Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.
Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and GPU acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n^2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and Methane Detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0 pm6.2% accuracy for a binary classification task compared to 72.0 pm5.0% for the standard radial basis function (RBF) kernel. For a four-class classification task, the quantum kernel reached 83.3 pm3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the Methane Detection dataset, the quantum approach yielded 58.5\pm5.0% accuracy versus 55.1\pm2.5% for the classical counterpart...
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and graphics processing unit acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and methane detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0±6.2% accuracy for a binary classification task compared to 72.0±5.0% for the standard radial basis function kernel. For a four-class classification task, the quantum kernel reached 83.3±3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the methane detection dataset, the quantum approach yielded 58.5±5.0% accuracy versus 55.1±2.5% for the classical counterpart. This study provides a foundation for future exploration of quantum machine learning in high-dimensional Earth observation tasks.
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation.
Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at α=0.05; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity r≥0.976 across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%).
A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance (ε2=0.73), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead.
Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
Quantum machine learning methods, including quantum kernels and variational quantum algorithms (VQAs), are poised to demonstrate quantum advantages in machine learning, chemistry, condensed matter physics, and materials science. However, these methods face critical challenges hindering practical quantum advantates: quantum kernels require meticulous design to outperform classical alternatives, while VQA training is obstructed by barren plateaus (BPs) in the optimization landscape. To address these issues, this thesis proposes two novel frameworks to guide quantum kernel design and tackle quantum neural network (QNN) training challenges in VQAs. Specifically, to resolve quantum kernel design challenges, we propose a data-driven method for automatic quantum kernel design, leveraging classical machine learning to learn from input data and identify optimal kernel structures. Experiments show this method finds suitable quantum kernels that avoid vanishing similarity, a common flaw in traditional designs. To improve VQA trainability, we propose an encoder-decoder parameter prediction framework, where a graph neural network (GNN) acts as the encoder to process information based on the QNN’s directed acyclic graph (DAG). Experiments confirm the parameters from this framework significantly enhance VQAs’ robustness, convergence speed, and trainability. In conclusion, we propose two schemes, QuKerNet and QuGHN, for automatic quantum kernel design and enhanced VQA trainability. QuKerNet considers optimal circuit layouts and variational parameters, and is more resource-efficient for contemporary quantum hardware by accounting for qubit topology and count. QuGHN is versatile, applicable to circuits with varying qubits, ansatzes, and tasks; its parameters enable faster convergence and more stable VQA solutions. These advancements enhance quantum machine learning practicality on near-term machines and its utility in large-scale quantum circuit simulations.