Potential and limitations of random Fourier features for dequantizing quantum machine learning

Aug 2, 2026

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Quantum machine learning for near-term devices is often studied through variational quantum machine learning, where parameterized quantum circuits (PQCs) are trained with classical optimizers. This work derives necessary and sufficient conditions for when random Fourier features (RFF) can efficiently dequantize PQC-based regression. The analysis translates into concrete guidance for PQC architecture design, and it identifies structural requirements for regression tasks to admit a potential quantum advantage through PQC optimization.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages44

Reading Time1 h 51 min

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Introduction

Variational quantum machine learning and dequantization

Dequantization in inference vs training stages

Classical simulability via noise and symmetries

arXiv :2309 . 11647v4 [ quant-ph] 18 Mar 2025 Potential and limitations of random Fourier features fordequantizing quantum machine learning Ryan Sweke 1 , Erik Recio-Armengol2,3 , Sofiene Jerbi4 , Elies Gil-Fuster4,5 , Bryce Fuller7 , Jens Eisert4,5,6 , and Johannes Jakob Meyer4 1 IBM Quantum, Almaden Research Center, San Jose, CA, USA 2 ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain 3 Eurecat, Centre Tecnologic de Catalunya, Multimedia Technologies, Barcelona, Spain 4 Dahlem Center for Complex Quantum Systems, Freie Universitt Berlin, Berlin, Germany 5 Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany 6 Helmholtz-Zentrum Berlin fr Materialien und Energie, 14109 Berlin, Germany 7 IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598 Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as learning models. These PQC models have a rich structure which suggests that they might be amenable to efficient dequantization via random Fourier features (RFF) . In this work, we establish necessary and sufficient conditions under which RFF does indeed provide an efficient dequantization of variational quantum machine learning for regression. We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization. 1 Introduction In recent years, the technique of using parameterized quantum circuits (PQCs) to define a model class, which is then optimized over via a classical optimizer, has emerged as one of the primary methods of using near-term quantum devices for machine learning tasks [CAB+21; BLS+19] . We will refer to this approach as variational quantum machine learning (variational QML), although it is often also referred to as hybrid quantum/classical optimization. While a large amount of effort has been invested in both understanding the theoretical properties of variational QML, and experimenting on trial datasets, it remains unclear whether variational QML on near-term quantum devices can offer any meaningful advantages over state-of-the-art classical methods. One approach to answering this question is via dequantization. In this context, the idea is to use insights into the structure of PQCs, and the model classes that they define, to design quantuminspired classical methods which can be proven to match the performance of variational QML. Ultimately, the goal is to understand when and why variational QML can be dequantized, in order to better identify the PQC architectures, optimization algorithms and problem types for which one might obtain a meaningful quantum advantage via variational QML. In order to discuss notions of dequantization of variational QML, we note that for typical applications variational QML consists of two distinct phases. Namely, a training stage and an Accepted in 2024-07-10, click title to verify. Published under CC-BY 4 .0. 1 inference stage. In the training stage, one uses the available training data to identify an optimal PQC model, and in the inference stage one uses the identified model to make predictions on previously unseen data, or in the case of generative modelling, to generate new samples from the unknown data distribution. A variety of works have recently proposed dequantization methods for inference with PQC models. The first such work was Ref. [SEM23], which used insights into the functional analytic structure of PQC model classes to show that, given a trained quantum model, one can sometimes efficiently extract a purely classical model – referred to as a classical surrogate – which performs inference just as well as the PQC model. More recentl

FAQs

How does the work connect dequantization to PQC architecture design?

It uses the derived conditions to give concrete suggestions for how PQC structures should be designed and which structures are necessary for regression problems to potentially yield a quantum advantage via PQC optimization.

Aug 2, 2026

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