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Understanding the electrical conductivity of warm dense hydrogen is critical for both fundamental physics and applications in planetary science and inertial confinement fusion. We demonstrate how to calculate the electrical conductivity using the continuum form of Ohm's law, with the current density obtained from real-time time-dependent density functional theory. This approach simulates the dynamic response of hydrogen under warm dense matter conditions, with temperatures around 30,000 K and mass densities ranging from 0.02 to 0.98 g/cc. We systematically address finite-size errors in real-time time-dependent density functional theory, demonstrating that our calculations are both numerically feasible and reliable. Our results show good agreement with other approaches, highlighting the effectiveness of this method for modeling electronic transport properties from ambient to extreme conditions., Comment: 9 pages, 6 figures

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT based electron dynamics simulations using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints and high-resolution training data, our model achieves superior accuracy and computational speed compared to traditional numerical solvers. We demonstrate the effectiveness of our model on a class of one-dimensional diatomic molecules. This method has potential in enabling real-time, on-the-fly modeling of laser-irradiated molecules and materials with varying experimental parameters., Comment: 9 pages, 5 figures

Mosaic crystals, with their high integrated reflectivities, are widely-employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 $\mu$m and 100 $\mu$m mosaic HAPG crystals, and how the broadening varies across the spectrometer in an energy range of 6.7-8.6 keV. Notably, we find a strong asymmetry in the shape of the IF towards higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas, and find that the temperature can be overestimated if an approximate symmetric IF is used. We therefore expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modelling and model-free approaches., Comment: 19 pages, 13 figures

Using a novel ultrahigh resolution ($\Delta E \sim 0.1\,$eV) setup to measure electronic features in x-ray Thomson scattering (XRTS) experiments at the European XFEL in Germany, we have studied the collective plasmon excitation in aluminium at ambient conditions, which we can measure very accurately even at low momentum transfers. As a result, we can resolve previously reported discrepancies between ab initio time-dependent density functional theory simulations and experimental observations. The demonstrated capability for high-resolution XRTS measurements will be a game changer for the diagnosis of experiments with matter under extreme densities, temperatures, and pressures, and unlock the full potential of state-of-the-art x-ray free electron laser (XFEL) facilities to study planetary interior conditions, to understand inertial confinement fusion applications, and for material science and discovery.

Electronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory (DFT), maps a set of real interacting electrons to a set of fictitious non-interacting electrons that share the same probability density. Ensuring that the density remains the same depends on the exchange-correlation (XC) energy and, by a derivative, the XC potential. Inversions provide a method to obtain exact XC potentials from target electronic densities, in hopes of gaining insights into accuracy-boosting approximations. Neural networks provide a new avenue to perform inversions by learning the mapping from density to potential. In this work, we learn this mapping using physics-informed machine learning (PIML) methods, namely physics informed neural networks (PINNs) and Fourier neural operators (FNOs). We demonstrate the capabilities of these two methods on a dataset of one-dimensional atomic and molecular models. The capabilities of each approach are discussed in conjunction with this proof-of-concept presentation. The primary finding of our investigation is that the combination of both approaches has the greatest potential for inverting the Kohn-Sham equations at scale.

Dynamic compression of iron to Earth-core conditions is one of the few ways to gather important elastic and transport properties needed to uncover key mechanisms surrounding the geodynamo effect. Herein a new machine-learned ab-initio derived molecular-spin dynamics (MSD) methodology with explicit treatment for longitudinal spin-fluctuations is utilized to probe the dynamic phase-diagram of iron. This framework uniquely enables an accurate resolution of the phase-transition kinetics and Earth-core elastic properties, as highlighted by compressional wave velocity and adiabatic bulk moduli measurements. In addition, a unique coupling of MSD with time-dependent density functional theory enables gauging electronic transport properties, critically important for resolving geodynamo dynamics., Comment: 3 Figures in main document, 8 Figures in the supplemental information

We created a computational workflow to analyze the potential energy surface (PES) of materials using machine-learned interatomic potentials in conjunction with the minima hopping algorithm. We demonstrate this method by producing a versatile machine-learned interatomic potential for iron hydride via a neural network using an iterative training process to explore its energy landscape under different pressures. To evaluate the accuracy and comprehend the intricacies of the PES, we conducted comprehensive crystal structure predictions using our neural network-based potential paired with the minima hopping approach. The predictions spanned pressures ranging from ambient to 100 GPa. Our results reproduce the experimentally verified global minimum structures such as \textit{dhcp}, \textit{hcp}, and \textit{fcc}, corroborating previous findings. Furthermore, our in-depth exploration of the iron hydride PES at different pressures has revealed complex alterations and stacking faults in these phases, leading to the identification of several new low-enthalpy structures. This investigation has not only confirmed the presence of regions of established FeH configurations but has also highlighted the efficacy of using data-driven, extensive structure prediction methods to uncover the multifaceted PES of materials.

