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

TL;DR

This paper introduces a relative entropy metric to assess the noise robustness of Variational Quantum Classifiers, linking circuit depth and entropy differences to performance on noisy quantum hardware.

Contribution

It proposes a novel entropy-based measure to predict VQC performance on noisy devices and clarifies the role of circuit depth in noise resilience.

Findings

Strong correlation between entropy difference and performance gap

Circuit depth alone does not determine noise robustness

Empirical validation across various datasets and devices

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.