Double descent in quantum kernel methods

TL;DR

This paper demonstrates that quantum kernel methods can exhibit the double descent phenomenon, where increasing model complexity initially worsens and then improves test performance, challenging traditional learning theories.

Contribution

It analytically and empirically shows double descent behavior in quantum models, a phenomenon previously observed mainly in classical machine learning.

Findings

Quantum models can exhibit double descent behavior.

Test error peaks are observed in quantum kernel methods.

Quantum models can operate effectively in overparameterized regimes.

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.