Hydrogen loss to space is a key control on the evolution of the Martian atmosphere and the desiccation of the red planet. Thermal escape is thought to be the dominant loss process, but both forward modeling studies and remote sensing observations have indicated the presence of a second, higher-temperature "nonthermal" or "hot" hydrogen component, some fraction of which also escapes. Exothermic reactions and charge/momentum exchange processes produce hydrogen atoms with energy above the escape energy, but H loss via many of these mechanisms has never been studied, and the relative importance of thermal and nonthermal escape at Mars remains uncertain. Here we estimate hydrogen escape fluxes via 47 mechanisms, using newly-developed escape probability profiles. We find that HCO$^+$ dissociative recombination is the most important of the mechanisms, accounting for 30-50% of the nonthermal escape. The reaction CO$_2^+$ + H$_2$ is also important, producing roughly as much escaping H as momentum exchange between hot O and H. Total nonthermal escape from the mechanisms considered amounts to 39% (27%) of thermal escape, for low (high) solar activity. Our escape probability profiles are applicable to any thermospheric hot H production mechanism and can be used to explore seasonal and longer-term variations, allowing for a deeper understanding of desiccation drivers over various timescales. We highlight the most important mechanisms and suggest that some may be important at Venus, where nonthermal escape dominates and much of the literature centers on charge exchange reactions, which do not result in significant escape in this study., Comment: 47 pages, 4 figures, 3 tables. Accepted manuscript. An edited version of this paper was published by AGU

Electron dynamics of anatase TiO$_2$ under the influence of ultrashort and intense laser field is studied using the real-time time-dependent density functional theory (TDDFT). Our findings demonstrate the effectiveness of TDDFT calculations in modeling the electron dynamics of solids during ultrashort laser excitation, providing valuable insights for designing and optimizing nonlinear photonic devices. We analyze the perturbative and non-perturbative responses of TiO$_2$ to 30 fs laser pulses at 400 and 800 nm wavelengths, elucidating the underlying mechanisms. At 400 nm, ionization via single photon absorption dominates, even at very low intensities. At 800 nm, we observe ionization through two-photon absorption within the intensity range of $1\times10^{10}$ to $9\times10^{12}$ W/cm$^2$, with a transition from multiphoton to tunneling ionization occurring at $9\times10^{12}$ W/cm$^2$. We observe a sudden increase in energy and the number of excited electrons beyond $1\times10^{13}$ W/cm$^2$, leading to their saturation and subsequent laser-induced damage. We estimate the damage threshold of TiO$_2$ for 800 nm to be 0.1 J/cm$^2$. In the perturbative regime, induced currents exhibit a phase shift proportional to the peak intensity of the laser pulse. This phase shift is attributed to the intensity-dependent changes in the number of free carriers, indicative of the optical Kerr effect. Leveraging the linear dependence of phase shift on peak intensities, we estimate the nonlinear refractive index ($n_2$) of TiO$_2$ to be $3.54\times10^{-11}$ cm$^2$/W., Comment: 27 Pages (Including 3 pages of supplemental material), 7 figures

Although deuterium (D) on Mars has received substantial attention, the deuterated ionosphere remains relatively unstudied. This means that we also know very little about non-thermal D escape from Mars, since it is primarily driven by excess energy imparted to atoms produced in ion-neutral reactions. Most D escape from Mars is expected to be non-thermal, highlighting a gap in our understanding of water loss from Mars. In this work, we set out to fill this knowledge gap. To accomplish our goals, we use an upgraded 1D photochemical model that fully couples ions and neutrals and does not assume photochemical equilibrium. To our knowledge, such a model has not been applied to Mars previously. We model the atmosphere during solar minimum, mean, and maximum, and find that the deuterated ionosphere behaves similarly to the H-bearing ionosphere, but that non-thermal escape on the order of 8000-9000 cm$^{-2}$s$^{-1}$ dominates atomic D loss under all solar conditions. The total fractionation factor, $f$, is $f=0.04$--0.07, and integrated water loss is 147--158 m GEL. This is still less than geomorphological estimates. Deuterated ions at Mars are likely difficult to measure with current techniques due to low densities and mass degeneracies with more abundant H ions. Future missions wishing to measure the deuterated ionosphere in situ will need to develop innovative techniques to do so., Comment: 37 pages, 8 figures, published in Journal of Geophysical Research: Planets

