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We extract a variable $X$ from electron orbitals ${\mathrm{\Psi }}_{n\mathbf{k}}$ and energies $E_{n\mathbf{k}}$ in the parent high-symmetry structure of a wide range of complex oxides: perovskites, rutiles, pyrochlores, and cristobalites. Even though calculation was done only in the parent structure, with no distortions, we show that $X$ dictates material's true ground-state structure. We propose using Wannier functions to extract concealed variables such as $X$ both for material structure prediction and for high-throughput approaches.

The calculation of interaction integrals is a bottleneck for the treatment of many-body quantum systems due to its high numerical cost. We conduct configuration interaction calculations of the few-electron states confined in III-V semiconductor two-dimensional structures using a shallow neural network to calculate the two-electron integrals, which can be used for general isotropic interaction potentials. This approach allows for a speedup of the evaluation of the energy levels and controllable accuracy.

Collider signals of dark photons are an exciting probe for new gauge forces and are characterized by events with boosted lepton jets. Existing techniques are efficient in searching for muonic lepton jets but due to substantial backgrounds have difficulty constraining lepton jets containing only electrons. This is unfortunate since upcoming intensity frontier experiments are sensitive to dark photon masses which only allow electron decays. Analyzing a recently proposed model of kinetic mixing, with new scalar particles decaying into dark photons, we find that existing techniques for electron jets can be substantially improved. We show that using lepton-jet-substructure variables, in association with a boosted decision tree, improves background rejection, significantly increasing the LHC’s reach for dark photons in this region of parameter space.

We implement a divide-and-concur iterative projection approach to context-free grammar inference. Unlike most state-of-the-art models of natural language processing, our method requires a relatively small number of discrete parameters, making the inferred grammar directly interpretable—one can read off from a solution how to construct grammatically valid sentences. Another advantage of our approach is the ability to infer meaningful grammatical rules from just a few sentences, compared to the hundreds of gigabytes of training data many other models employ. We demonstrate several ways of applying our approach: classifying words and inferring a grammar from scratch, taking an existing grammar and refining its categories and rules, and taking an existing grammar and expanding its lexicon as it encounters new words in new data.

A disciplinary profile of a country is defined as the versor whose components are the number of papers produced in a given discipline divided by the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject areas, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals 1988–1988 and 1992–2017, the fall of the Berlin Wall being the watershed. We analyze the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized $n_d$-dimensional Heisenberg model. The set of network interactions of the Heisenberg model has been inferred and to it, two clusterization methods, hierarchical clustering, and principal component analysis have been applied. This allows obtaining a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to a deeper historical analysis. In order to obtain the optimal set of pairwise interactions, we used a pseudolikelihood approach. We analytically computed the pseudolikelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving an $n_d$-dimensional Heisenberg model.

We study a phase transition in parameter learning of hidden Markov models (HMMs). We do this by generating sequences of observed symbols from given discrete HMMs with uniformly distributed transition probabilities and a noise level encoded in the output probabilities. We apply the Baum-Welch (BW) algorithm, an expectation-maximization algorithm from the field of machine learning. By using the BW algorithm we then try to estimate the parameters of each investigated realization of an HMM. We study HMMs with $n=4,8,$ and 16 states. By changing the amount of accessible learning data and the noise level, we observe a phase-transition-like change in the performance of the learning algorithm. For bigger HMMs and more learning data, the learning behavior improves tremendously below a certain threshold in the noise strength. For a noise level above the threshold, learning is not possible. Furthermore, we use an overlap parameter applied to the results of a maximum a posteriori (Viterbi) algorithm to investigate the accuracy of the hidden state estimation around the phase transition.

We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local external fields. More precisely, the appropriate combination of the algebraic transformations, namely the star-triangle and decoration-iteration transformations, allows one to express the model in terms of fewer-spin interactions at the expense of the degrees of freedom. Furthermore, the benefit of the mapping in Monte Carlo simulations is discussed. In particular, we demonstrate that the application of the method in conjunction with the Swendsen-Wang algorithm drastically reduces the critical slowing down in a model with two- and three-spin interactions on the Kagomé lattice.

