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NASA NTRS1991

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature.

Fu, Yibin B.↗
DOE OSTI2017

The Importance of the Scaffold for de Novo Enzymes: A Case Study with Kemp Eliminase

We report electric field values relevant to the reactant and transition states of designed Kemp eliminases KE07 and KE70 and their improved variants from laboratory directed evolution (LDE), using atomistic simulations with the AMOEBA polarizable force field. We find that the catalytic base residue contributes the most to the electric field stabilization of the transition state of the LDE variants of the KE07 and KE70 enzymes, whereas the electric fields of the remainder of the enzyme and solvent disfavor the catalytic reaction in both cases. By contrast, we show that the electrostatic environment plays a large and stabilizing role for the naturally occurring enzyme ketosteroid isomerase (KSI). These results suggest that LDE is ultimately a limited strategy for improving de novo enzymes since it is largely restricted to optimization of chemical positioning in the active site, thus yielding a ~3 order magnitude improvement over the uncatalyzed reaction, which we suggest may be an absolute upper bound estimate based on LDE applied to comparable de novo Kemp eliminases and other enzymes like KSI. Instead de novo enzymatic reactions could more productively benefit from optimization of the electrostatics of the protein scaffold in early stages of the computational design, utilizing electric field optimization as guidance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Comment on “QCD factorization with multihadron fragmentation functions”

We make several comments on the recent work in Rogers et al. [Phys. Rev. D 111, 056001 (2025)] while also reaffirming and adding to the work in Pitonyak et al. [Phys. Rev. Lett. 132, 011902 (2024)]. We show that the factorization formula for 𝑒 + ⁢𝑒 − → (ℎ 1 ⋯ ℎ 𝑛 )⁢𝑋 in Rogers et al. is equivalent to a version one can derive using the definition of a 𝑛-hadron fragmentation function (FF) introduced in Pitonyak et al.. In addition, we scrutinize how to generalize the number density definition of a single-hadron FF to a 𝑛-hadron FF, arguing that the definition given in Pitonyak et al. should be considered the standard one while the definition in Rogers et al. has no clear interpretation. We also emphasize that the evolution equations for dihadron FFs (DiFFs) in Pitonyak et al. have the same splitting functions as those for single-hadron FFs. Therefore, the DiFF (and 𝑛-hadron FF) definitions in Pitonyak et al. have a natural number density interpretation and, contrary to what is stated in Rogers et al., are consistent with collinear factorization using the standard hard factors and evolution kernels.

Pitonyak, D. [Lebanon Valley College, Annville, PA↗
DOE OSTI2026

Tuning Shinkarev’s Bicycle: Separating the Parallel Cycles of Photosystem II Using Empirical Wavelet Transform

The oxygen-evolving complex (OEC) of Photosystem II (PSII) catalyzes light-driven water oxidation, a process necessary to sustain Earth’s atmospheric oxygen. Oxygen yields measured during single-turnover flash sequences exhibit period-four oscillations, which form the basis of the Joliot–Kok (S-state) model. However, when the oscillations of other processes contribute to the measured oxygen yield, fitting methods can conflate these signals and distort estimates of inefficiencies and initial S-state populations. To address this, we applied the empirical wavelet transform (EWT) as a model-independent method to separate overlapping oscillators and capture damping dynamics that are not well represented in Fourier analysis. We tested this framework on polarographic flash-oxygen traces from both our Synechocystis sp. PCC 6803 thylakoid membrane preparations and archival datasets on Chlorella and isolated chloroplasts. EWT consistently resolves the expected period-four component alongside a distinct binary oscillation. Simulations suggest that fitting this isolated period-four signal recovers VZAD parameters more accurately than analysis of raw traces, yielding different estimates for S-state distributions and transition probabilities. Notably, this binary oscillation aligns closely with semiquinone dynamics predicted solely from period-four fit parameters. These findings indicate that EWT can effectively distinguish complex signals in oxygen evolution, offering a framework potentially applicable to other spectroscopic probes of the S-state cycle.

