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

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.