The work presented in this thesis is focused on quantum computing and in particular on the interplay between quantum devices and machine learning. This interaction gives birth to a relatively recent area of study, called Quantum Machine Learning (QML), which currently represents a hot research field. This work was carried out in collaboration with an important company with home in Turin, DATA Reply S.r.l., whose main focuses are Big Data, Artificial Intelligence, Machine Learning and Quantum Computing. We start by introducing the fundamental concepts of quantum mechanics, presenting the topic in a formal way from a mathematical point of view while keeping things as simple as possible, as long as they allow us to understand quantum computing basics. After an overview on motivations, possible employments of quantum devices and an analysis of risks and benefits of their development, we proceed to explain quantum computing main concepts, such as qubits and quantum gates. The introduced formalism is the so-called Discrete Variable (DV) formalism, which is the most prominent choice in literature for describing quantum systems. However, as extensively explained during the course of this work, this approach presents several drawbacks: one of the main goals of this thesis is to introduce the alternative formalism of Continuous Variables (CV) and investigate how it can contribute to improve this research area. Currently, one of the preferred tools for quantum machine learning algorithms are the Variational - or Parametrized - circuits: they allow to train the quantum devices in the same way as a classical neural network and allow to address ML problems, both supervised and unsupervised. After a detailed description of these tools, we proceed to introduce PennyLane, a Python library for QML which is very well suited for dealing with variational circuits. In the core part of this work, we concentrate on some QML examples, in particular we analyze some applications in which using the CV formalism turns out to be the most convenient choice. Integration, more specifically Monte Carlo integration, is one of those fields which the CV formalism suits best; in a similar way, Gaussian process regression in its continuous variables version provides a great advantage, namely an exponential speedup, as long as some hypothesis are satisfied. We only provide a brief overview of these applications, since we opted to leave more room to experiments involving variational classifiers and quantum neural networks. Three use cases are analyzed, all involving the CV formalism. The first one is a variational classifier, employed in a supervised setting for the classification of a simple dataset. The second one is a quantum neural network, used to solve a problem of function fitting. The results and the chosen hyperparameters are presented, together with a formal explanation of the theoretical concepts behind them. The last use case, the most complex and detailed one, focuses on a time series forecasting task, carried out with a quantum neural network, and also presents a comparison with the classical approach.
The work presented in this thesis is focused on quantum computing and in particular on the interplay between quantum devices and machine learning. This interaction gives birth to a relatively recent area of study, called Quantum Machine Learning (QML), which currently represents a hot research field. This work was carried out in collaboration with an important company with home in Turin, DATA Reply S.r.l., whose main focuses are Big Data, Artificial Intelligence, Machine Learning and Quantum Computing. We start by introducing the fundamental concepts of quantum mechanics, presenting the topic in a formal way from a mathematical point of view while keeping things as simple as possible, as long as they allow us to understand quantum computing basics. After an overview on motivations, possible employments of quantum devices and an analysis of risks and benefits of their development, we proceed to explain quantum computing main concepts, such as qubits and quantum gates. The introduced formalism is the so-called Discrete Variable (DV) formalism, which is the most prominent choice in literature for describing quantum systems. However, as extensively explained during the course of this work, this approach presents several drawbacks: one of the main goals of this thesis is to introduce the alternative formalism of Continuous Variables (CV) and investigate how it can contribute to improve this research area. Currently, one of the preferred tools for quantum machine learning algorithms are the Variational - or Parametrized - circuits: they allow to train the quantum devices in the same way as a classical neural network and allow to address ML problems, both supervised and unsupervised. After a detailed description of these tools, we proceed to introduce PennyLane, a Python library for QML which is very well suited for dealing with variational circuits. In the core part of this work, we concentrate on some QML examples, in particular we analyze some applications in which using the CV formalism turns out to be the most convenient choice. Integration, more specifically Monte Carlo integration, is one of those fields which the CV formalism suits best; in a similar way, Gaussian process regression in its continuous variables version provides a great advantage, namely an exponential speedup, as long as some hypothesis are satisfied. We only provide a brief overview of these applications, since we opted to leave more room to experiments involving variational classifiers and quantum neural networks. Three use cases are analyzed, all involving the CV formalism. The first one is a variational classifier, employed in a supervised setting for the classification of a simple dataset. The second one is a quantum neural network, used to solve a problem of function fitting. The results and the chosen hyperparameters are presented, together with a formal explanation of the theoretical concepts behind them. The last use case, the most complex and detailed one, focuses on a time series forecasting task, carried out with a quantum neural network, and also presents a comparison with the classical approach.
Quantum Computing (QC) was born as a purely theoretical subject. Thus, in the beginning, the main category of researchers in the area was physicists and mathematicians. Since IBM introduced the first quantum computer, global interest in this emerging technology has been growing more and more, involving computer science and engineering researchers. Machine learning is another rapidly growing technology, used in a wide range of applications where traditional computing is not sufficient. The two technologies are merged in the thesis work. The different ways in which a combination of them can occur are discussed, as well as the explanation why there is not a single definition of Quantum Machine Learning (QML). Firstly, quantum computing is examined in depth. The basic elements of quantum computation theory, based on the fundamental principles of quantum mechanics, are introduced. The attention is focused on the qubit description on the Bloch sphere, the fundamental quantum gates, and examples of quantum algorithms. Therefore, the differences between quantum simulators and quantum processors are analysed, including the frameworks that provide tools to interact with them. Focusing on Quantum Machine Learning, the different definitions of the technology are described. There are four distinct approaches that are differentiated by the type of data used (quantum or classical) and by the device processing them (quantum or classical). In this thesis, QML is defined as the approach that uses classical data to feed a quantum device. The two possible methods for developing QML algorithms are: 1) to translate existing classical models into the terms of quantum computing; 2) to leave the existing models of classical machine learning completely, and explore new possible ways of doing QML to take full advantage of the physical characteristics of a quantum computer. The strategy adopted is the first one, thus it is used a state-of-the-art hybrid model of Quanvolutional Neural Network (QNN), composed of both quanvolutional and classical convolutional layers. The quanvolutional layers reproduce the same concept of the classical ones: they are made of quantum filters that generate feature maps through locally transforming input data. The transformation can be performed by variational quantum circuits or random quantum circuits. The specific field where Quantum Machine Learning is applied is image classification. The considered case study is a labeled dataset with X-ray images of lungs (labels: pneumonia, normal). The images are pre-processed and cropped for being used by quantum circuits, thus some information is lost. The main aim of the thesis is to understand whether and in which ways Quantum Machine Learning could bring advantages in the mentioned classification in terms of timing, accuracy, or dataset reduction, despite the large decrease in images' resolution. Different configurations of the hybrid model (with a different number of quantum filters and different settings of convolutional layers) are analysed and tested. The current quantum devices have many limitations, thus the time is still immature to observe a significant change in perspective. Nevertheless, the obtained results are promising for the future of QML in terms of dataset and hyperparameters reduction.
Quantum machine learning (QML) provides a transformative approach to data analysis by integrating the principles of quantum computing with classical machine learning methods. With the exponential growth of data and the increasing complexity of computational tasks, quantum algorithms offer tremendous advantages in terms of processing speed, memory efficiency, and the ability to resolve issues intractable for classical systems. In this work, the use of QML techniques for both supervised and unsupervised learning problems is explored. Quantum-enhanced models such Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) show outstanding performance in classification and regression tasks by using quantum kernels and entanglement in supervised learning. Moreover, hybrid quantum-classical solutions offer useful implementations on noisy intermediate-scale quantum (NISQ) devices, hence bridging the gap between present quantum technology and practical uses. By means of comparative analysis, this paper emphasizes the possible benefits and drawbacks of QML, thereby providing understanding of its future importance in sectors including material science, finance, and healthcare. In the end, QML opens the path for a new era of intelligent data processing and solves until unthinkable difficult challenges.
Continuous Variable-based Quantum Computing (CVQC) has been developing at speed with a lot of promise in the field of quantum machine learning. It provides a direct and natural way to accommodate continuous values into the quantum computing framework. We carried out experiments on quantum simulators where we compared the results of time series forecasting on a type of continuous-variable quantum variational circuit, called CV-Quantum Neural Networks (CVQNN) for different types of time series like Energy Consumption data and stock price data. We compared their performance with a discrete variable-based variational quantum algorithm as well as with a classical Neural Network. Experiments showed that CVQNN can function just like a neural network but with a lesser number of parameters while tackling the two obstacles that are faced in qubit-based computing, which are, tackling continuous values and introducing controlled non-linearity into the circuits. We used the circuit for multi-step forecasting that performed better for a larger prediction window than one-step forecasting done iteratively on the predicted data. The resembling architecture of CVQNN with that of a neural network offers the flexibility of using a similar structure for both one-step and multi-step forecasting.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
Abstract Quantum Machine Learning (QML) is an emerging interdisciplinary field that merges quantum computing with classical machine learning (ML) to enhance computational efficiency, scalability, and accuracy in data-driven tasks. By leveraging quantum properties such as superposition, entanglement, and quantum parallelism, QML has the potential to solve complex problems that are intractable for classical models. This survey provides a comprehensive, systematic review of recent advancements in QML, conducted following the PRISMA 2020 guidelines and covering fundamental encoding techniques that enable quantum computers to process classical data, as well as essential tools, datasets, and evaluation metrics used in quantum model development. Furthermore, it explores various QML approaches, including supervised, semi-supervised, unsupervised, and reinforcement learning, alongside quantum deep learning (QDL) models such as Quantum Neural Networks (QNNs) and Variational Quantum Circuits (VQCs). The paper also discusses the challenges in QML, including hardware limitations, scalability issues, and the need for improved quantum error correction. A dual-axis taxonomy simultaneously classifies algorithms by learning paradigm and quantum-classical integration level – a structure not found in prior surveys. The survey also covers Quantum Transfer Learning, Quantum Graph Neural Networks, and hardware-aware encoding selection, and introduces the first structured adversarial robustness taxonomy and Explainable QML treatment in a comprehensive QML survey. Together, these contributions position this work as both a reference and a methodological guide for advancing QML research and applications.
Quantum machine learning (QML) represents a cutting-edge convergence of quantum computing and artificial intelligence, aiming to leverage quantum phenomena such as superposition, entanglement, and quantum parallelism to enhance machine learning algorithms. By exploiting the computational advantages of quantum systems, QML offers the potential for exponential speedups in data processing, optimization, and pattern recognition tasks, particularly for high-dimensional and complex datasets. This article explores the foundational principles, algorithmic approaches, and practical applications of quantum machine learning across domains including finance, chemistry, drug discovery, optimization, and natural language processing. It discusses quantum-enhanced supervised and unsupervised learning, quantum neural networks, variational quantum algorithms, and hybrid quantum-classical architectures. Additionally, the article addresses challenges related to hardware limitations, noise, scalability, and interpretability, as well as the emerging trends in near-term quantum devices, quantum simulators, and integration with classical AI pipelines. Quantum machine learning holds the promise of revolutionizing computational intelligence, offering transformative capabilities for solving problems that are currently intractable for classical systems.