Ferrari, Nicholas [Louisiana State Univ., Baton Ro↗
DOE OSTI2021

Characteristics of Ultralow Aspect Ratio Toroidal Plasmas and Non-Solenoidal Startup and Edge Stability Studies at Near-Unity Aspect Ratio (Final Report)

This grant supported a long-term research and development program to explore the physics and technology of spherical tokamak (ST) plasma behavior at near-unity aspect ratio ( A ). The PEGASUS Toroidal Experiment is a university-scale ( R ) ~ 0.40 m, α ~ .35 m, I p ≤ 0.3 MA, B T ≤ 0.15 T) experiment that accesses A → 1, to provide large values of the normalized plasma current, I N = I p /α B T , or equivalently the toroidal field utilization factor I p / I TF . The research activities focused on: 1) developing the technique of Local Helicity Injection (LHI) as a viable means of initiating and growing an ST plasma without the use of a central solenoid; 2) exploring the equilibrium and stability properties of spherical tokamak plasmas at extremely low aspect ratio; and 3) obtaining new insights in the properties of the enhanced confinement H-mode regime at A ~ 1. The initial (Phase I) facility employed a unique high-stress central solenoid Ohmic for current drive and heating with simple magnet current waveforms. A subsequent major upgrade (Phase II) offered more flexible control of the plasma evolution along with a powerful LHI system for plasma initiation, heating and sustainment. The LHI technique consists of injection of high-density current streams into vacuum toroidal and vertical magnetic fields. These streams become unstable and support magnetic reconnection to allow the system to relax into a tokamak-like magnetic configuration. This program focused on: 1) development of electron current sources that provide sufficiently high injection currents in the challenging edge plasma region; 2) validation of theoretical limits to achievable I p arising from magnetic helicity and energy conservation plus absolute limits arising from relaxation to a minimal energy states; 3) tests of a power balance model to describe the evolution of the plasma current I p (t); and 4) study of magnetic fluctuations and their role in the I p evolution. This culminated in the production of toroidal currents of I p ≥ 0.2 MA with only ~8 kA of injected current. Operation with Ohmic induction alone in Phase I created plasmas with soft limits on the achievable I p and field utilization ( I p / I TF ~ 1) due to the onset of large low-order (2/1 or 3/2) internal resonant tearing modes. With the expanded capabilities in Phase II operation, methods employed to mitigate those modes and achieve I p / I TF > 1 were: 1) I TF ramp-downs; 2) non-solenoidal startup via LHI; and 3) extremely low I TF Ohmic operations assisted by LHI current injector pre-ionization. Extensive use of LHI-driven startup and drive for non-solenoidal operation produced favorable current profiles to stably operate tokamak plasmas with unprecedentedly high I N = I p / aB T ~ 15 and I p / I TF > 2. With strong reconnection-driven anomalous ion heating, this in turn provided access to tokamak plasmas with B t up to 100%, a world record 2 times higher than that previously achieved in advanced or spherical tokamaks. This high B t regime had a large fraction (~50%) of the plasma volume in a region of an absolute minimum- B configuration. The MHD stability limit in this regime was the ideal external kink mode without a stabilizing wall. These results provided the first demonstration of access to tokamak plasmas with very high B t , high i N , high elongation κ, and low internal inductance ℓ i , and as such served as a proof-ofprinciple for access to this long-sought ST regime. The naturally low B T needed for stability at A ≤ 1.2 reduces the L-H mode power threshold, P LH , so that H-mode plasmas were achieved with Ohmic heating alone. The power threshold for the transition to the H-mode regime was found to be 10× the accepted values from the ITER international scaling, confirming initial trends indicated by experiments on MAST and NSTX, and suggesting that the physics behind this transition is not yet fully understood. The density dependence of the transition and the observed insensitivity to whether the plasma is bounded by a limiter or magnetic divertor are consistent with the recent FM 3 model. Multiple unstable toroidal magnetic modes were measured during ELM (Edge Localized Mode) crashes, with generally lower toroidal mode numbers than seen at higher A , which was attributed to the larger peeling mode instability drive at low A . First-ever edge current profile measurements through an ELM crash showed current-carrying filaments were generated, as seen in ELM simulations and in electromagnetic blob transport theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Light-Enhanced Spin Fluctuations and d -Wave Superconductivity at a Phase Boundary

