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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Hybrid Quantum-Classical Machine Learning for Robust Satellite Image Classification on EuroSAT</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Akansha Singh</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Krishna Kant Singh</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Delhi Technical Campus</institution>
          ,
          <addr-line>Greater Noida, UP</addr-line>
          ,
          <country country="IN">India</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of CSET, Bennett University</institution>
          ,
          <addr-line>Greater Noida, UP</addr-line>
          ,
          <country country="IN">India</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Satellite image classification is a crucial task in remote sensing for applications such as land cover mapping, environmental monitoring, and resource management. While classical machine learning models such as SVMs achieve strong accuracy, they are often sensitive to noise, parameter-heavy, and less eficient when training data is scarce. In this work, we propose a hybrid quantum-classical pipeline for binary land cover classification on the EuroSAT dataset, combining a convolutional autoencoder for feature extraction with a Variational Quantum Classifier (VQC) inspired by quantum convolutional neural networks. The proposed QCNN-VQC achieves 90.0% accuracy, but more importantly outperforms baselines on F1-score (0.9428 after threshold tuning), AUROC (0.9819), and AUPRC (0.9812), while requiring fewer parameters. The model also demonstrates superior robustness to label noise and attains exceptionally high recall for the SeaLake class (97.8%), ensuring reliable detection of water bodies. These results highlight the promise of quantum machine learning for practical remote sensing tasks, especially in noisy or low-data regimes.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Quantum Machine Learning</kwd>
        <kwd>Satellite Image Classification</kwd>
        <kwd>EuroSAT</kwd>
        <kwd>QCNN</kwd>
        <kwd>Variational Quantum Classifier</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Satellite image classification plays a critical role in Earth observation, supporting applications ranging
from agricultural monitoring and land-use mapping to climate change studies and disaster management.
Traditional machine learning models, particularly Support Vector Machines (SVMs) and Convolutional
Neural Networks (CNNs), have achieved notable success in remote sensing. However, these methods
often require large volumes of annotated data, sufer performance degradation under label noise, and
involve significant computational overhead.</p>
      <p>Quantum Machine Learning (QML) has emerged as a promising alternative, ofering new ways to
encode and process data through quantum states, entanglement, and variational circuits. By
leveraging quantum resources, QML can potentially deliver greater expressive power with fewer
parameters, improved generalization, and robustness in data-scarce settings. Recent advances in hybrid
frameworks—where classical feature extractors are combined with quantum classifiers—have shown
encouraging results for vision and geospatial tasks.</p>
      <p>In this paper, we propose a hybrid quantum–classical framework for land cover classification using
the EuroSAT dataset. A convolutional autoencoder compresses satellite images into a compact latent
representation, which is then encoded into quantum states and classified using a QCNN-inspired
Variational Quantum Circuit. While raw accuracy of 90.0% is slightly below SVM baselines, the quantum
model demonstrates superior F1 (0.9428), AUROC (0.9819), AUPRC (0.9812), and robustness to label
noise, alongside remarkable recall for the SeaLake class (97.8%). These results underscore the practical
advantages of QML in remote sensing scenarios where false negatives, noise resilience, and parameter
eficiency are critical.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Background and Related Work</title>
      <p>Land cover mapping from satellite imagery is traditionally tackled with supervised learning. Given
multi-spectral image inputs, models predict the land cover class for each pixel or image patch. Modern
deep learning approaches, like CNNs, have become the state-of-the-art for such tasks, achieving
high accuracy on benchmark datasets. For instance, Helber et al. created the EuroSAT dataset and
demonstrated a deep CNN could classify ten land-use classes with over 98% accuracy on the test set.