We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike most other ML models that use DFT data, our models directly predict the local density of states (LDOS) of the electronic structure. This provides several advantages, including access to multiple observables such as the electronic density and electronic total free energy. Moreover, our models account for both the electronic and ionic temperatures independently, making them ideal for applications like laser-heating of matter. We validate the efficacy of our LDOS-based models on a metallic test system. They accurately capture energetic effects induced by variations in ionic and electronic temperatures over a broad temperature range, even when trained on a subset of these temperatures. These findings open up exciting opportunities for investigating the electronic structure of materials under both ambient and extreme conditions.

Rapid access to accurate equation-of-state (EOS) data is crucial in the warm-dense matter regime, as it is employed in various applications, such as providing input for hydrodynamic codes to model inertial confinement fusion processes. In this study, we develop neural network models for predicting the EOS based on first-principles data. The first model utilizes basic physical properties, while the second model incorporates more sophisticated physical information, using output from average-atom calculations as features. Average-atom models are often noted for providing a reasonable balance of accuracy and speed; however, our comparison of average-atom models and higher-fidelity calculations shows that more accurate models are required in the warm-dense matter regime. Both the neural network models we propose, particularly the physics-enhanced one, demonstrate significant potential as accurate and efficient methods for computing EOS data in warm-dense matter., Comment: 57 pages, 16 figures. Accepted for publication in Machine Learning: Science and Technology

We present a study on the transport and materials properties of aluminum spanning from ambient to warm dense matter conditions using a machine-learned interatomic potential (ML-IAP). Prior research has utilized ML-IAPs to simulate phenomena in warm dense matter, but these potentials have often been calibrated for a narrow range of temperature and pressures. In contrast, we train a single ML-IAP over a wide range of temperatures, using density functional theory molecular dynamics (DFT-MD) data. Our approach overcomes computational limitations of DFT-MD simulations, enabling us to study transport and materials properties of matter at higher temperatures and longer time scales. We demonstrate the ML-IAP transferability across a wide range of temperatures using molecular-dynamics (MD) by examining the thermal conductivity, diffusion coefficient, viscosity, sound velocity, and ion-ion structure factor of aluminum up to about 60,000 K, where we find good agreement with previous theoretical data.

Simulations and diagnostics of high-energy-density plasmas and warm dense matter rely on models of material response properties, both static and dynamic (frequency-dependent). Here, we systematically investigate variations in dynamic electron-ion collision frequencies $\nu(\omega)$ in warm dense matter using data from a self-consistent-field average-atom model. We show that including the full quantum density of states, strong collisions, and inelastic collisions lead to significant changes in $\nu(\omega)$. These changes result in red shifts and broadening of the plasmon peak in the dynamic structure factor, an effect observable in x-ray Thomson scattering spectra, and modify stopping powers around the Bragg peak. These changes improve the agreement of computationally efficient average-atom models with first-principles time-dependent density functional theory in warm dense aluminum, carbon, and deuterium.

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

Matter at extreme temperatures and pressures -- commonly known as warm dense matter (WDM) in the literature -- is ubiquitous throughout our Universe and occurs in a number of astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion, and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are routinely probed in x-ray Thomson scattering (XRTS) experiments, and, in addition, are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear-response theory as well as nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques including ab initio path integral Monte Carlo (PIMC) simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrarily complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0-1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree-Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the nonempirical choice of the mixing coefficient at ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other type of functionals like screened hybrids.

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within Kohn-Sham density functional theory (KS-DFT) for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of warm dense matter. Generated by laser-induced compression and heating in the laboratory, warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing to exact quantum Monte-Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response for partial degeneracy when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used compared to the previously reported results for the PBE, PBEsol, LDA, AM05, and SCAN functionals; B3LYP, on the other hand, does not perform well for the considered system. Together with the reduction of self-interaction errors, this seems to be the rationale behind the relative success of the HSE03 functional for the description of the experimental data on aluminum and liquid ammonia at WDM conditions.

We demonstrate the utility of physics-informed neural networks (PINNs) as solvers for the non-relativistic, time-dependent Schr\"odinger equation. We study the performance and generalisability of PINN solvers on the time evolution of a quantum harmonic oscillator across varying system parameters, domains, and energy states.

