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.
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.
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.
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 (QML) has generated significant excitement as a potential game-changer in artificial intelligence. At the heart of any QML model lies a fundamental challenge: how do we translate classical data into the language of quantum mechanics? This encoding process is crucial because the way we represent information in a quantum system can make or break model performance. While researchers have proposed several encoding strategies over the years, most studies focus on idealized conditions, leaving a significant gap in our understanding of how these methods actually behave under the noisy, imperfect conditions of real quantum hardware. In this work, we address this gap through a systematic, simulation-based comparison of three widely used encoding strategies—Angle Encoding, Amplitude Encoding, and the entangling ZZFeatureMap—within a variational quantum classification framework. We evaluate these approaches on standard benchmark datasets under both noiseless and noisy conditions that mimic real quantum devices. To ensure our findings are statistically reliable, each noisy experiment is repeated across 10 independent runs, with results reported using mean accuracy, standard deviation, and 95% confidence intervals. Our results reveal a nuanced but sobering story. While the entangling ZZFeatureMap outperforms simpler methods in ideal noise-free settings, these advantages largely vanish under realistic depolarizing noise. When statistically averaged, all encoding strategies converge to near-random classification accuracy under moderate noise levels. These findings highlight the fragility of quantum advantages on today's noisy intermediate-scale quantum (NISQ) hardware and emphasize the critical need for noise-aware, statistically grounded evaluation protocols when assessing the practical viability of QML models.
We investigate the robustness of quantum neural networks (QNNs) trained as binary classifiers against bit flip and depolarizing noise, two channels that emulate a subset of noise present in noisy intermediate-scale quantum (NISQ) devices. The presence of decoherence and other forms of noise poses significant challenges to classification accuracy. To assess the impact of noise on label extraction, and to evaluate the performance and robustness of our models, we trained three different label assignment methods in the presence of various levels of noise. Each QNN model uses 2 qubits to implement a parameterized model and either the qubits of the QNN, or a set of ancilla qubits are used for label extraction. These three different methods project the state of either a single qubit or multiple qubits onto the computational basis. This generates a probability distribution that is post-processed to assign a class label and a class probability. Each QNN is trained using noisy numerical simulation on a dataset with 2 features. Depolarizing noise channels are interleaved with the parameterized gates of the QNN and we include bit flip error prior to extracting the labels. The noise levels for the depolarizing noise and bit flip error are swept over large ranges of values. We deploy QNNs trained at various noise levels on IBM quantum computers- this introduces an additional source of noise due to SWAP gate noise. We observe that the QNNs trained with simulated noise can have good performance on NISQ hardware.
uantum computing offers the potential to solve selected computational problems more efficiently than classical systems by leveraging quantum mechanical principles such as superposition and entanglement. However, current quantum devices operate in the noisy intermediatescale quantum (NISQ) regime, where limited coherence times, gate errors, measurement instability, and hardware variability significantly constrain practical performance. As a result, many quantum machine learning architectures that appear promising under idealized simulation conditions experience substantial degradation when executed under realistic noisy environments. This thesis investigates the problem of robustness in hybrid quantum neural network (HQNN) systems operating under realistic NISQ conditions. Rather than focusing primarily on quantum expressivity or claims of quantum advantage, the work examines whether practical hybrid quantum learning can maintain stable optimization and reliable inference in the presence of stochastic perturbations. A robustness-engineering framework is developed that integrates learned-readout decoding, multi-observable quantum feature extraction, architecture-level optimization, stability-aware training, and noise-augmented learning within a unified hybrid quantum-classical pipeline. To evaluate the framework, a comprehensive benchmarking methodology is developed across multiple datasets, architectures, perturbation environments, software frameworks, and hardware platforms. The experiments compare classical machine learning models, quantum kernel methods, and several HQNN architectures, including quanvolutional neural networks, quantum convolutional neural networks, and quantum transfer learning systems. Performance is evaluated under both noiseless and noisy conditions using standardized metrics, cross-noise validation, architecture-level comparisons, and real IBM Quantum hardware execution. The results demonstrate that baseline HQNN systems are highly sensitive to optimization instability, parity-based information loss, measurement variability, and perturbation accumulation. The experiments further reveal that robustness, rather than representational expressivity alone, is the dominant factor limiting practical hybrid quantum learning under realistic NISQ conditions. Through successive robustness-engineering stages, noisy performance improves from approximately 0.37 to 0.50 in baseline architectures to approximately 0.97 under several benchmark environments while maintaining substantially improved stability and reduced degradation under perturbation. These findings establish robustness as a central design objective for practical quantum machine learning. The thesis demonstrates that reliable hybrid quantum learning emerges through coordinated interaction between quantum feature generation, adaptive classical inference, stability-aware optimization, and hardware-aware architecture design. More broadly, the results suggest that hybrid quantum-AI systems are most effective when viewed as integrated quantum-classical computational frameworks in which quantum circuits function as probabilistic feature generators operating within larger robustness-oriented learning pipelines.
Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to model expressivity. We compare classical models and a variational quantum classifier on the XOR problem. Logistic regression, a one-hidden-layer multilayer perceptron, and a two-qubit variational quantum classifier with circuit depths 1 and 2 are evaluated on synthetic XOR datasets with varying Gaussian noise and sample sizes using accuracy and binary cross-entropy.
Performance is determined primarily by model expressivity. Logistic regression and the depth-1 quantum circuit fail to represent XOR reliably, whereas the multilayer perceptron and the depth-2 quantum circuit achieve perfect test accuracy under representative conditions. Robustness analyses across noise levels, dataset sizes, and random seeds confirm that circuit depth is decisive for quantum performance on this task. Despite matching accuracy, the multilayer perceptron achieves lower binary cross-entropy and substantially shorter training time. Hardware execution preserves the global XOR structure but introduces structured deviations in the decision function. Overall, deeper variational quantum classifiers can match classical neural networks in accuracy on low-dimensional XOR benchmarks, but no clear empirical advantage in robustness or efficiency is observed in the examined settings.