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Quantum Feature Maps as Nonlinear Encoders for Fused Sentinel-1/2 Data in Support Vector Machines

Sreejit Dutta, Sigurd Huber, Gerhard Krieger, Marco Körner

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

Remote sensing applications increasingly rely on multimodal Earth observation data to improve land-cover classification. However, conventional kernel methods may struggle to capture complex nonlinear relationships between modalities such as synthetic aperture radar (SAR) and multispectral optical imagery. In this work, we investigate a quantum kernel learning framework based on data reuploading feature maps for fused Sentinel-1 and Sentinel-2 data. Input features are first reduced using Tucker decomposition and mapped into quantum states via a parameterized multi-layer circuit consisting of non-commuting rotations and entangling operations. The feature map repeatedly encodes classical data across multiple layers with layer-specific scaling, enabling richer representations than shallow embeddings. Pairwise overlaps between quantum states define a kernel matrix used in a classical support vector machine for classification. We benchmark the proposed quantum kernel against classical linear, polynomial, and radial basis function kernels using multiple evaluation metrics, including accuracy, macro F1-score, and Matthews correlation coefficient. Results indicate that deeper quantum feature maps achieve competitive performance but do not consistently outperform well-tuned classical kernels. These findings highlight the importance of feature map design and parameterization in quantum kernel methods.

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IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing•Jan 1, 2026•0 citations
Remote sensing applications increasingly rely on multimodal Earth observation data to improve land-cover classification. However, conventional kernel methods may struggle to capture complex nonlinear relationships between modalities such as synthetic aperture radar (SAR) and multispectral optical imagery. In this work, we investigate a quantum kernel learning framework based on data reuploading feature maps for fused Sentinel-1 and Sentinel-2 data. Input features are first reduced using Tucker decomposition and mapped into quantum states via a parameterized multi-layer circuit consisting of non-commuting rotations and entangling operations. The feature map repeatedly encodes classical data across multiple layers with layer-specific scaling, enabling richer representations than shallow embeddings. Pairwise overlaps between quantum states define a kernel matrix used in a classical support vector machine for classification. We benchmark the proposed quantum kernel against classical linear, polynomial, and radial basis function kernels using multiple evaluation metrics, including accuracy, macro F1-score, and Matthews correlation coefficient. Results indicate that deeper quantum feature maps achieve competitive performance but do not consistently outperform well-tuned classical kernels. These findings highlight the importance of feature map design and parameterization in quantum kernel methods.
We investigate variational quantum classifiers (VQCs) for land-cover classification from multispectral satellite imagery, adopting a feature-map perspective in which the quantum circuit defines a nonlinear data embedding while the readout determines how this representation is exploited. Using the EuroSAT-MS dataset, we perform a systematic one-vs-one evaluation across all class pairs under a controlled experimental protocol, comparing classical baselines (logistic regression, SVMs, neural networks) with VQCs employing both linear readout and quantum-kernel SVM strategies. Our results show that, while VQCs with linear readout do not outperform strong classical baselines such as RBF-SVM, the same trained quantum feature map can significantly improve performance when reused within a kernel-based decision framework. A qubit-count sweep further reveals saturation effects consistent with the mismatch between exponential Hilbert space dimension and linear parameter scaling. Overall, our findings highlight that the effectiveness of quantum models depends critically on the interplay between representation and readout, and that meaningful gains may arise from combining learned quantum feature maps with classical decision mechanisms rather than seeking direct replacement of classical models.
Quantum computers consisting of hundreds of noisy qubits are already available and can run specific quantum algorithms although a large-scale fully error-corrected quantum computer is decades away. It is important to study their application to real-life computational problems. One such problem is Land Use and Land Cover classification of Earth Observation data set collected from the earth observation satellite mission using quantum machine learning methods. In this work, we compare the performance of the classical neural network on the re-labeled dataset of the Copernicus Sentinel-2 mission, when the model has access to Projected Quantum Kernel features. We show that classical neural net-work training accuracy increases drastically when the model has access to Projected Quantum Kernel features. This study shows the potential for quantum machine learning methods to Earth Observation data and provides key evidence for further investigation.
Quantum computers with hundreds of noisy qubits are already available for the research community. They have the potential to run complex quantum computations well beyond the computational capacity of any classical device. It is natural to ask the question, what application these devices could be useful for? Land Use and Land Cover classification of multispectral Earth observation data collected from the earth observation satellite mission is one such problem that is hard for classical methods due to its unique characteristics. In this work, we compare the performance of several classical machine learning algorithms on the stilted re-labeled dataset of the Copernicus Sentinel-2 mission, when the algorithm has access to Projected Quantum Kernel (PQK) features. We show that the classification accuracy increases drastically when the model has access to PQK features. We then naively study the performance of these algorithms with and without access to PQK features on the original Copernicus Sentinel-2 mission data set. This study provides key evidence that shows the potential of quantum machine learning methods for Earth Observation data.
Support Vector Machines (SVMs) are powerful machine learning models widely used for classification and regression tasks. However, their performance can be significantly impacted by the choice of the kernel function, which defines how data points are mapped into a higher-dimensional space. Traditional kernels often struggle to capture complex, non-linear relationships effectively, leading to suboptimal results. This paper proposes a novel approach to kernel design inspired by quantum mechanical principles. Specifically, we leverage concepts of quantum entanglement and superposition to generate kernels that can potentially capture richer and more nuanced data patterns. Our core claim is that employing these quantum-inspired designs can improve SVM performance and scalability. We present a theoretical framework outlining how quantum mechanical effects can be translated into kernel functions. The proposed method is based on constructing kernel functions that implicitly encode correlations between data points, mimicking the inherent interconnectedness observed in quantum systems. We explore specific kernel formulations based on these principles and discuss their potential advantages and challenges. The ultimate goal is to demonstrate that quantum inspiration can unlock new avenues for kernel design, leading to more effective SVM models.
Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) are presented. Here, the pixels are mapped to the Hilbert space using a family of parameterized quantum feature maps (related to quantum kernels). The parameters are optimized to maximize the kernel target alignment. The quantum kernels have been selected such that they enabled analysis of numerous relevant properties while being able to simulate them with classical computers on a real-life large-scale dataset. Specifically, we approach the problem of cloud detection in the multispectral satellite imagery, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy comparable to the classical SVM with the RBF kernel for large datasets. Interestingly, for large datasets, the high accuracy was also observed for the simple quantum kernels, lacking quantum entanglement.
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.