The properties of electrons in matter are of fundamental importance. They give rise to virtually all molecular and material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant gas planets. Modeling and simulation of such diverse applications rely primarily on density functional theory (DFT), which has become the principal method for predicting the electronic structure of matter. While DFT calculations have proven to be very useful to the point of being recognized with a Nobel prize in 1998, their computational scaling limits them to small systems. We have developed a machine learning framework for predicting the electronic structure on any length scale. It shows up to three orders of magnitude speedup on systems where DFT is tractable and, more importantly, enables predictions on scales where DFT calculations are infeasible. Our work demonstrates how machine learning circumvents a long-standing computational bottleneck and advances science to frontiers intractable with any current solutions. This unprecedented modeling capability opens up an inexhaustible range of applications in astrophysics, novel materials discovery, and energy solutions for a sustainable future.

We present a comprehensive investigation of the electrical and thermal conductivity of iron under high pressures at ambient temperature, employing the real-time formulation of time-dependent density functional theory (RT-TDDFT). Specifically, we examine the influence of a Hubbard correction (+\textit{U}) to account for strong electron correlations. Our calculations based on RT-TDDFT demonstrate that the evaluated electrical conductivity for both high-pressure body-centered cubic (BCC) and hexagonal close-packed (HCP) iron phases agrees well with experimental data. Furthermore, we explore the anisotropy in the thermal conductivity of HCP iron under high pressure, and our findings are consistent with experimental observations. Interestingly, we find that the incorporation of the +\textit{U} correction significantly impacts the ground state and linear response properties of iron at pressures below 50 GPa, with its influence diminishing as pressure increases. This study offers valuable insights into the influence of electronic correlations on the electronic transport properties of iron under extreme conditions.

We introduce a practical hybrid approach that combines orbital-free density functional theory (DFT) with Kohn-Sham DFT for speeding up first-principles molecular dynamics simulations. Equilibrated ionic configurations are generated using orbital-free DFT for subsequent Kohn-Sham DFT molecular dynamics. This leads to a massive reduction of the simulation time without any sacrifice in accuracy. We assess this finding across systems of different sizes and temperature, up to the warm dense matter regime. To that end, we use the cosine distance between the time series of radial distribution functions representing the ionic configurations. Likewise, we show that the equilibrated ionic configurations from this hybrid approach significantly enhance the accuracy of machine-learning models that replace Kohn-Sham DFT. Our hybrid scheme enables systematic first-principles simulations of warm dense matter that are otherwise hampered by the large numbers of atoms and the prevalent high temperatures. Moreover, our finding provides an additional motivation for developing kinetic and noninteracting free energy functionals for orbital-free DFT.

Average-atom models are an important tool in studying matter under extreme conditions, such as those conditions experienced in planetary cores, brown and white dwarfs, and during inertial confinement fusion. In the right context, average-atom models can yield results with similar accuracy to simulations which require orders of magnitude more computing time, and thus can greatly reduce financial and environmental costs. Unfortunately, due to the wide range of possible models and approximations, and the lack of open-source codes, average-atom models can at times appear inaccessible. In this paper, we present our open-source average-atom code, atoMEC. We explain the aims and structure of atoMEC to illuminate the different stages and options in an average-atom calculation, and to facilitate community contributions. We also discuss the use of various open-source Python packages in atoMEC, which have expedited its development., Comment: 9 pages, 8 figures. Published in Proceedings of the 21st Python in Science Conference (SciPy 2022)

We investigate shock-compressed copper in the warm dense matter regime by means of density functional theory molecular dynamics simulations. We use neural-network-driven interatomic potentials to increase the size of the simulation box and extract thermodynamic properties in the hydrodynamic limit. We show the agreement of our simulation results with experimental data for solid copper at ambient conditions and liquid copper near the melting point under ambient pressure. Furthermore, a thorough analysis of the dynamic ion-ion structure factor in shock-compressed copper is performed and the adiabatic speed of sound is extracted and compared with experimental data., Comment: 13 pages, 14 figures, 1 table, accepted at Physical Review B

Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known applications of quantum computing, enabling quantum computers to perform a database search (unsorted array) and quadratically outperform their classical counterparts in terms of time. Given the restricted access to database search for an oracle model (black-box), researchers have demonstrated various implementations of Grover's circuit for two to four qubits on various platforms. However, larger search spaces have not yet been explored. In this paper, a scalable Quantum Grover Search algorithm is introduced and implemented using 5-qubit and 6-qubit quantum circuits, along with a design pattern for ease of building an Oracle for a higher order of qubits. For our implementation, the probability of finding the correct entity is in the high nineties. The accuracy of the proposed 5-qubit and 6-qubit circuits is benchmarked against the state-of-the-art implementations for 3-qubit and 4-qubit. Furthermore, the reusability of the proposed quantum circuits using subroutines is also illustrated by the opportunity for large-scale implementation of quantum algorithms in the future.

