Does provable absence of barren plateaus imply classical simulability?

M. Cerezo (), Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz and Zoë Holmes
Additional contact information
M. Cerezo: Los Alamos National Laboratory
Martin Larocca: Los Alamos National Laboratory
Diego García-Martín: Los Alamos National Laboratory
N. L. Diaz: Los Alamos National Laboratory
Paolo Braccia: Los Alamos National Laboratory
Enrico Fontana: University of Strathclyde
Manuel S. Rudolph: Ecole Polytechnique Fédérale de Lausanne (EPFL)
Pablo Bermejo: Los Alamos National Laboratory
Aroosa Ijaz: Los Alamos National Laboratory
Supanut Thanasilp: Ecole Polytechnique Fédérale de Lausanne (EPFL)
Eric R. Anschuetz: Institute for Quantum Information and Matter Caltech
Zoë Holmes: Ecole Polytechnique Fédérale de Lausanne (EPFL)

Nature Communications, 2025, vol. 16, issue 1, 1-15

Abstract: 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.

Date: 2025
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DOI: 10.1038/s41467-025-63099-6

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