Margin-Based Generalisation Bounds for Quantum Kernel Methods under Local Depolarising Noise

TL;DR

This paper derives theoretical bounds on how local depolarising noise affects the generalisation ability of quantum kernel methods, validated through simulations and real hardware experiments.

Contribution

It introduces margin-based generalisation bounds for QSVMs under local noise and empirically shows margins as reliable indicators of performance.

Findings

Noise causes margin decay in QSVMs, degrading generalisation.

Margins are empirically validated as indicators of generalisation performance.

Local depolarising noise models better capture real hardware degradation than global models.

Abstract

Generalisation refers to the ability of a machine learning (ML) model to successfully apply patterns learned from training data to new, unseen data. Quantum devices in the current Noisy Intermediate-Scale Quantum (NISQ) era are inherently affected by noise, which degrades generalisation performance. In this work, we derive upper and lower margin-based generalisation bounds for Quantum Kernel-Assisted Support Vector Machines (QSVMs) under local depolarising noise. These theoretical bounds characterise noise-induced margin decay and are validated via numerical simulations across multiple datasets, as well as experiments on real quantum hardware. We further justify the focus on margin-based measures by empirically establishing margins as a reliable indicator of generalisation performance for QSVMs. Additionally, we motivate the study of local depolarising noise by presenting empirical evidence demonstrating that the commonly used global depolarising noise model is overly optimistic and fails to accurately capture the degradation of generalisation performance observed in the NISQ era.