Benign Overfitting with Quantum Kernels

Kernel methods compare inputs through feature maps.

Quantum kernels follow the same principle: input data are encoded into quantum states, which define quantum feature representations in Hilbert spaces.

Kernel values are then obtained by estimating inner products between these states using suitable quantum circuit measurements.

As a result, quantum kernels may be intractable to compute classically while remaining efficiently computable on quantum hardware, potentially leading to a quantum advantage.

However, designing effective quantum kernels remains a major challenge.

Many quantum kernels, such as the fidelity kernel, suffer from exponential concentration.

This results in near-identity kernel matrices that fail to capture meaningful data correlations and lead to overfitting and poor generalization.

In this paper, we propose a novel strategy for constructing quantum kernels that achieve good generalization performance, drawing inspiration from benign overfitting in classical machine learning.

We introduce the concept of Local-Global quantum kernels, which combine two components: a local quantum kernel based on measurements of small subsystems, and a global quantum kernel derived from full-system measurements.

To support the effectiveness of the proposed construction, we show theoretically and empirically that Local-Global quantum kernels exhibit benign overfitting.