The Average Relative Entropy and Transpilation Depth determines the noise robustness in Variational Quantum Classifiers

2026-03-22

AI Summary

This work addresses the challenge of effectively evaluating the robustness of Variational Quantum Classifiers (VQCs) on noisy quantum devices, where existing approaches fall short and the notion of “shallow” circuits remains ill-defined. The authors propose a novel metric that jointly models the combined influence of average inter-class relative entropy disparity and post-compilation circuit depth on noise robustness—demonstrating for the first time that circuit depth alone is insufficient to characterize shallowness. Extensive experiments across diverse VQC architectures, datasets, and real quantum hardware validate that the proposed metric exhibits strong correlation with actual noise resilience, offering a reliable tool for algorithm assessment and deployment in the NISQ era.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Adversarial Attacks & Robustness
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Variational Quantum Algorithms (VQAs) have been extensively researched for applications in Quantum Machine Learning (QML), Optimization, and Molecular simulations. Although designed for Noisy Intermediate-Scale Quantum (NISQ) devices, VQAs are predominantly evaluated classically due to uncertain results on noisy devices and limited resource availability. Raising concern over the reproducibility of simulated VQAs on noisy hardware. While prior studies indicate that VQAs may exhibit noise resilience in specific parameterized shallow quantum circuits, there are no definitive measures to establish what defines a shallow circuit or the optimal circuit depth for VQAs on a noisy platform. These challenges extend naturally to Variational Quantum Classification (VQC) algorithms, a subclass of VQAs for supervised learning. In this article, we propose a relative entropy-based metric to verify whether a VQC model would perform similarly on a noisy device as it does on simulations. We establish a strong correlation between the average relative entropy difference in classes, transpilation circuit depth, and their performance difference on a noisy quantum device. Our results further indicate that circuit depth alone is insufficient to characterize shallow circuits. We present empirical evidence to support these assertions across a diverse array of techniques for implementing VQC, datasets, and multiple noisy quantum devices.

Problem

• Variational Quantum Classifier
• noise robustness
• circuit depth
• NISQ
• shallow quantum circuits

Innovation

• Average Relative Entropy
• Transpilation Depth
• Noise Robustness
• Variational Quantum Classifier
• NISQ