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At least 1,171 records · Page 65

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗

Weak-form inference for hybrid dynamical systems in ecology

Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behaviour, especially given the inherent heterogeneity and stochasticity of exogenous driving factors over short timescales, is an ongoing challenge. A modelling paradigm gaining popularity in the ecological sciences for such multi-scale effects is to couple short-term continuous dynamics to long-term discrete updates. We develop a data-driven method utilizing weak-form equation learning to extract such hybrid governing equations for population dynamics and to estimate the requisite parameters using sparse intermittent measurements of the discrete and continuous variables. The method produces a set of short-term continuous dynamical system equations parametrized by long-term variables, and long-term discrete equations parametrized by short-term variables, allowing direct assessment of interdependencies between the two timescales. We demonstrate the utility of the method on a variety of ecological scenarios and provide extensive tests using models previously derived for epizootics experienced by the North American spongy moth ( Lymantria dispar dispar ).

54 ENVIRONMENTAL SCIENCES↗

Low-Density Parity-Check Codes as Stable Phases of Quantum Matter

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.

quantum error correction↗

High precision measurements of the proton elastic electromagnetic form factors and their ratio at 𝑄 2 = 0.50, 2.64, 3.20, and 4.10 GeV 2

The advent of high-intensity, high-polarization electron beams led to significantly improved measurements of the ratio of the proton’s charge to electric form factors, 𝐺 𝐸⁢ 𝑝 ⁡/𝐺 𝑀⁢ 𝑝 . However, high-𝑄 2 measurements of this ratio yielded significant disagreement with extractions based on unpolarized scattering measurements, raising questions about the reliability of the measurements and consistency of the techniques. Jefferson Lab experiment E01-001 was designed to provide a high precision extraction of 𝐺 𝐸⁢ 𝑝 ⁡/𝐺 𝑀⁢ 𝑝 from unpolarized cross-section measurements using a modified version of the Rosenbluth separation technique to allow for a more precise comparison with polarization data. Rosenbluth separations involve precise measurements of the angular dependence of the elastic 𝑒−𝑝 cross section at fixed momentum transfer, 𝑄 2 . Conventional Rosenbluth separations detect the scattered electron, requiring the comparisons of measurements with very different detected electron energy and rate for electrons at different angles. Our ‘‘super-Rosenbluth’’ measurement detected the struck proton, rather than the scattered electron to extract the elastic 𝑒−𝑝 cross section. This yielded a fixed momentum for the detected particle and dramatically reduced variation of the cross section with angle, significantly reducing rate- and momentum-dependent corrections and uncertainties. We measure the cross section vs angle with high relative precision, allowing for extremely high precision extractions of 𝐺 𝐸⁢ 𝑝 ⁡/𝐺 𝑀⁢ 𝑝 at 𝑄 2 = 2.64, 3.20, and 4.10 GeV 2 . Our results are consistent with traditional Rosenbluth extractions, but with much smaller corrections and systematic uncertainties, comparable to the uncertainties from polarization measurements. Our data confirm the discrepancy between Rosenbluth and polarization extractions of the proton form factor ratio using an improved Rosenbluth extraction that yields smaller and less-correlated uncertainties than those typical of previous Rosenbluth extractions. Here, we compare our results to calculations of two-photon exchange effects and find that the observed discrepancy can be relatively well explained by such effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantum Routing and Entanglement Dynamics Through Bottlenecks

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions 𝐿,𝑅 with 𝑁 𝐿 ,𝑁 𝑅 qubits, respectively, coupled only through an intermediate region 𝐶 with 𝑁 𝐶 qubits, for any 𝛿 > 0 we show a lower bound of Ω⁢(𝑁$^{1−𝛿}_{𝑅}$/√𝑁 𝐿⁢ 𝑁 𝐶 ) on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between 𝐿 and 𝐶,𝑅 that can be generated in time 𝑡 by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from 𝑂⁡(𝑁 𝐿⁢ 𝑡) to 𝑂⁡(√𝑁 𝐿⁢ 𝑡). As a special case, when applied to the star graph (i.e., one vertex connected to 𝑁 leaves), we obtain an Ω⁡(√𝑁 1−𝛿 ) lower bound on the routing time and on the time to prepare 𝑁/2 Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time Θ⁡(√𝑁) using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time Θ⁡(𝑁).