This success underscores the power of classical ML, but also sets a high bar for any novel approach like
QML to be competitive.</p>
      <p>Quantum Machine Learning (QML) leverages quantum computing for machine learning tasks. Notable
QML models include parameterized quantum circuits (PQCs)—also called variational quantum circuits
or quantum neural networks—and quantum kernel methods. In PQCs, data is encoded into quantum
states, then a circuit with trainable gate parameters is executed, and measurements yield the model
output. The parameters are optimized (with a classical optimizer) to minimize a loss, analogous to
training a neural network. Quantum kernel methods, on the other hand, map data to a quantum state
via a fixed feature-map circuit and use the quantum device to compute inner products (kernel values)
between data points in this quantum feature space. Havlíček et al. first demonstrated that a quantum
feature map can enable a support vector machine (SVM) classifier to separate classes that were hard to
separate classically. These approaches are particularly relevant to image classification, as images have
high-dimensional features that might benefit from quantum representations.</p>
      <p>Given the limitations of today’s quantum hardware (noisy qubits and small quantum memory), hybrid
models that combine classical preprocessing with quantum models have gained traction. A common
pattern is to reduce the input data dimensionality using classical techniques (e.g., downsampling,
principal component analysis, or neural network autoencoders) before feeding data to a quantum
model. This ensures the data fits within the few qubits available and mitigates quantum noise by
simplifying the task. There is increasing recognition that quantum components should complement
classical ones—leveraging classical strengths in data preprocessing and using quantum circuits for
specific parts of the pipeline.</p>
      <p>
        Sebastianelli et al. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] introduced a hybrid quantum–classical convolutional neural network (QCNN)
for land-use classification. They inserted a quantum circuit as one layer in a CNN and applied it to
EuroSAT land-cover data. Notably, their quantum-enhanced CNN outperformed a purely classical CNN
on the ten-class EuroSAT problem, with the best results achieved when the quantum layer exploited
qubit entanglement. This suggests that even in today’s NISQ era, a quantum layer can provide a small
boost in accuracy for image recognition tasks.
      </p>
      <p>
        Otgonbaatar and Datcu [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] experimented with a parameterized quantum circuit for classifying
satellite images. They tackled a simplified two-class version of the EuroSAT dataset (due to qubit limits)
and used a deep autoencoder to compress each image to sixteen essential features. The sixteen features
were then mapped onto sixteen qubits and fed into a variational quantum circuit classifier. Their PQC
achieved accuracy on par with a classical deep CNN, even slightly exceeding it in some instances. This
was a landmark result showing that a quantum model can match classical performance on a remote
sensing task, given proper dimensionality reduction.
      </p>
      <p>
        Delilbasic et al. and Zardini et al. [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] explored quantum-enhanced SVM classifiers for remote sensing
data using quantum annealers. By training SVMs on D-Wave quantum annealing hardware, they
demonstrated comparable performance to classical SVMs on tasks like classifying aerial scene imagery.
Their work introduced strategies to overcome limited qubit connectivity and scale to larger datasets
(such as dividing the problem into smaller subproblems). These studies indicate that quantum annealing
can be used to train ML models for geospatial data, though the benefit over classical training was mainly
in ofloading computation rather than accuracy gains.
      </p>
      <p>
        Zöllner et al. [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] conducted a comprehensive study on how diferent feature-extraction methods
impact quantum classifiers for satellite images. They tried nine dimensionality-reduction techniques
(including PCA, autoencoders, and deep CNN feature extractors) combined with four types of quantum
classifiers across two remote sensing datasets (EuroSAT and RESISC45). Their experiments (over 770
models in total) showed that hybrid quantum–classical systems can efectively classify satellite imagery,
given suitably chosen data representations. In particular, using a deep autoencoder or a pretrained
CNN to create a low-dimensional representation yielded the best accuracy for the quantum models.
They achieved around 90% accuracy on binary land-cover classification tasks with quantum classifiers
when using an autoencoder-based feature reduction, which is on par with classical benchmarks. This
highlights the importance of compressing image data into a small set of informative features to work
within current quantum hardware constraints.
      </p>
      <p>
        Rodríguez-Grasa et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] recently applied quantum machine learning to a real-world solar panel
detection task using satellite images. They developed neural quantum kernel (NQK) methods—essentially
quantum kernel classifiers where the kernel is learned via a quantum neural network. After reducing
the image data to just three features, their quantum model achieved 86–88% test accuracy in identifying
images containing solar photovoltaic panels. This is an encouraging result on an industry-relevant
classiifcation problem, demonstrating that QML can handle complex imagery (with appropriate preprocessing)
and approach practical performance levels.
      </p>
      <p>Overall, prior work suggests that QML models can learn to classify remote sensing images with
accuracy comparable to conventional methods, at least for small-scale or simplified tasks. Key lessons
include the eficacy of hybrid architectures, the necessity of aggressive dimensionality reduction, and
the observation that current quantum models do not yet vastly surpass classical accuracy but can
sometimes match or slightly exceed it in controlled experiments. These studies form the foundation for
our exploration of quantum machine learning for land-cover mapping.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Proposed Approach</title>
      <p>The proposed pipeline integrates classical dimensionality reduction with a quantum variational classifier,
as shown in Fig. 1. The methodology consists of four key stages: (i) data preparation and feature
extraction via a convolutional autoencoder (CAE), (ii) quantum data encoding, (iii) variational quantum
circuit (VQC) design, and (iv) measurement and classification.</p>
      <sec id="sec-3-1">
        <title>3.1. Data Preparation and Feature Extraction</title>
        <p>Input EuroSAT images of size 64 × 64 × 3 are preprocessed by normalization and reshaping. To address
the curse of dimensionality, a convolutional autoencoder (CAE) is employed to learn compact latent
representations.</p>
        <p>Let x ∈ R denote the flattened image vector. The encoder network ℰ(·) , parameterized by weights
, maps the input to a lower-dimensional latent feature vector x̃︀ ∈ R :</p>
        <p>Here,  corresponds to the number of qubits in the quantum classifier. The decoder reconstructs the
input, but only the encoder’s latent features x̃︀ are forwarded to the quantum stage.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Quantum Data Encoding</title>
        <p>The latent vector x̃︀ = (̃︀1, ̃︀2, . . . , ̃︀ ) is mapped to a quantum Hilbert space using angle encoding.
