Quantum Convolutional Neural Networks

Recent advances in quantum computing are opening new possibilities for Earth Observation (EO) data analysis. Quantum machine learning (QML) approaches offer novel ways to process information by exploiting quantum phenomena such as superposition and entanglement. These capabilities have motivated the exploration of whether quantum-enhanced models can address long-standing challenges in satellite remote sensing, where complex spectral and spatial signals often require sophisticated feature extraction. Among various fields of application, EO data allow the global monitoring of volcanic clouds and are crucial for aviation safety, hazard assessment, real-time eruption response, and evaluation of volcanic impacts on climate. Yet accurate detection of volcanic clouds remains difficult due to their similarity with meteorological clouds, the variability of eruption signatures, and the coarse spectral sampling of geostationary sensors. In this work, the potential of hybrid quantum convolutional neural networks (QCNNs) for the classification of satellite images containing volcanic clouds was investigated. These architectures integrate quantum computational layers into a classical convolutional framework. Two QCNN variants (with 2 and 4 qubits) have been considered to evaluate their ability to classify a dataset of SEVIRI images, including scenes with volcanic clouds (composed of ash, $SO_2$, or mixed components) as well as non-volcanic backgrounds. Finally, the performance of the hybrid QCNN models was compared with that of purely classical architectures.

Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads to trainability issues. In this work, we investigate whether small, classically-emulated quantum circuit components can play a meaningful role within complex models, offering an alternative to purely classical convolutional architectures. To this end, we present a systematic study of the effectiveness of a Hybrid Quantum-inspired Convolutional Neural Network (HQiCNN) compared with a parameter-matched classical Convolutional Neural Network (CNN) that differs only in an intermediate dense neural layer. Both models are evaluated on two real-world medical datasets while systematically varying the different hyperparameters, ensuring a fair model comparison that is both dataset and hyperparameter independent. The results show that no architecture consistently dominates the other: the HQiCNN achieves its largest gains in intermediate-data regimes, whereas the CNN reaches the highest accuracies for the largest training sets in both datasets. Furthermore, removing entanglement produces comparable performance while enabling substantially better scalability of quantum simulations, and richer observable sets become beneficial only when sufficient training data are available. Finally, we propose two SHAP-based explainability tools for comparing the predictions between both models, $|SHAP|$IoU and $EMD_{pos}$ metric, to demonstrate that both architectures consistently attend to anatomically plausible regions. Thus, we provide a comprehensive benchmark showing that, under certain conditions, hybrid quantum-inspired models are an alternative that can offer benefits in practical tasks such as medical image classification.

This work presents a study of an implementation of a novel Quantum Convolutional Neural Network (QCNN) for binary classification of images from the Modified National Institute of Standards and Technology (MNIST) dataset. Using a novel architecture inspired by previous QCNN and classical convolutional neural network (CNN) implementations, we use a hierarchical partitioning approach to implement a QCNN circuit that can be approximated and simulated efficiently on a classical machine for a large problem. First, the original image is partitioned such that each process handles a smaller portion of the image, which is encoded into independent states. Then, these partitions merge and combine, resulting in states that contain information from both partitions while halving the number of processes. After repeating this until one process remains, we reduce the dimensionality of the state until a single qubit remains for measurement. Using this approach, we can use multiple processes in parallel to simulate a large QCNN program without the need for exponentially growing hardware requirements as the number of qubits increases. In our work, we use this scheme to train a 128-qubit model, which is impossible to run on any classical supercomputer without the novel architecture. We also explore the impact of this new model architecture on prediction accuracy by training it to perform binary classification on the MNIST dataset with a small number of qubits, and comparing it to a model without partitioning. Our initial findings show that partitioning images into smaller sub-images with this architecture does not degrade the model's performance and sometimes even improves it, likely because it reduces the Barren plateaus issue in the partitioning process.

Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS). These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.

Quantum convolutional neural networks (QCNNs) combine the power of quantum computing and classical CNN for computational speedup in classification tasks. However, noise levels on state-of-the-art quantum devices remain too high for practical QCNN execution. In addition, despite the reliable surface code providing a method for error rates below a threshold value, they have a prohibitively large qubit cost. Recently introduced bivariate bicycle (BB) codes are of particular interest for their high error threshold, constant encoding rate, and linear code distance. Through simulation with realistic hardware noise sources, we demonstrate that a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate compared to numerical simulations. Addressing both limitations, we propose a distance-4 BB quantum error-correction (QEC) technique for QCNNs. In doing so, we validate that our low-overhead QEC technique for QCNNS represents a step toward practical QCNNs.

Quantum machine learning methods are increasingly explored for modeling complex environmental systems, including groundwater heat plume dynamics. In this work, we explore a Quantum Convolutional Neural Network (QCNN) as a surrogate model for predicting temperature variations in groundwater induced by geothermal heat pumps in the city of Munich. To comply with the scalability constraints of current quantum hardware, the original high-dimensional simulation output is reduced to a compact set of representative parameters that serve as training targets for the surrogate. The proposed QCNN architecture consists of a quantum convolutional layer, a quantum pooling layer, and a fully connected quantum readout stage. Convolution and pooling operations are realized via parameterized quantum circuits based on rotational gates and measurement-driven decoding, while a Hamiltonian-inspired feature-encoding scheme is used to prepare informative input states on the quantum device. We evaluate the QCNN across multiple execution backends, including an ideal statevector simulator, a noisy simulator, IBM's 127-qubit Kyiv quantum processor, and the same hardware augmented with advanced error-mitigation techniques. Realistic noise models are employed to approximate device behavior and to assess the impact of mitigation strategies. Model performance is benchmarked using mean squared error (MSE) on both training and testing sets. The results show that, although classical neural networks still achieve the highest predictive accuracy, the QCNN attains competitive and consistent performance on simulators and exhibits noticeable improvement under error-mitigated hardware conditions. These findings indicate that quantum-enhanced surrogate modeling is a promising direction for future groundwater temperature prediction as quantum hardware and error-mitigation techniques continue to mature.

Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94% fewer parameters and $\sim$ 75% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.

GBM is a highly aggressive primary malignancy in adults, necessitating personalized therapeutic strategies due to its inherent molecular heterogeneity. MGMT promoter methylation is a pivotal prognostic biomarker for anticipating response to temozolomide-based chemotherapy. Although various AI frameworks have been developed for non-invasive MGMT prediction, spatial heterogeneity of methylation status and the high-dimensional and correlated nature of MRI data frequently constrain discriminative feature learning and generalizability of classical models. To circumvent these limitations, a specialized IA-QCNN architecture is proposed, based on the principles of quantum mechanics, including superposition and entanglement, and enabling more efficient representation learning in high-dimensional Hilbert space. The framework establishes a methodological bridge between GBM radiogenomics and quantum deep learning by integrating energy-based slice selection, importance-aware weighting, ring-topology quantum convolution, and folding-based pooling layers. When the model predicts MGMT promoter methylation status using both mpMRI and T1Gd images, experimental results demonstrate that the IA-QCNN achieves high accuracy despite its low number of trainable parameters while effectively minimizing the overfitting problem observed in classical models. Quantitative analyses reveal that the T1Gd modality possesses higher discriminative power than mpMRI, establishing a clinically significant sequence preference. Furthermore, the model exhibits exceptional robustness in hybrid noise environments, effectively utilizing noise as a regularization mechanism to enhance predictive performance. Consequently, the specialized IA-QCNN architecture provides a robust and computationally efficient alternative to classical approaches in the analysis of heterogeneous radiogenomic data.