Double Descent in Quantum Kernel Ridge Regression

TL;DR

This paper investigates the double descent phenomenon in quantum kernel ridge regression, deriving asymptotic test risk expressions and showing how regularization can mitigate the interpolation peak, supported by numerical simulations.

Contribution

It provides the first rigorous analysis of double descent in quantum kernel methods using random matrix theory, highlighting regularization effects.

Findings

Double descent occurs in quantum kernel ridge regression.

Explicit regularization suppresses the interpolation peak.

Theoretical predictions match numerical simulations closely.

Abstract

Various classical machine learning models, including linear regression, kernel methods, and deep neural networks, exhibit double descent, in which the test risk peaks near the interpolation threshold and then decreases in the overparameterized regime. However, this phenomenon has received less attention in the quantum setting. In this work, we investigate the double descent phenomenon in quantum kernel ridge regression (QKRR). By applying deterministic equivalents from random matrix theory (RMT), we derive an asymptotic expression for the test risk of QKRR in the high-dimensional limit. Our analysis rigorously characterizes the interpolation peak and reveals how explicit regularization can effectively suppress it. We corroborate our theoretical results with numerical simulations, demonstrating close agreement even for finite-size quantum systems.