The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair potentials that take into account the effects of the complex many-body medium consistently. In this work, we present extensive, highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) results for the effective interaction and the effective force between two electrons in the presence of the uniform electron gas (UEG). This gives us a direct insight into finite-size effects, thereby opening up the possibility for novel domain decompositions and methodological advances. In addition, we present unassailable numerical proof for an effective attraction between two electrons under moderate coupling conditions, without the mediation of an underlying ionic structure. Finally, we compare our exact PIMC results to effective potentials from linear-response theory, and we demonstrate their usefulness for the description of the dynamic structure factor. All PIMC results are made freely available online and can be used as a thorough benchmark for new developments and approximations.

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties under Earth-core conditions calls for sophisticated theoretical methods that can support diagnostics. We present results of the electrical conductivity within the pressure and temperature ranges found in Earth's core from simulating microscopic Ohm's law using time-dependent density functional theory. Our predictions provide a new perspective on resolving discrepancies in recent experiments.

The mean ionization state (MIS) is a critical property in dense plasma and warm dense matter research, for example as an input to hydrodynamics simulations and Monte-Carlo simulations. Unfortunately, however, the best way to compute the MIS remains an open question. Average-atom (AA) models are widely-used in this context due to their computational efficiency, but as we show here, the canonical approach for calculating the MIS in AA models is typically insufficient. We therefore explore three alternative approaches to compute the MIS. Firstly, we modify the canonical approach to change the way electrons are partitioned into bound and free states; secondly, we develop a novel approach using the electron localization function; finally, we extend a method which uses the Kubo-Greenwood conductivity to our average-atom model. Through comparisons with higher-fidelity simulations and experimental data, we find that any of the three new methods usually out-performs the canonical approach, with the electron localization function and Kubo-Greenwood methods showing particular promise., Comment: 16 pages, 8 figures. Changes since v2: minor changes from referee reports

Classical Random Neural Networks (RNNs) have demonstrated effective applications in decision making, signal processing, and image recognition tasks. However, their implementation has been limited to deterministic digital systems that output probability distributions in lieu of stochastic behaviors of random spiking signals. We introduce the novel class of supervised Random Quantum Neural Networks (RQNNs) with a robust training strategy to better exploit the random nature of the spiking RNN. The proposed RQNN employs hybrid classical-quantum algorithms with superposition state and amplitude encoding features, inspired by quantum information theory and the brain's spatial-temporal stochastic spiking property of neuron information encoding. We have extensively validated our proposed RQNN model, relying on hybrid classical-quantum algorithms via the PennyLane Quantum simulator with a limited number of \emph{qubits}. Experiments on the MNIST, FashionMNIST, and KMNIST datasets demonstrate that the proposed RQNN model achieves an average classification accuracy of $94.9\%$. Additionally, the experimental findings illustrate the proposed RQNN's effectiveness and resilience in noisy settings, with enhanced image classification accuracy when compared to the classical counterparts (RNNs), classical Spiking Neural Networks (SNNs), and the classical convolutional neural network (AlexNet). Furthermore, the RQNN can deal with noise, which is useful for various applications, including computer vision in NISQ devices. The PyTorch code (https://github.com/darthsimpus/RQN) is made available on GitHub to reproduce the results reported in this manuscript.

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale electronic structure calculations are still challenging despite modern software approaches and advances in high-performance computing. The silver lining in this regard is the use of machine learning to accelerate electronic structure calculations -- this line of research has recently gained growing attention. The grand challenge therein is finding a suitable machine-learning model during a process called hyperparameter optimization. This, however, causes a massive computational overhead in addition to that of data generation. We accelerate the construction of neural network models by roughly two orders of magnitude by circumventing excessive training during the hyperparameter optimization phase. We demonstrate our workflow for Kohn-Sham density functional theory, the most popular computational method in materials science and chemistry.

