This chapter describes the usage of ML to study condensed matter. ML is shown to accelerate the sampling of spin glass configurations in computer simulations by up to five orders of magnitude. On the analysis side, ML is very efficient for evaluating the output of simulations of topological order transitions. The latter are characterized by the temperature-driven unbinding of vortex/antivortex pairs. Such transitions may be detected by analyzing configurations using neural networks implemented with the aim of learning vortices. Incorporated in the heart of computer simulations, ML is used to study quantum many-body systems. Here, the mathematical object describing the quantum-mechanical state of a system – the many-body wave function – is implemented in a neural-network representation. Away from pure theory, ML allows the quantum state of a system to be reconstructed based on experimental measurements. Here, the experimental data are used to train a neural network via unsupervised learning to output the state as a neural-network quantum state. As a more technological application, ML is efficient in predicting new materials with desired properties. Neural networks or other ML techniques enable the prediction of thermodynamically stable compounds with a desired structure by searching over the entire compound space.
This chapter describes the usage of ML to study condensed matter. ML is shown to accelerate the sampling of spin glass configurations in computer simulations by up to five orders of magnitude. On the analysis side, ML is very efficient for evaluating the output of simulations of topological order transitions. The latter are characterized by the temperature-driven unbinding of vortex/antivortex pairs. Such transitions may be detected by analyzing configurations using neural networks implemented with the aim of learning vortices. Incorporated in the heart of computer simulations, ML is used to study quantum many-body systems. Here, the mathematical object describing the quantum-mechanical state of a system – the many-body wave function – is implemented in a neural-network representation. Away from pure theory, ML allows the quantum state of a system to be reconstructed based on experimental measurements. Here, the experimental data are used to train a neural network via unsupervised learning to output the state as a neural-network quantum state. As a more technological application, ML is efficient in predicting new materials with desired properties. Neural networks or other ML techniques enable the prediction of thermodynamically stable compounds with a desired structure by searching over the entire compound space.
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.
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 simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
Quantum fluids, such as superfluid helium and Bose-Einstein condensates (BECs), exhibit a range of complex quantum phenomena that challenge traditional modeling techniques. These systems involve highly nonlinear interactions especially for thermal changes, many-body correlations, and quantum entanglement, making their accurate simulation and analysis a formidable task. Over the past decade, artificial intelligence (AI), particularly machine learning (ML), has emerged as a transformative tool in addressing these challenges, offering new avenues for simulation, data analysis, and experimental optimization. In this article, we focus on the multifaceted role of AI in quantum fluid research. We explore how AI enhances simulation accuracy and efficiency through models like neural networks approximating wave functions and physics-informed neural networks (PINNs) that embed fundamental quantum laws into predictive frameworks. AI techniques such as reinforcement learning (RL) facilitate dynamic control in experiments, optimizing parameters like magnetic fields to stabilize quantum states. Data analysis methods including deep learning for pattern recognition, unsupervised clustering, and dimensionality reduction enable researchers to interpret large, multidimensional datasets, revealing hidden phase transitions, vortex structures, and turbulence phenomena. Furthermore, neural operators and foundation models offer rapid, scalable predictions of quantum dynamics and phase behaviors, accelerating discovery and understanding. Our paper highlights the advantages of AI over traditional methods, including reduced computational costs, improved scalability, and enhanced interpretability. Despite current limitations, ongoing developments point toward increasingly sophisticated AI-driven approaches that will deepen insights into quantum hydrodynamics, superfluid thermodynamics, and quantum turbulence. The merging of AI into quantum fluid research promises to unlock new levels of control and understanding, ultimately advancing quantum technology applications such as quantum computing, sensing, and cryogenics. As AI algorithms and experimental techniques continue to evolve, their synergy will play a critical role in shaping the future of quantum fluid physics.
Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.
Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.