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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
DOE OSTI2013

Dark halos and elliptical galaxies as marginally stable dynamical systems

The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions—a context in which subtle spurious effects originating from the singularity in the two-body potential become particularly clear. We focus on the case of spherical systems, which support only regular orbits in the collisionless limit, despite the persistence of local exponential instability of N-body trajectories in the anomalous case of discrete point particle representation even as N → ∞. When the singularity in the potential is removed, this apparent contradiction disappears. In the absence of fluctuations, equilibrium configurations generally correspond to positive scalar curvature and thus support stable trajectories. A null scalar curvature is associated with an effective, averaged equation of state describing dynamically relaxed equilibria with marginally stable trajectories. The associated configurations are quite similar to those of observed elliptical galaxies and simulated cosmological halos and are necessarily different from the systems dominated by isothermal cores, expected from entropy maximization in the context of the standard theory of violent relaxation. It is suggested that this is the case because a system starting far from equilibrium does not reach a 'most probable state' via violent relaxation, but that this process comes to an end as the system finds and (settles in) a configuration where it can most efficiently wash out perturbations. We explicitly test this interpretation by means of direct simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Surface plasmon resonance induced Er{sup 3+} photoluminescence enhancement in tellurite glass

The melt quenching method is used to prepare tellurite glasses co-activated with erbium ions and silver nanoparticles (Ag NPs). The glass samples are characterized by x-ray diffraction, UV-vis-NIR absorption, transmission electron microscopy (TEM) imaging, and photoluminescence spectroscopy. The XRD pattern shows no sharp peak indicating an amorphous nature of the glasses. The presence of Ag NPs is confirmed from TEM micrograph. The absorption spectra reveal not only the peaks due to Er{sup 3+} ions, but also the surface plasmon resonance band of silver NPs in the 510–535 nm range. The J-O model has been applied to the room temperature absorption intensities of Er{sup 3+} (4f{sup 11}) transitions to establish the so-called J-O intensity parameters: Ω{sub 2}, Ω{sub 4}, and Ω{sub 6}. The intensity parameters are used to determine the radiative decay rates (emission probabilities of transitions) and branching ratios of the Er{sup 3+} transitions from the excited state J manifolds to the lower-lying J' manifolds. Intensified of 1.53 μm band is obtained for the sample containing 0.5 mol. % of AgNO{sub 3} (Ag0.5 glass) using for excitation a laser operating at 980 nm. The simultaneous influence of the Ag NPs → Er{sup 3+} energy transfer and the contribution of the intensified local field effect due to the silver NPs give origin to the enhancement of both the Photoluminescence (PL) intensity and the PL lifetime relative to the {sup 4}I{sub 13/2} → {sup 4}I{sub 15/2} transition, whereas the quenching is ascribed to the energy transfer from Er{sup 3+} ions to silver NPs. Based on the analysis of the temperature dependence of the PL intensity and decay time, we identified a weak back transfer process from Er to the glass host that makes the quenching of the PL intensity weak. Large magnitudes of calculated emission cross-section (σ{sub e}), effective bandwidth (Δλ{sub eff}), and bandwidth quality factor (FWHM × σ{sub e}) relatives to {sup 4}I{sub 13/2} → {sup 4}I{sub 15/2} transition in Er doped Ag0.5 glass have been shown. They indicate that this glass sample has good prospect as a gain medium applied for 1.53 μm band broad and high-gain erbium-doped fiber amplifiers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

By extending the Kac–Rice approach to manifolds of finite internal dimension, we show that the mean number ⟨N{sub tot}⟩ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension d=1+1, grows exponentially ⟨N{sub tot}⟩ ~exp(r L) with its length L. The growth rate r is found to be directly related to the generalized Lyapunov exponent (GLE) which is a moment-generating function characterizing the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schrödinger operator of the 1D Anderson localization problem. For strong confinement, the rate r is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate r is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape “topology trivialization” phenomenon, we obtain an upper bound for the depinning threshold f{sub c}, in the presence of an applied force, for elastic lines and d-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spectral broadening and ultrafast dynamics of a nitrogen-vacancy center ensemble in diamond

Abstract Many applications of nitrogen-vacancy (NV) centers in diamond crucially rely on a spectrally narrow and stable optical zero-phonon line transition. Though many impressive proof-of-principle experiments have been demonstrated, much work remains in engineering NV centers with spectral properties that are sufficiently robust for practical implementation. To elucidate the mechanisms underlying their interactions with the environment, we apply multi-dimensional coherent spectroscopy to an NV center ensemble in bulk diamond at cryogenic temperatures. Our spectra reveal thermal dephasing due to quasi-localized vibrational modes as well as ultrafast spectral diffusion on the picosecond timescale. The intrinsic, ensemble-averaged homogeneous linewidth is found to be in the tens of GHz range by extrapolating to zero temperature. We also observe a temperature-dependent Stark splitting of the excited state manifold, relevant to NV sensing protocols.

