Fundamentals of Quantum Machine Learning and Robustness

TL;DR

This chapter introduces the fundamentals of QML for readers from both communities, establishing a shared conceptual foundation and motivating the study of QML in adversarial settings, outlining distinctions between classical and quantum data and computations when the adversary is a core element.

Abstract

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.

Figures (3)

• Figure 1: A conceptual map positions learning settings along data generation, computation mode, and complexity analysis dimensions, showing where adversarial models naturally arise (such as the shaded area in orange) and why robustness considerations may vary across this spectrum.
• Figure 2: Taxonomy of quantum machine learning approaches. This diagram maps QML methods along two axes: the nature of the data (classical or quantum) and the computational resource (classical or quantum). The top-right quadrant corresponds to quantum-enhanced machine learning, where quantum models are applied to classical data. The bottom-right represents machine learning for quantum data, where quantum systems or outputs are analyzed. Classical machine learning occupies the top-left along with quantum-inspired classical models, while the bottom-left includes classical models used to support quantum computing tasks such as control and error correction.
• Figure 3: Extension of the quantum-classical data-device paradigm to adversarial settings. The figure illustrates classical vs. quantum distinctions along the well-known data (vertical) and device (horizontal) axes, and introduces the adversary as a third component. This extension makes it possible to ask systematic questions such as: How does the nature of the adversary change when data or computation is quantum?Which attack surfaces exist in each quadrant? In this way, the framework helps map out where robustness challenges and opportunities arise in hybrid quantum–classical learning systems.