Warm dense matter is a highly active research area both at the frontier and interface of material science and plasma physics. We assess the performance of commonly used exchange-correlation (XC) approximation (LDA, PBE, PBEsol, and AM05) in the spin-polarized inhomogeneous electron gas under warm dense conditions based on exact path-integral quantum Monte-Carlo calculations. This extends our recent analysis on the relevance of inhomogeneities in the spin-unpolarized warm dense electron gas [Z.~Moldabekov et al., J. Chem. Phys. 155, 124116 (2021)]. We demonstrate that the predictive accuracy of these XC functionals deteriorates with (1) a decrease in density (corresponding to an increase in the inter-electronic correlation strength) and (2) an increase of the characteristic wave number of the density perturbation. We provide recommendations for the applicability of the considered XC functionals at conditions typical for warm dense matter. Furthermore, we hint at future possibilities for constructing more accurate XC functionals under these conditions.

With the growth of computational resources, the scope of electronic structure simulations has increased greatly. Artificial intelligence and robust data analysis hold the promise to accelerate large-scale simulations and their analysis to hitherto unattainable scales. Machine learning is a rapidly growing field for the processing of such complex datasets. It has recently gained traction in the domain of electronic structure simulations, where density functional theory takes the prominent role of the most widely used electronic structure method. Thus, DFT calculations represent one of the largest loads on academic high-performance computing systems across the world. Accelerating these with machine learning can reduce the resources required and enables simulations of larger systems. Hence, the combination of density functional theory and machine learning has the potential to rapidly advance electronic structure applications such as in-silico materials discovery and the search for new chemical reaction pathways. We provide the theoretical background of both density functional theory and machine learning on a generally accessible level. This serves as the basis of our comprehensive review including research articles up to December 2020 in chemistry and materials science that employ machine-learning techniques. In our analysis, we categorize the body of research into main threads and extract impactful results. We conclude our review with an outlook on exciting research directions in terms of a citation analysis.

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental and theoretical physics and is challenging traditional concepts of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of X-Ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpoint where the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

We predict the emergence of novel collective electronic excitations in warm dense matter with an inhomogeneous electronic structure based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. Most importantly, these modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.

The electronic structure in matter under extreme conditions is a challenging complex system prevalent in astrophysical objects and highly relevant for technological applications. We show how machine-learning surrogates in terms of neural networks have a profound impact on the efficient modeling of matter under extreme conditions. We demonstrate the utility of a surrogate model that is trained on \emph{ab initio} quantum Monte Carlo data for various applications in the emerging field of warm dense matter research.

Finite-temperature Kohn--Sham density-functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remains uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modelling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analysing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model -- such as boundary conditions and XC functionals -- on common properties in WDM, for example equation-of-state data, ionization degree and the behaviour of the frontier energy levels. Furthermore, drawing upon insights from ground-state KS-DFT, we discuss the likely sources of error in KS-AA models and possible strategies for mitigating such errors., Comment: To be published in Physical Review Research. 29 pages, 15 figures. Derivation of Hamiltonian clarified since v3 and added appendix B on computation of free energy

Correlated many-fermion systems emerge in a broad range of phenomena in warm dense matter, plasmonics, and ultracold atoms. Quantum hydrodynamics (QHD) complements common first-principles methods for many-fermion systems and enables simulations at larger length and longer time scales. While the quantum Bohm potential is central to QHD, we illustrate its failure for strong perturbations. We extend QHD to this regime by utilizing the many-fermion quantum Bohm potential. This opens up the path to more accurate simulations in strongly perturbed warm dense matter, inhomogeneous quantum plasmas, and on nano-structure surfaces at scales unattainable with first-principles algorithms. The many-fermion quantum Bohm potential might also have important astrophysical applications in developing conformal-invariant cosmologies.

A data-driven framework is presented for building magneto-elastic machine-learning interatomic potentials (ML-IAPs) for large-scale spin-lattice dynamics simulations. The magneto-elastic ML-IAPs are constructed by coupling a collective atomic spin model with an ML-IAP. Together they represent a potential energy surface from which the mechanical forces on the atoms and the precession dynamics of the atomic spins are computed. Both the atomic spin model and the ML-IAP are parametrized on data from first-principles calculations. We demonstrate the efficacy of our data-driven framework across magneto-structural phase transitions by generating a magneto-elastic ML-IAP for {\alpha}-iron. The combined potential energy surface yields excellent agreement with first-principles magneto-elastic calculations and quantitative predictions of diverse materials properties including bulk modulus, magnetization, and specific heat across the ferromagnetic-paramagnetic phase transition., Comment: 15 pages, 6 figures, 2 tables