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arXiv:2603.15522

Quantum-Inspired Unitary Pooling for Multispectral Satellite Image Classification

Georgios Maragkopoulos, Aikaterini Mandilara, Ralntion Komini, Dimitris Syvridis

quant-phSubmitted Mar 16, 2026• Announced Mar 17, 2026• 0 citations
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Abstract

Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability, accelerates convergence, and substantially reduces variance compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.

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Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability, accelerates convergence, and substantially reduces variance compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.
Abstract Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability and accelerates convergence, compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.
Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.
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.
Abstract Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently, this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show a clear dependence of classification accuracy on the underlying embedding, especially for initial training iterations. The improvement in classification accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used. The noisy simulation using simple noise models shows that certain EQCNNs are more robust to noise than non-equivariant QCNNs. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.
Quantum neural network architectures that have little to no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks the action of which commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a comprehensive theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group. We develop multiple methods to construct equivariant layers for EQNNs and analyze their advantages and drawbacks. Our methods can find unitary or general equivariant quantum channels efficiently even when the symmetry group is exponentially large or continuous. As a special implementation, we show how standard quantum convolutional neural networks (QCNNs) can be generalized to group-equivariant QCNNs where both the convolution and pooling layers are equivariant to the symmetry group. We then numerically demonstrate the effectiveness of a S U ( 2 ) -equivariant QCNN over symmetry-agnostic QCNN on a classification task of phases of matter in the bond-alternating Heisenberg model. Our framework can be readily applied to virtually all areas of quantum machine learning. Lastly, we discuss about how symmetry-informed models such as EQNNs provide hopes to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity. Published by the American Physical Society 2024
Remote sensing imagery classification remains a formidable challenge, primarily attributed to the high dimensionality and complexity inherent in the data. While deep learning has demonstrated efficacy in this domain, its computational demands and reliance on extensive training data pose significant hurdles. This research investigates how quantum computing could be able to overcome these constraints and improve deep learning’s capacity for classifying remote sensing data. The study provides an extensive review of recent developments in quantum deep learning techniques specifically tailored for remote sensing applications. Various quantum algorithms designed for image feature extraction and classification are discussed, shedding light on their potential to revolutionize the field. As a practical demonstration, the chapter presents a case study focused on leveraging quantum deep learning for land cover classification using Sentinel-2 imagery. This chapter’s main focus is on hybrid quantum convolutional neural networks (QCNNs) based on circuits as effective tools for remote sensing picture classification. These hybrid models integrate quantum layers within traditional neural networks, introducing a novel paradigm for image analysis. To evaluate the efficacy of this approach, the proposed QCNN architecture is applied to land-use and land-cover classification, employing the Euro SAT dataset as a benchmark.