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Double Descent in Quantum Kernel Methods

Marie Kempkes1,2,*, Aroosa Ijaz3,4,5,†, Elies Gil-Fuster5,6, Carlos Bravo-Prieto5, Jakob Spiegelberg2, Evert van Nieuwenburg1, and Vedran Dunjko1

  • *Contact author: marie.kempkes@volkswagen.de
  • †Contact author: a4ijaz@uwaterloo.ca
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PRX Quantum 7, 010312 – Published 16 January, 2026

DOI: https://doi.org/10.1103/cn64-gs6b

Abstract

The double descent phenomenon challenges traditional statistical learning theory by revealing scenarios where larger models do not necessarily lead to reduced performance on unseen data. While this counterintuitive behavior has been observed in a variety of classical machine learning models, particularly modern neural network architectures, it remains elusive within the context of quantum machine learning. In this work, we analytically demonstrate that linear regression models in quantum feature spaces can exhibit double descent behavior by drawing on insights from classical linear regression and random matrix theory. Additionally, our numerical experiments on quantum kernel methods across different real-world datasets and system sizes further confirm the existence of a test error peak, a characteristic feature of double descent. Our findings provide evidence that quantum models can operate in the modern, overparameterized regime without experiencing overfitting, potentially opening pathways to improved learning performance beyond traditional statistical learning theory.

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Popular Summary

In machine learning, it has long been thought that making models too complex leads to worse performance on new data, leading to a classic U-shaped curve of error versus model size. But recent studies in classical deep learning have turned that idea on its head: sometimes, making models even larger can actually improve performance again. This surprising twist is called “double descent.” Until now, it was not clear if quantum machine learning models—those using the principles of quantum physics—could show the same behavior.

In this study, we show both analytically and experimentally that quantum models can indeed exhibit double descent. We analyzed quantum models that process data using “quantum feature maps,” and we explored how their performance changes as we vary the number of training examples. Using ideas from random matrix theory, we proved that these models can hit a peak in test error as they cross from having too few parameters to having too many, which is a hallmark of double descent. Our experiments on real-world datasets confirmed this effect, showing consistent patterns across different quantum setups.

This discovery has major implications for how we design and scale quantum machine learning systems. It suggests that bigger quantum models might actually perform better than predicted by traditional wisdom, much like their classical counterparts. Future research could explore whether this trend extends to other types of quantum models, and how to harness it to make quantum learning more practical and powerful.

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PRX Quantum 7, 010312– Published 16 January, 2026
  • Received 12 February 2025
  • Revised 9 May 2025
  • Accepted 15 September 2025
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