Comparisons of quantum data-encoding strategies are rarely accompanied by a registered estimand, an explicit treatment of where simulated noise is applied, or a classical reference point. This study reports a registered simulation study of the interaction between data encoding (angle versus ZZ feature map) and circuit noise (noiseless versus single-Pauli errors with probability p = 0.02 after every CNOT, plus readout flips) for an 8-qubit variational quantum classifier trained with SPSA. Three binary datasets, ten confirmatory seeds (240 runs) and circuit size as a secondary factor were used. Hyperparameters were tuned symmetrically on separate seeds and frozen before the confirmatory runs. The registered primary estimand, the Encoding x Noise interaction on validation balanced accuracy, was -0.154 (95% seed-cluster bootstrap CI [-0.181, -0.124]), which supports the registered directional hypothesis. ZZ-encoded models trained under noise met the pre-declared convergence criterion in 1 of 60 runs, against 48 of 60 for angle encoding, so training failure and signal degradation are not separated by the registered design. An exploratory follow-up, in which ZZ models were trained without noise and evaluated under noise, showed accuracy falling to 0.55-0.63 at p = 0.02, which points to the number of noisy two-qubit gates (56 additional CNOTs) as the main driver. The registered transfer hypothesis was not supported: robust selection did not differ from naive selection (+0.003, CI [-0.012, +0.016]). A class-balanced logistic regression exceeded every quantum configuration on validation accuracy. No quantum advantage is claimed.
Comparisons of quantum data-encoding strategies are rarely accompanied by a registered estimand, an explicit treatment of where simulated noise is applied, or a classical reference point. This study reports a registered simulation study of the interaction between data encoding (angle versus ZZ feature map) and circuit noise (noiseless versus single-Pauli errors with probability p = 0.02 after every CNOT, plus readout flips) for an 8-qubit variational quantum classifier trained with SPSA. Three binary datasets, ten confirmatory seeds (240 runs) and circuit size as a secondary factor were used. Hyperparameters were tuned symmetrically on separate seeds and frozen before the confirmatory runs. The registered primary estimand, the Encoding x Noise interaction on validation balanced accuracy, was -0.154 (95% seed-cluster bootstrap CI [-0.181, -0.124]), which supports the registered directional hypothesis. ZZ-encoded models trained under noise met the pre-declared convergence criterion in 1 of 60 runs, against 48 of 60 for angle encoding, so training failure and signal degradation are not separated by the registered design. An exploratory follow-up, in which ZZ models were trained without noise and evaluated under noise, showed accuracy falling to 0.55-0.63 at p = 0.02, which points to the number of noisy two-qubit gates (56 additional CNOTs) as the main driver. The registered transfer hypothesis was not supported: robust selection did not differ from naive selection (+0.003, CI [-0.012, +0.016]). A class-balanced logistic regression exceeded every quantum configuration on validation accuracy. No quantum advantage is claimed.
This study presents a noise-aware evaluation framework for hybrid quantum–classical machine learning models applied to medical binary classification. Using three healthcare datasets—Pima Indians Diabetes, Heart Disease, and Breast Cancer Wisconsin—the performance of a Variational Quantum Classifier (VQC) was analyzed under multiple depolarizing noise levels (0.00–0.10). Classical baselines, Logistic Regression (LR) and Support Vector Machine (SVM), were implemented for comparison. The research investigates the impact of noise on predictive accuracy, F1-score, and training time, highlighting the computational overhead of hybrid quantum–classical models. Zero Noise Extrapolation (ZNE), using linear and Richardson methods, was applied to mitigate noise effects, revealing that while ZNE improves performance under certain conditions, extrapolation instability can occur. Transpiler optimization also contributed to improved VQC stability by reducing circuit complexity. Results show that classical models consistently outperformed the VQC in accuracy, stability, and training efficiency. VQC exhibited fluctuating performance under noise, requiring significantly higher training time, and increasing SPSA iterations did not always yield stable accuracy improvements. These findings underscore the challenges of noise robustness, optimization instability, and computational cost in the NISQ era, and suggest directions for future work, including alternative optimizers, adaptive ansatz design, advanced error mitigation, and real hardware benchmarking. This research provides a systematic benchmarking framework for evaluating training time versus noise-level trade-offs, contributing to the development of more reliable quantum machine learning models for medical applications. Keywords: Quantum Machine Learning, Variational Quantum Classifier, Depolarizing Noise, Zero Noise Extrapolation, Medical Classification, Hybrid Quantum–Classical Models, Training Time Analysis
Near-term quantum machine learning (QML) models operate in environments wherein noise is unavoidable, arising from both imperfect classical data acquisition and the limitations of noisy intermediate-scale quantum (NISQ) hardware. Although most existing studies have focused primarily on quantum circuit noise in isolation, the combined influence of corrupted classical inputs and quantum hardware noise has received comparatively little attention.