97 MATHEMATICS AND COMPUTING↗

Tuning the magnetic properties of the spin-split antiferromagnet MnTe through pressure

The hexagonal antiferromagnet MnTe has attracted enormous interest as a prototypical example of a spin-compensated magnet in which the combination of crystal and spin symmetries lifts the spin degeneracy of the electron bands without the need for spin-orbit coupling, a phenomenon called nonrelativistic spin splitting (NRSS). Subgroups of NRSS are determined by the specific spin-interconverting symmetry that connects the two opposite-spin sublattices. In MnTe, this symmetry is rotation, leading to the subgroup with spin splitting away from the Brillouin zone center, often called altermagnetism. MnTe also has the largest spontaneous magnetovolume effect of any known antiferromagnet, implying strong coupling between the magnetic moment and volume. This magnetostructural coupling offers a potential knob for tuning the spin-splitting properties of MnTe. Here, we use neutron diffraction with in situ applied pressure to determine the effects of pressure on the magnetic properties of MnTe and further explore this magnetostructural coupling. We find that applying pressure significantly increases the Néel temperature, but decreases the ordered magnetic moment. We explain this as a consequence of strengthened magnetic exchange interactions under pressure, resulting in higher 𝑇 N , with a simultaneous reduction of the local moment of individual Mn atoms, described here via density functional theory. This reflects the increased orbital hybridization and electron delocalization with pressure. In conclusion, these results shed light on the competition between magnetic exchange interactions and the strength of individual magnetic moments and show that the magnetic properties of MnTe can be controlled by pressure, opening the door to improved properties for spintronic applications through tuning via physical or chemical pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

Here, we introduce a route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and “lifting” to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a route to higher-dimensional strong fragmentation, and also a route to fractonic behavior. Meanwhile, lifting one-dimensional fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust fragmentation. In three or more spatial dimensions, one can also “mix and match” subsystem and higher-form symmetries, leading to canonical fracton models such as X cube. We speculate that this approach could also yield a route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with unique properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals

Three-dimensional (3D) crystals offer a route to scaling up trapped-ion systems for quantum sensing and quantum simulation applications; however, engineering coherent spin-motion couplings and effective spin-spin interactions in large crystals poses technical challenges associated with decoherence and prolonged timescales to generate appreciable entanglement. Here, we explore the possibility of speeding up these interactions in 3D crystals via parametric amplification. For this purpose, we derive a general Hamiltonian for the parametric amplification of spin-motion coupling that is broadly applicable to normal modes with motion transverse to or along the spatial extent of the crystal. Unlike in lower-dimensional crystals, we find that the ability to faithfully (uniformly) amplify the spin-spin interactions in 3D crystals depends on the physical implementation of the spin-motion coupling. We consider the light-shift gate, and the so-called phase-insensitive and phase-sensitive Mølmer-Sørensen (MS) gates, and we find that only the phase-sensitive MS gate can be faithfully amplified in general 3D crystals. We discuss a situation where nonuniform amplification can be advantageous. We also reconsider the effect of counter-rotating terms on parametric amplification and find that they are not as detrimental as previous studies suggest.

Optical parametric oscillators & amplifiers↗

Hadronic vacuum polarization for the muon 𝑔 − 2 from lattice QCD: Complete short and intermediate windows

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment 𝑎 𝜇 in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to 𝑎 𝜇 , respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain 𝑎$^{𝑙⁢𝑙,SD}_{𝜇⁡}$(conn) = 48.139⁢(11) stat ⁢(91) syst ⁢[92] total × 10 −10 and 𝑎$^{𝑙⁢𝑙,W}_{𝜇}$⁡(conn) = 206.90⁢(14) stat ⁢(61) syst ⁢[63] total × 10 −10 . We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are 𝑎$^{SD}_{𝜇}$ = 69.05⁢(1) stat⁢ (21) syst ⁢[21] total × 10 −10 and 𝑎$^{W}_{𝜇}$ = 236.45⁢(17) stat⁢ (83) syst ⁢[85] total × 10 −10 . This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Enhancing stability, magnetic anisotropy, and coercivity of manganese aluminum: Machine learning, ab initio , and micromagnetic modeling

The binary manganese aluminum (MnAl) alloy with L⁢1 0 crystal structure is a promising rare earth (RE) element-free permanent magnetic material because of its exceptional magnetic properties. However, experimentally synthesizing it in a stable bulk form is extremely challenging. Here, in this study, an alternative method of stabilizing the material, a pathway for experimental synthesis and validation, is proposed and theoretically verified. This is done by partially substituting Mn and Al sites with Fe and Ni and identifying its enhanced phase stability, saturation magnetization density, magnetic anisotropy, and coercivity from density functional theory (DFT), machine learning (ML) crystal graph convolution neural network (CGCNN), and micro-magnetic modeling. When considering a fixed 50% Ni, the magnetic anisotropy increases with the increasing Fe content but decreases the formation energy. The calculated formation energies, elastic constants, and phonon frequencies demonstrate that the binary and quaternary compositions are stable. Most importantly, in 50% Fe and Ni-substituted-equiatomic phase, magnetic anisotropy constants and saturation magnetization density increase by 56% and 23% as compared to the MnAl. Further, the coercivity of the equiatomic phase predicted with micro-magnetic modeling is higher by 17% than the parent compound.

