Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.
This paper presents a qualitative analysis of hybrid quantum-classical computing approaches aimed at solving complex optimization problems using near-term quantum processors. Hybrid algorithms leverage the strengths of quantum and classical computing to tackle computationally intensive tasks often constrained by current quantum hardware limitations. Through an extensive literature review and synthesis of recent empirical studies, we benchmark various hybrid algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), focusing on their performance, scalability, and practical applicability on noisy intermediate-scale quantum (NISQ) devices. The study highlights the advantages, challenges, and future prospects of integrating hybrid quantum-classical computation in optimization domains, providing a comprehensive framework and qualitative insights into benchmarking methodologies and critical performance metrics.
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.
Abstract—Quantum Machine Learning (QML) operating on Noisy Intermediate-Scale Quantum (NISQ) hardware represents an emerging computational paradigm to address high-dimensional optimization problems that challenge classical Von Neumann supercomputing architectures. By mapping complex feature vectors into exponentially large 2^N Hilbert state spaces via Parameterized Quantum Circuits (PQCs) and Variational Quantum Algorithms (VQAs), QML targets computational advantages in combinatorial optimization, high-dimensional classification, and quantum-enhanced molecular modeling. However, the theoretical promise of NISQ-era variational computing is severely constrained by three fundamental bottlenecks: (1) Barren Plateaus, characterized by the exponential concentration of measure and vanishing variance of cost function gradients; (2) Hardware Decoherece Noise and readout error rates that corrupt quantum state fidelity; and (3) Classical-to-Quantum State Preparation bottlenecks that can erase theoretical computational speedups. This paper delivers an exhaustive, mathematically formal technical investigation and empirical benchmark of QML architectures for high-dimensional optimization. We formalize the Haar-distributed geometric mechanics of barren plateaus under 2-design unitary assumptions, evaluate barren plateau mitigation through shallow local cost operators and layer-by-layer parameter initialization, and contrast Variational Quantum Eigensolvers (VQE) with Quantum Kernel Support Vector Machines (Q-SVM). Furthermore, we construct an empirical benchmarking testbed executing across both state-vector simulators and superconducting quantum backends (IBM Quantum Heron / Eagle architectures), evaluating 127-qubit Hamiltonian optimization and high-dimensional financial portfolio allocation. Our findings demonstrate that while global cost functions suffer exponential gradient decay Var[grad] ~ O(2^-N) across circuit depth d >= 4, local Hamiltonian decomposition maintains trainable variance, achieving a 98.2% ground-state fidelity under zero-noise extrapolation (ZNE) error mitigation. Finally, we formulate open challenges in quantum error mitigation scaling, non-perturbative barren plateau escapes, and quantum data loading efficiency. Index Terms—Quantum Machine Learning (QML), Parameterized Quantum Circuits (PQCs), Variational Quantum Eigensolver (VQE), Barren Plateaus, Quantum Kernel Methods, NISQ Computing, Error Mitigation, Hilbert Space.
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.
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.
Quantum machine learning has emerged as a promising approach to enhance computational efficiency by leveraging the principles of quantum computing. However, the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, such as noise, limited qubit availability, and circuit depth constraints, restrict the implementation of fully quantum models. To address these challenges, this study focuses on the design, implementation, and performance evaluation of hybrid quantum-classical machine learning (HQML) models. The proposed approach integrates parameterized quantum circuits with classical optimization techniques to enable efficient learning within NISQ environments. The study employs standard benchmark datasets, including Iris, Breast Cancer, and MNIST, to evaluate the performance of the hybrid model. The results indicate that the HQML model achieves competitive accuracy on small and medium-sized datasets while maintaining balanced precision, recall, and F1-score. However, performance declines for complex datasets due to hardware limitations and noise effects. Additionally, the hybrid model demonstrates a lower number of parameters compared to classical deep learning models but requires higher training time due to iterative quantum-classical optimization. The findings highlight that hybrid quantum-classical models provide a practical and scalable approach for utilizing quantum computing in the current technological landscape. Although challenges related to noise, scalability, and computational overhead persist, advancements in quantum hardware and algorithm design are expected to improve performance. This study contributes to the growing field of quantum machine learning by providing a systematic framework for evaluating hybrid models on NISQ devices and identifying key areas for future research.