Pitfalls when tackling the exponential concentration of parameterized quantum models

Abstract:Identifying scalable circuit architectures remains a central challenge in variational quantum computing and quantum machine learning. Many approaches have been proposed to mitigate or avoid the barren plateau phenomenon or, more broadly, exponential concentration. However, due to the intricate interplay between quantum measurements and classical post-processing, we argue these techniques often fail to circumvent concentration effects in practice. Here, by analyzing concentration at the level of measurement outcome probabilities and leveraging tools from hypothesis testing, we develop a practical framework for diagnosing whether a parameterized quantum model is inhibited by exponential concentration. Applying this framework, we argue that several widely used methods (including quantum natural gradient, sample-based optimization, and certain neural-network-inspired initializations) do not overcome exponential concentration with finite measurement budgets, though they may still aid training in other ways.

arXiv:2507.22054 [quant-ph]

(or arXiv:2507.22054v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.22054 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1088/2058-9565/ae2202 Focus to learn more DOI(s) linking to related resources

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