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.
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.
Abstract Quantum machine learning models trained under ideal (noiseless) conditions often exhibit significant performance degradation when executed on noisy quantum systems. Ideal simulation accuracy or circuit depth alone does not explain why classifiers with similar structures can show markedly different robustness. A practical question is therefore what factors can explain this difference in accuracy, and whether it can be anticipated and classically verified before costly hardware execution. We propose combining the average quantum relative entropy between classes and backend-specific transpilation depth as a practical pre-hardware indicator of the discrepancy in accuracy between ideal and noisy execution in Quantum Parameterized Binary Classification(QPBC) models. Average quantum relative entropy captures the distinguishability of learned class states, while transpilation depth serves as a practical indicator for cumulative noise exposure following compilation. Building on distinguishability and the contraction of quantum relative entropy under noisy channels, we theoretically derived indicators for both noisy-execution accuracy and simulation-to-device accuracy loss. We support this analysis with controlled experiments across multiple QPBC architectures, ansatz families, encoding methods, measurement strategies, datasets, and noisy backends. Our results show that classifiers with similar ideal accuracy and comparable transpilation depth can nonetheless exhibit substantially different degradation under noise. In contrast, the combined behavior of transpilation depth and average quantum relative entropy provides a more consistent interpretation of these robustness differences than either quantity alone. These findings support a practical pre-hardware assessment approach for screening trained quantum classifiers according to expected noisy-execution robustness.
The limited supply of qubits and significant quantum noise impose limitations on the capability of quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era. NISQ devices have a variety of applications, such as Variational Quantum Circuit (VQC), which provides answers to difficult optimization and machine learning problems. This paper presents a thorough investigation of quantum variational classification in the NISQ context, with a focus on comprehending noise's impact on various feature maps and VQCs. We evaluate the effectiveness of quantum classifiers using a variety of datasets, ranging from straightforward binary classification problems to more complex tasks. Our results reveal the critical role that feature maps and variational circuit selection play in mitigating the effect of noise, identifying specific quantum circuit designs that exhibit robustness even in noisy situations. In order to highlight the potential of quantum machine learning in solving complex problems within in the NISQ setting, this study emphasizes the delicate interaction between feature map selection, variational circuit design, dataset complexity, and quantum noise.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.
The rapid advancement of Noisy Intermediate-Scale Quantum (NISQ) devices necessitates a systematic evaluation of quantum machine learning (QML) algorithms to determine their feasibility for near-term applications. This study aims to benchmark the Variational Quantum Classifier (VQC)and the Quantum Kernel Support Vector Machine (QSVM) under realistic noise conditions modeled using Qiskit Aer. The primary objective is to investigate the impact of depolarizing and amplitude damping noise on the classification performance of these algorithms. Using the Iris binary classification task, we simulated four noise levels (0, 0.01, 0.05, 0.1) and evaluated accuracy across 1024 measurement shots. Results show that QSVM achieves superior accuracy (70%) under ideal and lownoise conditions, while VQC exhibits higher resilience at moderate noise (50% at 0.05 noise level) due to its adaptive Variational parameters. At higher noise levels (0.1), both models converge to ~35–40% accuracy, indicating significant degradation. These findings provide actionable insights for algorithm selection on NISQ hardware, with VQC favored for moderately noisy devices and QSVM preferable for low-noise or error-mitigated systems. The study concludes by highlighting the need for noise-aware ansatz design and error mitigation techniques to enhance QML performance in NISQ regimes.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
Quantum machine learning faces a big problem with noise in quantum computers. When quantum algorithms run on real devices or emulators with noise, accuracy becomes very bad compared to classical methods. This paper shows implementation of quantum classifiers that work better in noisy conditions using the Qiskit framework. The method combines three simple techniques. First technique compares different feature maps like ZZFeatureMap and PauliFeatureMap to find which one is more stable when noise exists. Second technique adds measurement error mitigation inside the training loop of the variational quantum classifier. Third technique uses a Qiskit transpiler for making circuits shorter which reduces noise effects. Testing happened on a Qiskit Aer simulator with a noise model taken from an IBM quantum computer. Three datasets used for testing-Iris data with 4 features, Wine data with 13 features, and a small part of breast cancer data. Results show that good feature map choice plus error mitigation give about 15% more accuracy than normal VQC in noisy environments. Circuit optimization makes the circuit 40% less deep than the original. The research demonstrates noise resilient quantum machine learning. Our Qiskit implementation achieves reproducible results while accurately modeling real quantum noise on classical simulators.