This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems.
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief summary of quantum computing and an in-depth analysis of variational quantum algorithms. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models. Next, several novel contributions to the field based on previous work are presented, namely: a newly introduced model for a quantum perceptron with applications to recognition and classification tasks; a variational generalization of such a model to reduce the circuit footprint of the proposed architecture; an industrial use case of a quantum autoencoder followed by a quantum classifier used to analyze classical data from an industrial power plant; a study of the entanglement features of quantum neural network circuits; and finally, a noise deconvolution technique to remove a large class of noise when performing arbitrary measurements on qubit systems.
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 advancement of artificial intelligence has positioned Machine Learning (ML) as a cornerstone technology across scientific and industrial domains. In parallel, the emergence of quantum computing has catalyzed a new interdisciplinary field—Quantum Machine Learning (QML)—which promises to transcend the computational barriers faced by classical algorithms. This review paper systematically examines the evolution of ML from foundational statistical models to contemporary transformer architectures, and provides a structured analysis of QML paradigms including variational quantum circuits (VQCs), quantum kernel methods, and quantum neural networks (QNNs). Drawing from 95+ peer-reviewed publications indexed in Scopus and Science Citation Index (SCI) journals—with particular emphasis on 2025–2026 publications in IEEE Access, Nature Communications, Nature Computational Science, and Physical Review Letters—we analyze performance benchmarks, identify hardware constraints, and outline algorithmic innovations shaping the near-term quantum advantage landscape. Our findings indicate that while classical ML retains superiority in large-scale perception tasks, QML demonstrates significant advantages in combinatorial optimization and quantum chemistry simulation. Recent 2025 advances in error mitigation on superconducting qubits and improved VQC barren-plateau mitigation are narrowing this gap rapidly. The paper concludes with a forward-looking research agenda covering fault-tolerant QML, hybrid architectures, and quantum NLP.
Despite its undeniable success, classical machine learning remains a resource-intensive process. Practical computational efforts for training state-of-the-art models can now only be handled by high speed computer hardware. As this trend is expected to continue, it should come as no surprise that an increasing number of machine learning researchers are investigating the possible advantages of quantum computing. The scientific literature on Quantum Machine Learning is now enormous, and a review of its current state that can be comprehended without a physics background is necessary. The objective of this study is to present a review of Quantum Machine Learning from the perspective of conventional techniques. Departing from giving a research path from fundamental quantum theory through Quantum Machine Learning algorithms from a computer scientist's perspective, we discuss a set of basic algorithms for Quantum Machine Learning, which are the fundamental components for Quantum Machine Learning algorithms. We implement the Quanvolutional Neural Networks (QNNs) on a quantum computer to recognize handwritten digits, and compare its performance to that of its classical counterpart, the Convolutional Neural Networks (CNNs). Additionally, we implement the QSVM on the breast cancer dataset and compare it to the classical SVM. Finally, we implement the Variational Quantum Classifier (VQC) and many classical classifiers on the Iris dataset to compare their accuracies.
This thesis presents original contributions at the intersection of quantum computing and machine learning, investigating how these two fields can benefit from each other. The first part of the thesis presents two applications of machine learning techniques in quantum computing. The first contribution involves the use of artificial neural networks for the decoding of quantum error correction codes, resulting in faster decoding times while maintaining a high level of accuracy. The originality of this work lies in the application of explainable machine learning techniques to both improve the decoding performance and to provide insights into the decoding process. The second contribution introduces a novel technique based on reinforcement learning to characterize and simulate the noise affecting a quantum chip. This technique reduces the heuristic assumption on the noise model, making it more adaptable to the specific noise characteristics of the quantum device. In the second part of the thesis, we demonstrate, with two examples, how it is possible to implement machine learning algorithms on quantum devices by replacing artificial neural networks with parametrized quantum circuits. The first contribution in this section introduces a quantum anomaly detection algorithm, applied to the field of high-energy physics. This algorithm allows for the identification of anomalous patterns in quantum data, maintaining a level of accuracy comparable to classical algorithms. The novelty of this work lies in the first use of quantum circuits for the task of anomaly detection in a muon drift chamber trigger system, with possible future applications to quantum detector systems in high-energy physics experiments. The second contribution presents the quantum version of a generative diffusion model, able to sample quantum states from a well-defined distribution. This first implementation of a quantum diffusion model is not meant to outperform classical models, but rather to show potential advantages and limitations of these kinds of algorithms. The aim of the thesis is to show how quantum computing can benefit from machine learning, and how machine learning can be implemented on quantum devices, setting the stage for future advancements in both fields.
There has been remarkable development in the data-driven decision-making domain of Artificial Intelligence (AI). However, the complexity of the AI models and the amount of data have shown some drawbacks with conventional computing models. One of the interdisciplinary branches of quantum computing and machine learning is Quantum Machine Learning (QML), which is a combination of quantum computing and machine learning and relies on the unique characteristics of quantum computing, such as superposition, entanglement, and quantum parallelism, to enhance the performance of the machines. This review provides a comprehensive description of theory, architectures, algorithms, implementational approaches, applications, problems, and future directions of QML. The core concepts of quantum computing and machine learning are introduced. Different representations of quantum states, quantum data encoding, variational quantum circuits, quantum kernel methods, and hybrid quantum or classical optimization are discussed. Significant QML algorithms like Quantum Support Vector Machines, Quantum Neural Networks, Variational Quantum Eigen solvers, Quantum Approximate Optimization Algorithms, and Quantum reinforcement learning are explored and evaluated for computational power and applications. The scaling up of quantum computer sizes, data encoding overhead, complexity of optimizations, benchmarking, and decoherence are discussed in detail, as well as recent developments in fault-tolerant quantum computing and hybrid learning approaches. Finally, a conceptual framework is given to demonstrate the unification of classical computation and quantum computation to intelligently process data. This review demonstrates how QML could be the next-generation computational method to accelerate scientific advancements and enable new advanced AI technologies.
In the past few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of quantum machine learning aims at bringing together these two ongoing revolutions. Here, we first review a series of recent works describing the implementation of artificial neurons and feedforward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. We investigate different learning strategies involving global and local layerwise cost functions, and we assess their performances also in the presence of statistical measurement noise. While keeping full compatibility with the overall memory-efficient feedforward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach toward the use of quantum neural networks for pattern classification on near-term quantum hardware.