Bhandari, Churna [Ames National Laboratory, and Io↗

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗

Topological Rigidity and Non-Abelian Defect Junctions in Chiral Nematic Systems with Effective Biaxial Symmetry

We study topologically stable defect structures in systems where the defect line classification in three dimensions and associated algebra of interactions (the fundamental group) are governed by the non-Abelian eight-element group, the quaternions 𝑄 8 . The non-Abelian character of the defect algebra leads to a topological rigidity of bound defect pairs, and trivalent junctions which are the building blocks of multijunction trivalent networks. We realize such structures in laboratory chiral nematics and analyze their behavior analytically, along with numerical modeling.

Liquid crystals↗

High-precision scale setting with the Ω-baryon mass and gradient flow

The gradient-flow scale 𝑤 0 in lattice QCD is determined using the mass of the Ω − baryon to set the physical scale. Nine ensembles using the highly improved staggered quark (HISQ) action with lattice spacings of 0.15 fm down to 0.04 fm are used, seven of which have nearly physical light-quark masses. Electromagnetic corrections to the Ω − mass are defined in order to compute a pure-QCD Ω mass. The final result is 𝑤 0 = 0.17187⁢(68) fm, corresponding to a relative uncertainty of 0.40% and a central value in good agreement with previous calculations in the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.

decoherence↗

Measurement of 𝐷-line energies in sodiumlike Ir

We report measurements of the 𝐷 1 and 𝐷 2 transition energies in Na-like Ir (Ir 66+ ). The 𝐷 1 3⁢𝑠−3⁢𝑝 1/2 transition energy, measured in the extreme ultraviolet (EUV) region at 169.977 ± 0.005 eV with a relative uncertainty of 29 ppm, represents one of the most precise 𝐷-line energy measurements to date for high atomic numbers 𝑍 ≥ 30. The 𝐷 2 3⁢𝑠−3⁢𝑝 3/2 transition energy, measured in the x-ray region, is 621.11 ± 0.06 eV. Therefore, there is a fine-structure separation of 451.13 ± 0.06 eV for the Na-like Ir 3⁢𝑝 levels. We present theoretical calculations of these energies using quantum electrodynamic-extended relativistic many-body perturbation theory and multiple-configuration Dirac-Hartree-Fock methods, and discuss the discrepancies between experimental and theoretical values. The prospect of determining the absolute nuclear charge radii of heavy elements, including rare isotopes, from these measurements is explored.

Atomic spectra↗

Ultraviolet Fluorescence Imaging for Photovoltaic Module Metrology: Best Practices and Survey of Features Observed in Fielded Modules

As the photovoltaics (PV) industry grows in sophistication, so must the extent to which systems are characterized. UV Fluorescence (UVF) imaging is a valuable, easy-to-perform, high-throughput, nonintrusive technique for characterizing modules in the field and in the lab. However, UVF is still a relatively new technique, and many in the PV industry are still unaware of its potential. We provide a guideline for obtaining, processing, and interpreting UVF images. We have provided a list of considerations for imaging hardware and settings, a suggested pipeline for image processing, and details on a survey of features shown in UVF images. As a result, a new database with UVF images of 7190 modules and another database curated by BrightSpot Automation are publicly available.

14 SOLAR ENERGY↗

Acceleration of Power System Dynamic Simulations Using a Deep Equilibrium Layer and Neural ODE Surrogate

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based resources exacerbates the computational burden of running time domain simulations. Here, in this paper, we propose a data-driven surrogate model based on implicit machine learningspecifically deep equilibrium layers and neural ordinary differential equationsto learn a reduced order model of a portion of the full underlying system. The data-driven surrogate achieves similar accuracy and reduction in simulation time compared to a physics-based surrogate, without the constraint of requiring detailed knowledge of the underlying dynamic models. This work also establishes key requirements needed to integrate the surrogate into existing simulation workflows; the proposed surrogate is initialized to a steady state operating point that matches the power flow solution by design.

Neural ordinary differential equations↗