Classifying different phases and the transitions between them is a major task in condensed matter physics. Machine learning, which has achieved dramatic success recently in a broad range of artificial intelligence applications, may bring an unprecedented perspective for this challenging task. In this paper, we study the robustness of this intriguing machine-learning approach to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial examples: adding a tiny amount of carefully-crafted noises, which are imperceptible to human eyes and ineffective to traditional methods, into the original legitimate data obtained from numerical simulations or real experiments will cause the classifiers to make incorrect predictions at a notably high confidence level. Our results reveal a novel vulnerability aspect in applying machine learning techniques to condensed matter physics, which provides a valuable guidance for both theoretical and experimental future studies along this direction.
Classifying different phases and the transitions between them is a major task in condensed matter physics. Machine learning, which has achieved dramatic success recently in a broad range of artificial intelligence applications, may bring an unprecedented perspective for this challenging task. In this paper, we study the robustness of this intriguing machine-learning approach to adversarial perturbations, with a focus on supervised learning scenarios. We find that typical phase classifiers based on deep neural networks are extremely vulnerable to adversarial examples: adding a tiny amount of carefully-crafted noises, which are imperceptible to human eyes and ineffective to traditional methods, into the original legitimate data obtained from numerical simulations or real experiments will cause the classifiers to make incorrect predictions at a notably high confidence level. Our results reveal a novel vulnerability aspect in applying machine learning techniques to condensed matter physics, which provides a valuable guidance for both theoretical and experimental future studies along this direction.
The identification and characterization of phase transitions is one of the oldest and most central problems in condensed matter physics, traditionally approached through order parameters, free-energy expansions, renormalization-group analysis, and direct numerical simulation. Over the past decade, machine learning (ML) has emerged as a complementary and, in some regimes, transformative methodology for this task. Supervised classifiers can learn to distinguish phases directly from raw configurations without an a priori order parameter; unsupervised and self-supervised techniques such as principal component analysis, autoencoders, and learning-by-confusion can locate transition points with minimal or no labeled data; and generative and variational architectures, including neural-network quantum states, now approximate ground-state wavefunctions of strongly correlated systems well beyond the reach of exact diagonalization. This paper reviews the theoretical foundations of phase transitions relevant to machine-learning applications, surveys the principal families of algorithms used to detect and classify phases, and examines their application across classical spin systems, percolation, topological and quantum phases, strongly correlated electron systems, and experimentally measured spectroscopic data. Representative case studies are discussed, including convolutional and graph-neural-network classifiers of lattice configurations, explainable-ML detection of thermodynamic transitions in photoemission spectra, and deep-learning-guided discovery of high-temperature superconductors. The review closes with a critical discussion of persistent challenges interpretability, data scarcity in correlated-electron experiments, generalization across Hamiltonians, and the reliability of learned order parameters near criticality and outlines directions for future research, including physics-informed architectures, uncertainty quantification, and closed-loop integration with autonomous experimentation.
Abstract Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could outperform classical computers in solving certain notable machine learning tasks. Yet, quantum learning systems may also suffer from the vulnerability problem: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we study the universality of adversarial examples and perturbations for quantum classifiers. Through concrete examples involving classifications of real-life images and quantum phases of matter, we show that there exist universal adversarial examples that can fool a set of different quantum classifiers. We prove that for a set of k classifiers with each receiving input data of n qubits, an O(2nlnk) increase of the perturbation strength is enough to ensure a moderate universal adversarial risk. In addition, for a given quantum classifier we show that there exist universal adversarial perturbations, which can be added to different legitimate samples and make them to be adversarial examples for the classifier. Our results reveal the universality perspective of adversarial attacks for quantum machine learning systems, which would be crucial for practical applications of both near-term and future quantum technologies in solving machine learning problems.
Quantum artificial intelligence exploits the interplay between artificial intelligence and quantum physics: on the one hand, a plethora of tools and ideas from artificial intelligence can be adopted to tackle intricate quantum problems; on the other hand, quantum computing could also bring unprecedented opportunities to enhance, speed up, or innovate artificial intelligence. Yet, quantum learning systems, similar to classical ones, may also suffer adversarial attacks: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we introduce the basic concepts and ideas of classical and quantum adversarial learning, as well as some recent advances along this line. First, we introduce the basics of both classical and quantum adversarial learning. Through concrete examples, involving classifications of phases of two-dimensional Ising model and three-dimensional chiral topological insulators, we reveal the vulnerability of classical machine learning phases of matter. In addition, we demonstrate the vulnerability of quantum classifiers with the example of classifying hand-written digit images. We theoretically elucidate the celebrated no free lunch theorem from the classical and quantum perspectives, and discuss the universality properties of adversarial attacks in quantum classifiers. Finally, we discuss the possible defense strategies. The study of adversarial learning in quantum artificial intelligence uncovers notable potential risks for quantum intelligence systems, which would have far-reaching consequences for the future interactions between the two areas.
Identifying phase transitions and classifying phases of matter is central to understanding the properties and behavior of a broad range of material systems. In recent years, machine-learning (ML) techniques have been successfully applied to perform such tasks in a data-driven manner. However, the success of this approach notwithstanding, we still lack a clear understanding of ML methods for detecting phase transitions, particularly of those that utilize neural networks (NNs). In this work, we derive analytical expressions for the optimal output of three widely used NN-based methods for detecting phase transitions. These optimal predictions correspond to the results obtained in the limit of high model capacity. Therefore, in practice they can, for example, be recovered using sufficiently large, well-trained NNs. The inner workings of the considered methods are revealed through the explicit dependence of the optimal output on the input data. By evaluating the analytical expressions, we can identify phase transitions directly from experimentally accessible data without training NNs, which makes this procedure favorable in terms of computation time. Our theoretical results are supported by extensive numerical simulations covering, e.g., topological, quantum, and many-body localization phase transitions. We expect similar analyses to provide a deeper understanding of other classification tasks in condensed matter physics.
The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as powerful tools to complement these standard approaches, offering valuable insights into phase and structure determination. Additionally, they have been shown to enhance the application of traditional methods. In this work, we review recent advancements in this area, with a focus on our contributions to phase and structure determination using supervised and unsupervised learning methods in several systems: (a) 2D site percolation, (b) the 3D Anderson model of localization, (c) the 2D J1-J2 Ising model, and (d) the prediction of large-angle convergent beam electron diffraction patterns.
State-of-the-art classical neural networks are observed to be vulnerable to small crafted adversarial perturbations. A more severe vulnerability has been noted for quantum machine learning (QML) models classifying Haar-random pure states. This stems from the concentration of measure phenomenon, a property of the metric space when sampled probabilistically, and is independent of the classification protocol. To provide insights into the adversarial robustness of a quantum classifier on real-world classification tasks, we focus on the adversarial robustness in classifying a subset of encoded states that are smoothly generated from a Gaussian latent space. We show that the vulnerability of this task is considerably weaker than that of classifying Haar-random pure states. In particular, we find only mildly polynomially decreasing robustness in the number of qubits, in contrast to the exponentially decreasing robustness when classifying Haar-random pure states and suggesting that QML models can be useful for real-world classification tasks.