Fermion sampling is to generate probability distribution of a many-body Slater-determinant wave function, which is termed “determinantal point process” in statistical analysis. For its inherently embedded Pauli exclusion principle, its application reaches beyond simulating fermionic quantum many-body physics to constructing machine learning models for diversified datasets. Here we propose a fermion sampling algorithm, which has a polynomial time complexity—quadratic in the fermion number and linear in the system size. This algorithm is about $100\%$ more efficient in computation time than the best known algorithms. In sampling the corresponding marginal distribution, our algorithm has a more drastic improvement, achieving a scaling advantage. We demonstrate its power on several test applications, including sampling fermions in a many-body system and a machine learning task of text summarization, and confirm its improved computation efficiency over other methods by counting floating-point operations.

Entanglement, which quantifies nonlocal correlations in quantum mechanics, is the fascinating concept behind much of the aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here, we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare regions which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.

Though robustness of networks to random attacks has been widely studied, intentional destruction by an intelligent agent is not tractable with previous methods. Here we devise a single-player game on a lattice that mimics the logic of an attacker attempting to destroy a network. The objective of the game is to disable all nodes in the fewest number of steps. We develop a reinforcement learning approach using deep $Q$-learning that is capable of learning to play this game successfully, and in so doing, to optimally attack a network. Because the learning algorithm is universal, we train agents on different definitions of robustness and compare the learned strategies. We find that superficially similar definitions of robustness induce different strategies in the trained agent, implying that optimally attacking or defending a network is sensitive to the particular objective. Our method provides an approach to understand network robustness, with potential applications to other discrete processes in disordered systems.

The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency of internal codes or labels follows power laws in both supervised and unsupervised learning models. This scale-invariant distribution implies that machine learning largely compresses frequent typical data, and simultaneously, differentiates many atypical data as outliers. In this study, we derive the process by which these power laws can naturally arise in machine learning. In terms of information theory, the scale-invariant representation corresponds to a maximally uncertain data grouping among possible representations that guarantee a given learning accuracy.

We demonstrate a method to obtain the spectra of $1/f$ noises in spin-qubit devices from randomized benchmarking, assisted by supervised learning. The noise exponent, which indicates the correlation within the noise, is determined by training a double-layer neural network with the ratio between the randomized benchmarking results of pulse sequences that correct noise or not. After the training is completed, the neural network is able to predict the exponent within an absolute error of about 0.05, comparable with existing methods. The noise amplitude is then evaluated by training another neural network with the decaying fidelity of randomized benchmarking results from the uncorrected sequences. The relative error for the prediction of the noise amplitude is as low as 5% provided that the noise exponent is known. Our results suggest that the neural network is capable of predicting noise spectra from randomized benchmarking, which can be an alternative method to measure noise spectra in spin-qubit devices.

The transmission coefficient of the free-space channel is fluctuating due to the occurrence of random fluctuations of the refractive index and noise. The Gaussian-modulated quantum states of light may degrade into a non-Gaussian mixture at a certain probability after being transmitted through the free-space channel. In such a situation, Eve can apply an entanglement-distillation attack to steal secret information without it being revealed if Alice and Bob regard the practical fluctuation losses as constant. However, the entanglement-distillation attack is available only when the transmitting states are a non-Gaussian mixture; otherwise, Eve will expose herself. Exploiting this loophole and considering the limitations of the attack, we enhance Eve's eavesdropping ability by integrating a machine-learning technique with the entanglement-distillation attack. With the help of convolutional neural network (CNN, one of the most popular machine leaning tools), Eve can choose the best opportunity to launch the entanglement-distillation attack. Therefore, Eve has a chance to bias the estimation of the parameters by improving the entanglement resource of the mixed states, which allows Eve to render the final keys shared between the legitimate parties insecure. Our proposed CNN-based entanglement-distillation attack does not require additional resources and can be implemented using simple means based on the present technologies.

