.

Copyright and License

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Acknowledgement

We are extremely grateful to Hsin-Yuan Huang for his invaluable contributions to this work. We thank Andrew Sornborger, Lukasz Cincio, Nathan Wiebe, Chae-Yeun Park, Nathan Killoran, Maria Schuld, Xanadu’s Toronto office staff, and the QTML 2023 community for thoughtful and insightful conversations. M.C. acknowledges support from Los Alamos National Laboratory (LANL) ASC Beyond Moore’s Law project. M.L. was supported by the Center for Nonlinear Studies at LANL. M.C., D.G.M., N.L.D. and P.B. were supported by Laboratory Directed Research and Development (LDRD) program of LANL under project numbers 20230527ECR and 20230049DR. Also, N.L.D. acknowledges support from CONICET Argentina, and P.B acknowledges support of DIPC. A.I. acknowledges support by the U.S. Department of Energy (DOE) through a quantum computing program sponsored by the LANL Information Science & Technology Institute and by the U.S. DOE, Office of Science, Office of Advanced Scientific Computing Research, under Computational Partnerships program. E.F. acknowledges the support of the UK department for Business, Energy and Industrial Strategy through the National Quantum Technologies Programme, and the support of an industrial CASE (iCASE) studentship, funded by the Engineering and Physical Sciences Research Council (grant EP/T517665/1), in collaboration with the University of Strathclyde, the National Physical Laboratory, and Quantinuum. E.R.A. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. S.T. and Z.H. acknowledge support from the Sandoz Family Foundation-Monique de Meuron program for Academic Promotion. ST further acknowledges the grants for development of new faculty staff, Ratchadaphiseksomphot Fund, Chulalongkorn University [grant number 3230120336 DNS_68_052_2300_012], as well as funding from National Research Council of Thailand (NRCT) [grant number N42A680126]. M.C., Z.H., and E.R.A. thank the organizers of the PennyLane Research Retreat, where part of this work was undertaken, for their hospitality. This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center (LC). This work was also supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. DOE.

Supplemental Material

Supplementary Information

Files

s41467-025-63099-6.pdf

Files (1.9 MB)

Name	Size	Download all
s41467-025-63099-6.pdf md5:858fc1b059d65616e99fc8919bbdad9d	1.3 MB	Preview Download
41467_2025_63099_MOESM1_ESM.pdf md5:c3016eef0eb3ae9a3d3949b8097008a3	572.2 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes