Quantum machine learning (QML) sits at the intersection of quantum computing and classical machine learning, offering the prospect of new computational paradigms and advantages for processing complex data. This chapter introduces the fundamentals of QML for readers from both communities, establishing a shared conceptual foundation. We connect the worst-case, adversarial perspective from theoretical computer science with the physical principles of quantum systems, highlighting how superposition, entanglement, and measurement collapse influence learning and robustness. Special attention is given to adversarial robustness, understood as the ability of QML models to resist inputs designed to cause failure. We motivate the study of QML in adversarial settings, outlining distinctions between classical and quantum data and computations when the adversary is a core element. This chapter serves as a starting point to adversarial and robust quantum machine learning in subsequent chapters.
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This book chapter has been accepted for Springer Nature Quantum Robustness in Artificial Intelligence and will appear in the book: https://link.springer.com/book/9783032111524#accessibility-information
Quantum machine learning (QML) sits at the intersection of quantum computing and classical machine learning, offering the prospect of new computational paradigms and advantages for processing complex data. This chapter introduces the fundamentals of QML for readers from both communities, establishing a shared conceptual foundation. We connect the worst-case, adversarial perspective from theoretical computer science with the physical principles of quantum systems, highlighting how superposition, entanglement, and measurement collapse influence learning and robustness. Special attention is given to adversarial robustness, understood as the ability of QML models to resist inputs designed to cause failure. We motivate the study of QML in adversarial settings, outlining distinctions between classical and quantum data and computations when the adversary is a core element. This chapter serves as a starting point to adversarial and robust quantum machine learning in subsequent chapters.
Abstract Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers being capable of running quantum machine learning (QML) algorithms has therefore generated intense interest in their adversarial vulnerability. Here we show that quantum properties of QML algorithms can confer fundamental protections against such attacks, in certain scenarios guaranteeing robustness against classically-armed adversaries. We leverage tools from many-body physics to identify the quantum sources of this protection. Our results offer a theoretical underpinning of recent evidence which suggest quantum advantages in the search for adversarial robustness. In particular, we prove that quantum classifiers are: (i) protected against weak perturbations of data drawn from the trained distribution, (ii) protected against local attacks if they are insufficiently scrambling, and (iii) show evidence that they are protected against universal adversarial attacks if they are sufficiently chaotic. Our analytic results are supported by numerical evidence demonstrating the applicability of our theorems and the resulting robustness of a quantum classifier in practice. This line of inquiry constitutes a concrete pathway to advantage in QML, orthogonal to the usually sought improvements in model speed or accuracy.
This chapter introduces the field of quantum machine learning (QML) by outlining its motivations, foundational concepts, and scope. It provides a high-level overview of how quantum computing principles can be leveraged to enhance or reframe learning tasks, and presents a taxonomy of QML approaches based on the type of data and model used. By bridging classical learning theory with quantum computational models, this chapter sets the stage for deeper exploration of algorithms, architectures, and applications in the chapters that follow.
Quantum machine learning sits at the intersection of two paradigm-shifting technologies: quantum computing and deep learning. By exploiting quantum mechanical phenomena – superposition, entanglement, and interference – QML promises exponential or quadratic speedups over classical algorithms for certain learning tasks, as well as the ability to model quantum data natively. However, the path to practical quantum advantage remains contested, constrained by noisy intermediate-scale quantum (NISQ) hardware, limited qubit counts (50–1,000), coherence times (50–500 μs), and high gate error rates (10⁻³–10⁻⁴). This paper provides a rigorous, technically deep survey of QML: mathematical foundations (Hilbert spaces, unitary evolution, measurement, quantum circuits), canonical algorithms (quantum kernel methods, variational quantum circuits (VQCs), quantum neural networks (QNNs), QSVMs, quantum generative adversarial networks (QGANs), encoding strategies (angle, amplitude, basis, and Hamiltonian encoding), optimization landscapes (barren plateaus, parameter shift rules, ansatz design), hardware aware implementation on superconducting (IBM, Google), trapped ion (IonQ), and neutral atom (Pasqal) platforms, empirical benchmarks on near term devices for classification, generative modeling, and quantum chemistry, and pathways to fault tolerant quantum machine learning (FTQML) with error correction (surface codes, logical qubits). Researchers critically assess claims of quantum advantage, identify scenarios where QML may outperform classical ML (small data, high-dimensional feature spaces from quantum systems, kernel estimation), and propose concrete evaluation metrics (quantum-classical cross-validation, resource estimation).
Artificial Intelligence has achieved remarkable success across diverse application domains. However, its vulnerability to adversarial attacks poses significant challenges to reliability, security, and trustworthiness. Adversarial machine learning demonstrates that even highly accurate models can be manipulated through carefully crafted perturbations, raising serious concerns in safety critical systems such as healthcare, finance, and autonomous technologies. In parallel, quantum computing has emerged as a transformative paradigm capable of addressing complex computational problems through principles such as superposition, entanglement, and quantum interference. The convergence of these fields has led to the emergence of quantum artificial intelligence, which explores how quantum techniques can enhance learning efficiency, scalability, and robustness. This chapter provides a comprehensive overview of adversarial machine learning and existing defense strategies, followed by an accessible introduction to quantum computing and quantum machine learning models. It further presents conceptual frameworks for quantum-enhanced adversarial robustness, emphasizing quantum optimization, feature mapping, and hybrid quantum classical architectures. Practical applications, key challenges, and future research directions are also discussed to support the development of secure and trustworthy AI systems.
The rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.
The integration of quantum computing with machine learning emerged as an approach to solving complex computational problems. This chapter provides an overview of quantum machine learning (QML), exploring the fundamental concepts, algorithms, and applications at the intersection of quantum computing and machine learning. We begin by introducing the basic principles of quantum mechanics relevant to QML, including qubits, quantum gates, and quantum parallelism. Then, we explore key topics such as quantum entanglement, superposition, and their role in quantum algorithms. We then discuss the landscape of QML, contrasting classical and quantum approaches and highlighting the potential of quantum computing to enhance machine learning algorithms. Furthermore, we discuss prominent QML algorithms, such as quantum support vector machines (QSVM) and quantum neural networks (QNN), elucidating their mathematical formulations and differences from classical counterparts. Real-world examples showcasing quantum speedup in machine learning tasks are presented to underscore the transformative potential of quantum computing. Finally, an overview of QML tools and frameworks is provided, enabling researchers to embark on their journey in exploring the exciting field of QML.