Time-domain techniques have shown the potential of photomanipulating existing orders and inducing new states of matter in strongly correlated materials. Using time-resolved exact diagonalization, we perform in this paper numerical studies of pump dynamics in a Mott-Peierls system with competing charge and spin density waves. A light-enhanced d-wave superconductivity is observed when the system resides near a quantum phase boundary. By examining the evolution of spin, charge, and superconducting susceptibilities, we show that a subdominant state in equilibrium can be stabilized by photomanipulating the charge order to allow superconductivity to appear and dominate. Finally, this work provides an interpretation of light-induced superconductivity from the perspective of order competition and offers a promising approach for designing novel emergent states out of equilibrium.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2015

Coupled pulsating and cellular structure in the propagation of globally planar detonations in free space

The globally planar detonation in free space is numerically simulated, with particular interest to understand and quantify the emergence and evolution of the one-dimensional pulsating instability and the two-dimensional cellular structure which is inherently also affected by pulsating instability. It is found that the pulsation includes three stages: rapid decay of the overdrive, approach to the Chapman-Jouguet state and emergence of weak pulsations, and the formation of strong pulsations; while evolution of the cellular structure also exhibits distinct behavior at these three stages: no cell formation, formation of small-scale, irregular cells, and formation of regular cells of a larger scale. Furthermore, the average shock pressure in the detonation front consists of fine-scale oscillations reflecting the collision dynamics of the triple-shock structure and large-scale oscillations affected by the global pulsation. The common stages of evolution between the cellular structure and the pulsating behavior, as well as the existence of shock-front pressure oscillation, suggest highly correlated mechanisms between them. Detonations with period doubling, period quadrupling, and chaotic amplitudes were also observed and studied for progressively increasing activation energies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Light dark matter search with nitrogen-vacancy centers in diamonds

We propose an approach to directly search for light dark matter, such as the axion or the dark photon, by using magnetometry with nitrogen-vacancy centers in diamonds. If the dark matter couples to the electron spin, it affects the evolution of the Bloch vectors consisting of the spin triplet states, which may be detected through several magnetometry techniques. We give several concrete examples with the use of dc and ac magnetometry and estimate the sensitivity on dark matter couplings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Explicitly Solvable Models of Redistribution of the Conflict Space

We analyze a class of explicitly solvable models for the problems of redistribution of the conflict space between two alternative opponents. The existence of equilibrium state is proved for a complex nonlinear system whose time evolution is generated by the conflict interaction between its components. Explicit formulas are obtained for the limit compromise distributions in terms of the densities of probability measures. We consider a number of specific model examples of the dynamics of redistribution of the conflict territory and formation of an equilibrium (compromise) distribution of the space. We propose an interpretation of the results for the case of social and territorial conflicts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Comparison of Different Ion Mobility Setups Using Poly (Ethylene Oxide) PEO Polymers: Drift Tube, TIMS, and T-Wave Comparison of Different Ion Mobility Setups Using Poly (Ethylene Oxide) PEO Polymers: Drift Tube, TIMS, and T-Wave

Over the years, polymer analyses using ion mobility-mass spectrometry (IM-MS) measurements have been performed on different ion mobility spectrometry (IMS) setups. In order to be able to compare literature data taken on different IM(-MS) instruments, ion heating and ion temperature evaluations have already been explored. Nevertheless, extrapolations to other analytes are difficult and thus straightforward same-sample instrument comparisons seem to be the only reliable way to make sure that the different IM(-MS) setups do not greatly change the gas-phase behavior. We used a large range of degrees of polymerization (DP) of poly(ethylene oxide) PEO homopolymers to measure IMS drift times on three different IM-MS setups: a homemade drift tube (DT), a trapped (TIMS), and a traveling wave (T-Wave) IMS setup. The drift time evolutions were followed for increasing polymer DPs (masses) and charge states, and they are found to be comparable and reproducible on the three instruments. .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Radiation effects on stress evolution and dimensional stability of large fusion energy structures

