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Artifact for Validating the Quantum Fisher Kernel: Towards Scalable and Effective Quantum Learning

Marco Lacagnina, Marco Garlini, Elisabetta Di Nitto

Published Apr 28, 2026• 0 citations
Publisher

Abstract

This artifact includes the software we have developed to conduct an experimental analysis of QFK, providing its first implementation with real-world datasets and exploring its behavior with different quantum circuit architectures. Wedemonstrate that QFK is capable of creating models useful for learning and that it can be effectively executed on currentNISQ devices, successfully mitigating exponential concentration and offering high accuracy both in ideal and noisy simulations. Furthermore, we show that QFK can compete with state-of-the-art kernel methods, offering promising scalability even in settings involving an increasing number of qubits and highly expressive quantum circuits. This is an initial demonstration that QFK may offer a quantum advantage in learning tasks, making it a competitive alternative to the standard approaches.

DOI
10.5281/zenodo.19852151

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This artifact includes the software we have developed to conduct an experimental analysis of QFK, providing its first implementation with real-world datasets and exploring its behavior with different quantum circuit architectures. Wedemonstrate that QFK is capable of creating models useful for learning and that it can be effectively executed on currentNISQ devices, successfully mitigating exponential concentration and offering high accuracy both in ideal and noisy simulations. Furthermore, we show that QFK can compete with state-of-the-art kernel methods, offering promising scalability even in settings involving an increasing number of qubits and highly expressive quantum circuits. This is an initial demonstration that QFK may offer a quantum advantage in learning tasks, making it a competitive alternative to the standard approaches.
A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
Abstract Quantum kernel (QK) methods exploit quantum computers to calculate QKs for the use of kernel-based learning models. Despite a potential quantum advantage of the method, the commonly used fidelity-based QK suffers from a detrimental issue, which we call the vanishing similarity issue; the exponential decay of the expectation value and the variance of the QK deteriorates implementation feasibility and trainability of the model with the increase of the number of qubits. This implies the need to design QKs alternative to the fidelity-based one. In this work, we propose a new class of QKs called the quantum Fisher kernels (QFKs) that take into account the geometric structure of the data source. We analytically and numerically demonstrate that the QFK can avoid the issue when shallow alternating layered ansatzes are used. In addition, the Fourier analysis numerically elucidates that the QFK can have the expressivity comparable to the fidelity-based QK. Moreover, we demonstrate synthetic classification tasks where QFK outperforms the fidelity-based QK in performance due to the absence of vanishing similarity. These results indicate that QFK paves the way for practical applications of quantum machine learning toward possible quantum advantages.
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)O(n^2)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%78.0±6.2\%78.0±6.2% accuracy for a binary classification task compared to 72.0±5.0%72.0±5.0\%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%83.3±3.1\%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%58.5±5.0\%58.5±5.0% accuracy versus 55.1±2.5%55.1±2.5\%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.