Each feature is encoded as a rotation around the  -axis:
|( x̃︀, Θ)⟩ =
︃(  )︃
∏︁ (Θ ) enc(x̃︀)|0⟩⊗
=1
where Θ = {Θ
of  qubits.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.4. Measurement and Prediction</title>
        <p>A measurement is performed on the first qubit using the Pauli-  operator. The model prediction is
given by the expectation value:
1, . . . , Θ } are the trainable circuit parameters, and |0⟩⊗ is the all-zero initial state
x̃︀ = ℰ(x),</p>
        <p>≪ 

enc(x̃︀) = ∏︁  ()</p>
        <p>̃︀
=1
where  () = exp(− /2)</p>
        <p>is the rotation gate around the Pauli- axis applied on the -th qubit.</p>
      </sec>
      <sec id="sec-3-4">
        <title>3.3. Variational Quantum Circuit (VQC)</title>
        <p>On top of the encoded state, a variational quantum circuit is constructed using Strongly Entangling
Layers (SEL). Each layer consists of parameterized single-qubit rotations followed by entangling gates
across qubits.</p>
        <p>Let (Θ ) denote the unitary operation for the -th layer with learnable parameters Θ . For  layers,
the variational state is given by:</p>
        <p>
          To map this to a probability, the output is rescaled to [
          <xref ref-type="bibr" rid="ref1">0, 1</xref>
          ]:
ˆ = ⟨( x̃︀, Θ)||(
        </p>
        <p>x̃︀, Θ)⟩
( = 1 | x̃︀, Θ) =
The final class label is assigned by thresholding at 0.5.
(1)
(2)
(3)
(4)
(5)</p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Training Objective</title>
        <p>The variational parameters Θ are optimized via gradient-based methods (Adam optimizer) by minimizing
the binary cross-entropy (BCE) loss:</p>
        <p>=1
where  are ground-truth labels and  are predicted probabilities. Early stopping based on validation
loss is applied to prevent overfitting.</p>
        <p>ℒ(Θ) = −
 log() + (1 −  ) log(1 −  )</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experiments and Results</title>
      <p>All experiments were conducted in Google Colab using TensorFlow 2.15, scikit-learn 1.5, and PennyLane
0.36. We used the EuroSAT dataset and selected two representative land-cover categories — Annual Crop
and Sea Lake. Images were resized to 64×64 RGB, and a convolutional autoencoder (CAE) compressed
them into latent features of dimension K=8. These latent vectors were then used for classification
with Logistic Regression, SVM (RBF), and the proposed QCNN-inspired Variational Quantum Classifier
(VQC). A 70/15/15 stratified split was used for training, validation, and testing.</p>
      <sec id="sec-4-1">
        <title>4.1. Dataset Samples</title>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Classification Results</title>
        <p>The proposed QCNN–VQC achieved 90.0% accuracy, which is close to the performance of the SVM
baseline (92.8%) and superior to Logistic Regression (87.2%). However, when evaluating with more
robust metrics such as F1-score (after threshold tuning), AUROC, and AUPRC, the quantum model
clearly outperforms classical baselines. Table 1 summarizes performance. The VQC matches or exceeds
strong baselines on F1, AUROC, and AUPRC, and achieves high recall for SeaLake, which is valuable
for environmental monitoring. Table 2 shows that the quantum model achieves a high recall of 97.8%
for the SeaLake class, with only four false negatives. This indicates that nearly all water-body instances
are correctly identified, which is particularly important for environmental monitoring applications.</p>
        <p>Beyond raw accuracy, the QCNN–VQC shows state-of-the-art AUROC (0.9819) and AUPRC (0.9812),
both surpassing SVM. These metrics confirm that the quantum model produces well-calibrated decision
boundaries and superior precision–recall trade-ofs, particularly valuable for imbalanced or noisy data.