Here we assess the effects of neutron irradiation on the deformation and stress evolution of large-scale fusion energy structures. This is accomplished through non-linear finite element structural analysis of the coupled thermal and mechanical fields at the Beginning-Of-Life (BOL), at 45 dpa, and at 90 dpa. Radiation effects include volumetric swelling and the influence of radiation on the mechanical properties. The system studied here is a large section of a full inboard module of an integrated structure comprising the First Wall and Blanket (FW/B) of a Dual Cooled Lithium-Lead (DCLL) energy conversion unit in the Fusion Nuclear Science Facility (FNSF). The structural material is the ferritic/martensitic steel F82H. We analyze several radiation effects phenomena that can lead to significant impact on the mechanical design and lifetime of the structure. These include volumetric swelling effects on the assembly and disassembly of modules and the impact of spatial gradients in neutron damage and helium generation on deformation, stress evolution, and plastic strain accumulation. We show that the stress state is strongly influenced by the accumulation of swelling strains, radiation hardening and softening, and by spatial gradients in displacement damage and helium gas generation. Several key regions in the FW/B structure are identified where severe plastic strains accumulate and may be potential sites for failure, especially during cyclic reactor operations. We finally show that minimum gaps between Inboard (IB) blanket sectors must be present during assembly so as to avoid excessive stress and strain in FW/B modules critical regions and raising chances of failure. A range of structural displacements are shown, from as low as 4 mm at BOL for free side walls to as high as 46 mm at 90 dpa for fully constrained side walls.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Evolution and characterization of a new reversibly photoswitching chromogenic protein, Dathail

In this paper, we report the engineering of a new reversibly switching chromogenic protein, Dathail. Dathail was evolved from the extremely thermostable fluorescent proteins thermal green protein (TGP) and eCGP123 using directed evolution and ratiometric sorting. Dathail has two spectrally distinct chromogenic states with low quantum yields, corresponding to absorbance in a ground state with a maximum at 389 nm, and a photo-induced metastable state with a maximum at 497 nm. In contrast to all previously described photoswitchable proteins, both spectral states of Dathail are non-fluorescent. The photo-induced chromogenic state of Dathail has a lifetime of ~ 50 min at 293 K and pH 7.5 as measured by UV–Vis spectrophotometry, returning to the ground state through thermal relaxation. X-ray crystallography provided structural insights supporting a change in conformation and coordination in the chromophore pocket as being responsible for Dathail's photoswitching. Neutron crystallography, carried out for the first time on a protein from the green fluorescent protein family, showed a distribution of hydrogen atoms revealing protonation of the chromophore 4-hydroxybenzyl group in the ground state. Additionally, the neutron structure also supports the hypothesis that the photo-induced proton transfer from the chromophore occurs through water-mediated proton relay into the bulk solvent. Beyond its spectroscopic curiosity, Dathail has several characteristics that are improvements for applications, including low background fluorescence, large spectral separation, rapid switching time, and the ability to switch many times. Therefore, Dathail is likely to be extremely useful in the quickly developing fields of imaging and biosensors, including photochromic Förster resonance energy transfer, high-resolution microscopy, and live tracking within the cell.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Scan strategies in EBM-printed IN718 and the physics of bulk 3D microstructure development

Three-dimensional (3D) characterization provides opportunities for understanding processing-structure relationships in additively manufactured (AM) materials. Bulk samples of Inconel 718 were fabricated via electron beam melting (EBM) in order to study microstructural development as a function of energy input and beam scan strategy. TriBeam tomography of bulk Inconel 718 microstructures built under steady-state growth conditions reveals the sensitivity of microstructure formation and evolution to machine process parameters. Here, samples manufactured using a narrow range of energy input per unit build area result in varied grain morphologies and crystallographic textures. Using TRUCHAS, a thermal simulation software, the thermal history of bulk scan strategies was predicted, and combined with a calibrated microstructure-processing map to accurately predict bulk grain morphologies. The solidification parameters and the 3D measured nucleation density are used to predict the transition between columnar and equiaxed grain morphologies, providing a process map to guide AM parameter choices to locally control as-printed microstructure. A two-dimensional metric for characterizing bulk grain morphology was also found to agree well with predictions from the process map calibrated by 3D data. Combined with 3D tomography and thermal modelling, the physics of structure development were understood at a new level of detail with respect to the competing processes of grain nucleation and epitaxial growth.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Soft X-ray spectroscopy studies of adsorption and reaction of CO in the presence of H 2 over 6 nm MnO nanoparticles supported on mesoporous Co 3 O 4

