• Quantum Convolutional Neural Network

The Noisy Intermediate-Scale Quantum (NISQ) era marks a crucial phase
in the development of quantum computing. The term "intermediate scale" refers to the number of qubits that characterized quantum computers, ranging from tens to a few hundred qubits. This era, as defined by John Preskill in 2018, represents a transition period in which quantum
computers are powerful enough to perform certain tasks beyond the capacity
of classical computers.

The term “noisy” underlines one of the main limitations of quantum computers, namely the sensitivity to the external environment which may affect the reliability of results.

Machine Learning (ML) is a rapidly evolving branch of the computer science field, particularly in recent years. Machine learning is an artificial intelligence discipline that develops algorithms and statistical models. Neural networks are a specific branch of ML.

Machine Learning can learn from data autonomously, without explicit instructions.

This has led to the emergence of a new field that combines both quantum computing and ML: Quantum Machine Learning (QML). QML uses quantum computing to improve the performance of classical networks, with the aim of achieving improvements in speed and efficiency. One of the most promising proposals is the creation of hybrid models, i.e. systems in which quantum and classical systems are combined, with the hope of being able to benefit from the strengths of both. In this thesis different hybrid models that combine classical and quantum techniques are tested to verify the possible superiority of quantum machine learning compared to classical methods. However, the latter one has yet to be definitively demonstrated. QML is still a nascent field, with many theoretical and practical challenges to overcome.

The aim of this thesis is the development of a quantum convolutional layer, which represents the quantum version of the classical convolutional layer. The convolutional operation is a fundamental component of neural networks. Its action on input images allows the extraction of features (such as edges, corners etc.) relevant to their classification. This technique is therefore of crucial importance, especially for tasks such as object classification and recognition. My goal is to test whether using a quantum circuit convolutional operation can improve feature extraction. The properties of quantum mechanics, such as superposition and entanglement, allow the creation of highly correlated states. These effects could facilitate a more efficient or expressive representation of features in the data.

The development of this quantum convolutional layer has allowed me to construct a hybrid model: a Quantum Convolutional Neural Network (QCNN) that integrates both classical and quantum layers. Hybrid models exploit the possibility of using both classical optimization techniques, which are extremely efficient, and the advantages of quantum computing.

The QCNN models developed in this work are designed to classify images, with a specific focus on remote sensing imagery captured by satellites.

The thesis is organized as follows: In the first chapter (Chapter 1), I present the fundamentals of quantum computation. The subsequent chapters, Chapter 2 and Chapter 3, introduce the core concepts of Machine Learning and Neural Networks, respectively. This theoretical foundation is essential for transitioning to the topic of Quantum Machine Learning, which is explored in Chapter 4.

This chapter provides the theoretical tools necessary for developing the hybrid model presented in this thesis.

The focus of this work lies in Quantum Convolutional Neural Networks (QCNNs). In Chapter 5, I explain the operation of the quantum convolutional layer, which is key to applying the present approach to an image dataset. This layer forms the foundation for developing various QCNN architectures, whose performance is evaluated to determine the most effective model.

In the thesis I developed multiple QCNN architectures, systematically evaluating their performance to identify the best-performing model. This selected architecture is then benchmarked against a classical convolutional neural network to assess the potential for quantum advantage. Furthermore, I extend the comparison to other hybrid models reported in the literature, particularly those that incorporate only classical convolutional layers. This allows me to understand whether, in the field of hybrid models, quantum convolution may bring benefits.

The QCNN model that seems to perform best is characterized by the presence of two classical convolutional layers, each followed by a classical Max-Pooling operation, and by a quantum convolution layer. The tensor output from the convolutions is then flattened and the final outcome is obtained after the application of three fully connected layers.
The most relevant aspect of the comparison with the Classical Convolutional Neural Network is certainly the significant jump in accuracy observed during the very first epochs of training: while the classical network achieves an accuracy of approximately 52%, my QCNN reaches 85%.

This seems to be a notable quantum advantage.

The fast increase in accuracy is especially valuable in scenarios where early-stage model performance is critical. For example, in applications where fast and reliable preliminary predictions are needed, such as real-time data analysis for resonance detection like X-ray photoelectron spectroscopy data analysi.

This study represents a significant step forward in demonstrating quantum advantages in the field of quantum machine learning. The thesis offers opportunities for further research, for example on the identification of quantum circuits that can improve the performance of QCNNs. In fact, the results reveal the possibility of researching quantum circuits capable of exploring different forms of correlation between qubits, with the aim of improving the effectiveness of extracting the characterizing features and consequently the performance of the network