In summary, although the SVM achieves slightly higher raw accuracy, the proposed quantum model
delivers superior F1, AUROC, AUPRC, and robustness, making it the strongest overall choice in practical
scenarios where false negatives and noise resilience are critical. Figure 3 shows autoencoder
reconstructions, demonstrating that salient features are retained in the compressed latent space. Although minor
blurring is visible, the reconstructed images preserve essential class information, validating the CAE
as an efective dimensionality reduction stage. To assess separability, we applied t-SNE to the latent
vectors. Figure 4 shows clear clustering of the two classes, supporting the suitability of the learned
features for quantum encoding. The quantum model used only 144 parameters (6 layers × 8 qubits × 3),
compared to 181 for a parameter-matched MLP.</p>
        <p>Under 20% label noise, QCNN–VQC accuracy dropped by only 0.6%, compared to 3.6% for MLP.</p>
        <p>This indicates superior robustness of the quantum classifier to noisy labels. Table 4 shows calibration
results. Both models produce reasonably calibrated probabilities, with the MLP slightly outperforming
QCNN–VQC.</p>
        <p>Figure 5 plots accuracy vs. training samples per class. The QCNN–VQC performs well with as few as
100–200 samples, showing potential in data-scarce scenarios. At higher data volumes, MLP maintains
an advantage.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion and Future Work</title>
      <p>This paper presented a hybrid quantum–classical pipeline for land cover mapping using the EuroSAT
dataset. The proposed QCNN-inspired Variational Quantum Classifier achieved 90% accuracy and
a best-threshold F1 of 0.9428, while delivering superior AUROC (0.9819), AUPRC (0.9812), and high
recall for the SeaLake class (97.8%). These results demonstrate that hybrid quantum machine learning
approaches can be not only competitive with strong classical models such as SVM, but can also surpass
them under critical evaluation criteria such as noise robustness, parameter eficiency, and recall of
minority-critical classes. Future work will extend this framework to multi-class land cover classification
using the full EuroSAT dataset, incorporate multispectral bands beyond RGB, and explore larger remote
sensing datasets such as RESISC45. Furthermore, as quantum hardware matures, deeper circuits with
more qubits may unlock greater accuracy and scalability, reinforcing the promise of quantum-enhanced
Earth observation systems.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>The authors have not used Generative AI tools.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <p>We thank colleagues and reviewers for constructive feedback.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>A.</given-names>
            <surname>Sebastianelli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. A.</given-names>
            <surname>Zaidenberg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Spiller</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B. L.</given-names>
            <surname>Saux</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. L.</given-names>
            <surname>Ullo</surname>
          </string-name>
          ,
          <article-title>On circuit-based hybrid quantum neural networks for remote sensing imagery classification</article-title>
          ,
          <source>IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing</source>
          <volume>15</volume>
          (
          <year>2022</year>
          )
          <fpage>565</fpage>
          -
          <lpage>580</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>S.</given-names>
            <surname>Otgonbaatar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Datcu</surname>
          </string-name>
          ,
          <article-title>Classification of remote sensing images with parameterized quantum gates</article-title>
          ,
          <source>IEEE Geoscience and Remote Sensing Letters</source>
          <volume>19</volume>
          (
          <year>2021</year>
          )
          <fpage>1</fpage>
          -
          <lpage>5</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>G.</given-names>
            <surname>Cavallaro</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Willsch</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Willsch</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Michielsen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Riedel</surname>
          </string-name>
          ,
          <article-title>Approaching remote sensing image classification with ensembles of svms on the d-wave quantum annealer</article-title>
          ,
          <source>in: Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS)</source>
          ,
          <year>2020</year>
          , pp.
          <fpage>1973</fpage>
          -
          <lpage>1976</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>J. M.</given-names>
            <surname>Zöllner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Walther</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Werner</surname>
          </string-name>
          ,
          <article-title>Satellite image representations for quantum classifiers</article-title>
          ,
          <source>Datenbank-Spektrum</source>
          <volume>24</volume>
          (
          <year>2024</year>
          )
          <fpage>33</fpage>
          -
          <lpage>41</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>P.</given-names>
            <surname>Rodríguez-Grasa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Farzan-Rodriguez</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Novelli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Ban</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Sanz</surname>
          </string-name>
          ,
          <article-title>Satellite image classification with neural quantum kernels, arXiv preprint (</article-title>
          <year>2023</year>
          ). arXiv:
          <volume>2409</volume>
          .
          <fpage>20356</fpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>