Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.
Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.
Configurable arrays of optically trapped Rydberg atoms are a versatile platform for quantum computation and quantum simulation, also allowing controllable decoherence. We demonstrate theoretically that they also enable proof-of-principle demonstrations for a technique to build models for open quantum dynamics using machine learning with artificial neural networks, recently proposed by Mukherjee et al. [Quantum Sci. Technol. 10, 02LT01 (2025)]. Using the outcome of quantum transport through a network of sites that correspond to excited Rydberg atoms, the multistage neural-network algorithm successfully identifies the number of atoms (or nodes in the network) and, subsequently, their location. It further extracts an effective interaction Hamiltonian and decoherence operators induced by the environment. To probe the Rydberg array, one initiates dynamics repeatedly from the same initial state and then measures the transport probability to an output atom. Large datasets are generated by varying the position of the latter. Measurements are required in only one single basis, making the approach complementary to, e.g., quantum process tomography. Due to steeply increasing requirements for training data size, the present implementation appears best suited for networks of just a few sites. The cold-atom platform discussed in this article can be used to explore the performance of the proposed protocol when training the neural network with simulation data but then applying it to construct models based on experimental data.
In quantum mechanical systems with exponentially large Hilbert space, the need to represent and identify states of quantum many-body system with few variables is of significant importance. The representation and identification of the states are based on the spin configurations of the ferromagnetic Ising model without knowledge of the respective Hamiltonian. The state identification process is of high importance in quantum technology applications and testing such as D-wave machine comparison to classical optimization algorithms using large number of qubits. This paper proposes a new method to classify phases and phase transitions in condensed matter systems, which can further be used in quantum technologies to identify the state of qubits. The proposed method is based on the combination of Principle component analysis (PCA) and support vector machine (SVM). The simulation results of the proposed method show that the trained model is able to identify the phase and phase transition with high accuracy in different Ising spin topologies with a variety of lattice sizes, while reducing the dimensionality of the feature space compared to existing optimization methods.
As ultracold atom experiments become highly controlled and scalable quantum simulators, they require sophisticated control over high-dimensional parameter spaces and generate increasingly complex measurement data that need to be analyzed and interpreted efficiently. Machine learning (ML) techniques have been established as versatile tools for addressing these challenges, offering strategies for data interpretation, experimental control, and theoretical modeling. In this review, we provide a perspective on how machine learning is being applied across various aspects of quantum simulation, with a focus on cold atomic systems. Emphasis is placed on practical use cases -- from classifying many-body phases to optimizing experimental protocols and representing quantum states -- highlighting the specific contexts in which different ML approaches prove effective. Rather than presenting algorithmic details, we focus on the physical insights enabled by ML and the kinds of problems in quantum simulation where these methods offer tangible benefits.
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 Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network (NN) and a conventional NN and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: H 2 with four orbitals, LiH with five orbitals, and H 4 with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and NNs) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.
Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM)\nis closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.