The Average Relative Entropy and Transpilation Depth determines the noise robustness in Variational Quantum Classifiers
This work addresses the reproducibility challenge for quantum machine learning practitioners by providing a measure to assess noise robustness in variational quantum classifiers, though it is incremental as it builds on prior studies of noise resilience.
The paper tackled the problem of uncertain performance of variational quantum classifiers on noisy hardware by proposing a relative entropy-based metric to predict whether simulated results will match noisy device performance, finding a strong correlation with average relative entropy difference and transpilation circuit depth across diverse datasets and devices.
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.