Normalizing flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in the diagrammatic Monte Carlo (DMC) method, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables one to construct a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC method is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables' statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in the DMC method.

Cryo-EM is a powerful tool for understanding macromolecular structures, yet current methods for structure reconstruction are slow and computationally demanding. To accelerate research on pose estimation, we present CESPED, a data set specifically designed for supervised pose estimation in cryo-EM. Alongside CESPED, we provide a PyTorch package to simplify cryo-EM data handling and model evaluation. We evaluate the performance of a baseline model, Image2Sphere, on CESPED, which shows promising results but also highlights the need for further improvements. Additionally, we illustrate the potential of deep learning-based pose estimators to generalize across different samples, suggesting a promising path toward more efficient processing strategies.

We present two two-body Hamiltonians that approximate the exact particle-hole Pfaffian wave function with their ground states for all the system sizes where this wave function has been numerically constructed to date. The approximate wave functions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimization procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a noninteracting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the particle-hole Pfaffian. We diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the particle-hole Pfaffian shift appears energetically more favorable. The possibility to interpret the data in terms of composite fermions is discussed.

We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\widehat{U}$ that transforms a given unknown state $|{\psi }_{\tau }\rangle$ to a known fiducial state $|f\rangle$. Then, after completion of the learning process, we can estimate and reproduce $|{\psi }_{\tau }\rangle$ based on the learned $\widehat{U}$ and $|f\rangle$. To realize this idea, we cast a random-based learning algorithm, called “single-shot measurement learning,” in which the learning rule is based on an intuitive and reasonable criterion: the greater the number of success (or failure), the less (or more) changes are imposed. Remarkably, the learning process occurs by means of a single-shot measurement outcome. We demonstrate that our method works effectively, i.e., the learning is completed with a finite number, say $N$, of unknown-state copies. Most surprisingly, our method allows the maximum statistical accuracy to be achieved for large $N$, namely $\simeq O\left(N^{-1}\right)$ scales of average infidelity. It highlights a nontrivial message, that is, a random-based strategy can potentially be as accurate as other standard statistical approaches.

Motivated by the question whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum-mechanical two-body scattering problem with short-range potentials—a problem that by itself plays an important role in many branches of physics. After training, the neural network can accurately predict $s$-wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schrödinger equation or obtaining the wave function explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws.

The constrained-search formulation of Levy and Lieb provides a concrete mapping from $N$-representable densities to the space of $N$-particle wave functions and explicitly defines the universal functional of density-functional theory. We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer, using a modified variational quantum eigensolver approach. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme featuring real-time computation of the Levy-Lieb functional along the search trajectory. We further illustrate a fidelity-based quantum kernel associated with the density to pure-state embedding implied by the Levy-Lieb procedure and employ the kernel for learning observable functionals of the density. We study the kernel's ability to generalize with high accuracy through numerical experiments on the Hubbard dimer.

Gravitational-wave astronomy is a vibrant field that leverages both classic and modern data processing techniques for the understanding of the Universe. Various approaches have been proposed for improving the efficiency of the detection scheme, with hierarchical matched filtering being an important strategy. Meanwhile, deep learning methods have recently demonstrated both consistency with matched filtering methods and remarkable statistical performance. In this work, we propose a hierarchical detection network (HDN), a novel approach to efficient detection that combines ideas from hierarchical matching and deep learning. The network is trained using a novel loss function, which encodes simultaneously the goals of statistical accuracy and efficiency. We discuss the source of complexity reduction of the proposed model and describe a general recipe for initialization with each layer specializing in different regions. We demonstrate the performance of the HDN with experiments using open LIGO data and synthetic injections, and observe with two-layer models a 79% efficiency gain compared with matched filtering at an equal error rate of 0.2%. Furthermore, we show how training a three-layer HDN initialized using a two-layer model can further boost both accuracy and efficiency, highlighting the power of multiple simple layers in efficient detection.