MnO nanoparticles (6 nm) were supported on mesoporous spinel Co 3 O 4 and studied using ambient pressure X-ray photoelectron spectroscopy (APXPS) and in situ X-ray absorption spectroscopy (XAS) during hydrogenation of CO. The nature and evolution of surface adsorbed species as well as the oxidation states of the metal oxide surfaces were evaluated under oxidizing, reducing, and H 2 + CO (2:1) reaction atmospheres. From APXPS, MnO nanoparticle surfaces were found to be progressively reduced in H 2 atmospheres with increasing temperature. Surface adsorbed CO was found to be formed at the expense of lattice O under H 2 + CO reaction conditions. In situ XAS indicated that the dominant oxide species were Co(OH) 2 , Co (II) oxides, MnO, and Mn 3 O 4 under reaction conditions. In situ XAS also indicated the formation of gas phase CO 2 , the disappearance of lattice O, and the further reduction of Mn 3 O 4 to MnO upon prolonged reaction in H 2 + CO. Mass spectroscopy measurements showed the formation of CO 2 and hydrocarbons. Finally, the spent catalyst was investigated using scanning transmission X-ray microscopy and (scanning) transmission electron microscopy; the catalyst grains were found to be homogeneous.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Insights into the distinct lithiation/sodiation of porous cobalt oxide by in operando synchrotron x-ray techniques and ab initio molecular dynamics simulations

Sodium-ion batteries (SIBs) have been considered as one of the promising power source candidates for the stationary storage industries owing to the much lower cost of sodium than lithium. It is well-known that the electrode materials largely determine the energy density of the battery systems. However, recent discoveries on the electrode materials showed that most of them present distinct lithium and sodium storage performance, which is not yet well understood. In this work, we performed a comparative understanding on the structural changes of porous cobalt oxide during its electrochemical lithiation and sodiation process by in operando synchrotron small angel X-ray scattering, X-ray diffraction, and X-ray absorption spectroscopy. It was found that compared to the lithiation process, the porous cobalt oxide undergoes less pore structure changes, oxidation state, and local structure changes as well as crystal structure evolution during its sodiation process, which is attributed to the intrinsic low sodiation activity of cobalt oxide as evidenced by ab initio molecular dynamics simulations. Moreover, it was indicated that the sodiation activity of metal sulfides is higher than that of metal oxides, indicating a better candidate for SIBs. Furthermore, such understanding is crucial for future design and improvement of high-performance electrode materials for SIBs.

25 ENERGY STORAGE↗
DOE OSTI2025

Modification of Ni-20Cr corrosion dealloying behavior in molten fluorides via cold work induced plastic deformation

The corrosion dealloying behavior of cold-worked (CW) Ni20Cr alloy (wt%) was studied in molten LiF-NaF-KF (or FLiNaK) salts at 600 °C, equal to a homologous temperature (TH) of 0.52. Alloys were cold-rolled to achieve reductions of thickness of 10%, 30%, and 50% introducing plastic deformation and a high density of dislocations. Potentiostatic holds (Eapplied) were applied in two different electrode potential regimes. At 1.75VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, Cr dealloying to Cr(II) and Cr(III) is predominant, while at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, both Ni and Cr are oxidized in molten FLiNaK at 600 °C. In these potential regimes, dealloyed Ni20Cr displayed bicontinuous porosity within the grain interior and at grain boundaries, driven by the high driving force for Cr dissolution and sustained by defect mediated outward solid state diffusion of Cr in parallel with surface diffusion of Ni. The bicontinuous porous structure developed was observed to undergo further coarsening and densification of the Ni-rich ligaments at a higher electrode potential. The main effect of CW observed is the introduction of plastic deformation and dislocation substructures that serve as short-circuit paths for Cr solid state diffusion to surfaces exposed to FLiNaK. This modified the evolution of the bicontinuous porous structure which increased with CW substantially. Kinetic analysis reveals that the Cr dealloying at +1.75 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ and 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ is initially charge transfer controlled, except for the 50% CW condition at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, where the process becomes limited by slow Cr defect mediated bulk diffusion. The rate determining factors are explored and compared to experimental results.

Chan, Ho Lun↗
DOE OSTI2024

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Abstract Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states 1,2 . However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices 2–5 , and it remains unsolved how to estimate the actual entanglement content of experiments 6 . Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement 6 , finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution 2–5 . Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Science & Technology - Other Topics↗