In this work, we present a systematic experimental study of the robustness of a variational quantum classifier under realistic multi-level noise conditions. Using the Titanic dataset as a benchmark, a range of dataset-level noise models-including speckle noise, impulse noise, quantization noise, and feature dropout are applied to classical features prior to quantum encoding using a ZZ feature map. In parallel, hardware-inspired quantum noise channels such as depolarizing noise, amplitude damping, phase damping, Pauli errors, and readout errors are incorporated at the circuit level using the Qiskit Aer simulator.
The experimental results indicate that noise in classical input data can significantly intensify the effects of quantum decoherence, resulting in less stable training and noticeably lower classification accuracy. Together, these observations emphasize the importance of designing and evaluating quantum machine learning pipelines with noise in mind, and highlight the need to consider classical and quantum noise simultaneously when assessing QML performance in the NISQ era
Gate-level noise degrades the classification accuracy of Quantum Support Vector Machines (QSVMs) on Noisy Intermediate-Scale Quantum (NISQ) hardware, and the degree of degradation depends on how classical data is encoded into quantum states. We tested Z, ZZ, a Pauli, and an amplitude-inspired feature maps under depolarizing, bit-flip, and phase-flip noise channels in 52 controlled experiments with error probabilities p=0.01,0.05,0.10, and 0.50. The amplitude-inspired feature map had 100\% test accuracy up to p=0.10 across all three noise channels, while other feature maps fell to 65-90\% under the same noise level and type. The Z feature map was found to be immune to phase-flip noise to a significantly high error rate, a consequence of the commutation relation [RZ,Z]=0. Entangled circuit variants produced generalization gaps in train-test sets of up to 17.5\% under noise, whereas the amplitude variants maintained zero gap throughout. These results give practitioners data-driven criteria for a feature map on near-term quantum hardware.
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.
This thesis presents a systematic empirical evaluation of quantum machine learning performance under noisy intermediate-scale quantum (NISQ) era constraints. Through 670 controlled experiments, it evaluated quantum kernel support vector machines and variational quantum classifiers against classical baselines on MNIST binary and multiclass classification tasks with systematic variation of problem difficulty, feature dimensionality (4, 8 qubits), and training set size (n ∈{100, 250, 400, 500, 2000, 4000}). Statistical rigor was ensured through five random seeds per condition and comprehensive significance testing. During the testing with binary datasets, classical methods (SVM, logistic regression, k-NN, neural networks) achieved 85.9% to 99.6% accuracy with training times under one second across all sample sizes. Quantum kernel methods utilizing ZZ feature maps yielded 70.5% to 96.0% accuracy, requiring 129 to 2,140 seconds training with quadratic sample size scaling. Larger scale quantum experiments (n = 4000 for both architectures, 8-qubit encoding with n = 2000 for quantum kernels) proved computationally impossible on available hardware leading to out of memory errors, highlighting practical NISQ-era scalability constraints. Variational quantum classifiers exhibited persistent performance stagnation, failing to exceed 66.5% accuracy despite increases in training data and feature dimensionality. Performance gaps ranged from 3.3 to 35.2 percentage points. All quantum classical differences achieved statistical significance (p< 0.05, with 13 of 14 comparisons meeting p< 0.01) and exhibited large to very large efect sizes (d> 1.0, with 13 of 14 comparisons exceeding d> 2.0). To further evaluate performance and scalability, a 4 class classification experiment was conducted following an identical experimental protocol, with training set sizes of n ∈{100, 250, 400}. Across 180 runs, classical baselines achieved mean accuracies between 87.2% and 95% across both 4 and 8 dimensional data. Quantum Kernel SVM struggled during runs with 4 dimensions, accuracy varying between 64.6% and 74%. Quantum Kernel SVM accuracy declined 16%-25% when the dimension and qubit count were increased to 8, showing findings of exponential kernel concentration. The Variational Quantum Classifier also performed poorly, with accuracy ranging from 43.4% to 44.6% across all runs, providing further evidence that it failed to leverage additional features or training data. Experiments employed noiseless statevector simulation, establishing that quantum underperformance stems from fundamental algorithmic limitations independent of hardware noise. A further extension to 8 class classification (digits 0–7) confirmed and amplified these findings: classical methods maintained 65–83% accuracy while Quantum Kernel SVM degraded to 34–47% and VQC collapsed to 21–23%, approaching the 12.5% random baseline. Supplementary appendix experiments further examined amplitude encoding on raw 784 dimensional pixel features and an alternative angle encoding scheme on the 8-class task; the latter demonstrated that replacing the ZZ Feature Map with simple per qubit rotations substantially recovered quantum kernel performance, suggesting feature map design as a more consequential variable than circuit depth or qubit count in near-term quantum classification.
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.