Benign Overfitting with Quantum Kernels

2026-07-08 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation, Quantum Computing · Depth: Expert, extended

Summary

This paper introduces local-global quantum kernels, a novel strategy to overcome poor generalization in quantum machine learning, particularly with fidelity kernels that suffer from exponential concentration and near-identity kernel matrices. Inspired by classical benign overfitting, this approach combines a local quantum kernel, derived from small subsystem measurements, with a global quantum kernel from full-system measurements. Numerical experiments, utilizing both angle encoding and Fourier representation for the local component, demonstrate that these local-global kernels exhibit benign overfitting. This effectively enhances generalization performance, especially as the number of qubits increases, where traditional quantum fidelity kernels typically fail due to their kernel matrices approaching identity.

Key takeaway

For research scientists developing quantum machine learning models, this work offers a critical solution to pervasive generalization issues in quantum kernels. By adopting the local-global quantum kernel framework, you can design models that achieve robust generalization even when interpolating training data, moving beyond the limitations of traditional fidelity kernels. Consider implementing this approach to improve the practical viability of your quantum algorithms.

Key insights

Local-global quantum kernels enable benign overfitting by combining local and global measurement components.

Principles

• Exponential concentration in quantum kernels hinders generalization.
• Benign overfitting allows interpolation without generalization loss.
• Local-global kernel design balances smooth and spiky components.

Method

Construct a local-global quantum kernel as a weighted sum of a local kernel (from s-qubit subsystem measurement) and a global kernel (from t-qubit full-system measurement), leveraging separable global encoding.

In practice

• Implement local-global kernels using angle encoding or Fourier representation.
• Utilize a hybrid classical-quantum scheme for resource-efficient evaluation.
• Adjust parameter q to control the global component's bandwidth.

Topics

• Quantum Machine Learning
• Quantum Kernels
• Benign Overfitting
• Generalization
• Quantum Circuits
• Angle Encoding

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.