Liu, Albert (ORCID:0000000167183719)↗
NASA NTRS2011

180-GHz Interferometric Imager

A 180-GHz interferometric imager uses compact receiver modules, combined high- and low-gain antennas, and ASIC (application specific integrated circuit) correlator technology, enabling continuous, all-weather observations of water vapor with 25-km resolution and 0.3-K noise in 15 minutes of observation for numerical weather forecasting and tropical storm prediction. The GeoSTAR-II prototype instrument is broken down into four major subsystems: the compact, low-noise receivers; sub-array modules; IF signal distribution; and the digitizer/correlator. Instead of the single row of antennas adopted in GeoSTAR, this version has four rows of antennas on a coarser grid. This dramatically improves the sensitivity in the desired field of view. The GeoSTAR-II instrument is a 48-element, synthetic, thinned aperture radiometer operating at 165-183 GHz. The instrument has compact receivers integrated into tiles of 16 elements in a 4x4 arrangement. These tiles become the building block of larger arrays. The tiles contain signal distribution for bias controls, IF signal, and local oscillator signals. The IF signals are digitized and correlated using an ASIC correlator to minimize power consumption. Previous synthetic aperture imagers have used comparatively large multichip modules, whereas this approach uses chip-scale modules mounted on circuit boards, which are in turn mounted on the distribution manifolds. This minimizes the number of connectors and reduces system mass. The use of ASIC technology in the digitizers and correlators leads to a power reduction close to an order of magnitude.

Kangaslahti, Pekka P.↗
DOE OSTI2015

Multidimensional smooth loops with universal elasticity

Let E-tilde be a universal (isotopically invariant) identity that is derived from the elasticity identity E:(xy)x=x(yx). One of the authors has previously shown that a) each local loop of dimension r with identity E-tilde (briefly, a loop E-tilde ) is a smooth middle Bol loop of dimension r; b) smooth two-dimensional loops E-tilde are Lie groups; c) up to isotopy, there exist only two three-dimensional loops E-tilde : the loops E{sub 1} and E{sub 2}. In this paper, the loops E{sub 1} and E{sub 2} are extended to the multidimensional case. The fact that each smooth loop E-tilde of dimension r corresponds to a unique multidimensional three-web on a manifold of dimension 2r is key to our work. In addition, the class of loops under investigation is characterized by the fact that the torsion tensor of the corresponding web has rank 1 (that is, the algebra generated by this tensor has a one-dimensional derived algebra). This enables us to express the differential equations of the problem in an invariant form. The system of equations thus obtained was found to be amenable to integration in the most general case, and the equations of the required loops have been obtained in local coordinates. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

C{sup ∗}-Quadratic Quantization

In the first part of the paper we introduce a new parametrization for the manifold underlying quadratic analogue of the usual Heisenberg group introduced in Accardi et al. (Infin Dimens Anal Quantum Probab Relat Top 13:551–587, 2010) which makes the composition law much more transparent. In the second part of the paper the new coordinates are used to construct an inductive system of ∗-algebras each of which is isomorphic to a finite tensor product of copies of the one-mode quadratic Weyl algebra. We prove that the inductive limit ∗-algebra is factorizable and has a natural localization given by a family of ∗-sub-algebras each of which is localized on a bounded Borel subset of ℝ. Moreover, we prove that the family of quadratic analogues of the Fock states, defined on the inductive family of ∗-algebras, is projective hence it defines a unique state on the limit ∗-algebra. Finally we complete this ∗-algebra under the (minimal regular) C{sup ∗}-norm thus obtaining a C{sup ∗}-algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping

The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. This is particularly pertinent today, as the SPM community has seen a rapidly growing trend towards simultaneous capture of multiple imaging channels and complex modes of operation involving high-dimensional information-rich datasets, bringing forward the challenges of visualization and analysis, particularly for cases where the underlying dynamic model is poorly understood. To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical mapping on a mixed polymer thin film and resolving irregular hydration structure of calcite at atomic resolution. Using the proposed methodology, we can efficiently reveal and hierarchically represent salient material features with rich local details, further enabling denoising, classification, and high-resolution functional imaging.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions

We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice constructions of chiral gauge theories. We point out that there are two notions of chiral symmetry for Kähler-Dirac fermions, both having a mixed perturbative anomaly with gravity leading to index theorems on closed manifolds. By formulating these theories on a manifold with boundary, we find the APS index theorems corresponding to each of these symmetries, necessary for a complete picture of anomaly inflow, using a recently discovered physics-motivated proof. We comment on a fundamental difference between the nature of these two symmetries by showing that a sensible local, symmetric boundary condition only exists for one of the two symmetries. This sheds light on how these symmetries behave under lattice discretization, and in particular on their use for recent symmetric-mass generation proposals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Topological prethermal strong zero modes on superconducting processors

Abstract Symmetry-protected topological phases 1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model 5 . They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations 1–4,6–8 . In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay 9–11 . Here we report the observation of a distinct type of topological edge mode 12–14 , which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach 15–18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.

Science & Technology - Other Topics↗
DOE OSTI2024

Scanning electrochemical probe microscopy investigation of two-dimensional materials

Research interests in two-dimensional (2D) materials have seen exponential growth owing to their unique and fascinating properties. The highly exposed lattice planes coupled with tunable electronic states of 2D materials have created manifold opportunities in the design of new platforms for energy conversion and sensing applications. Still, challenges in understanding the electrochemical (EC) characteristics of these materials arise from the complexity of both intrinsic and extrinsic heterogeneities that can obscure structure–activity correlations. Scanning EC probe microscopic investigations offer unique benefits in disclosing local EC reactivities at the nanoscale level that are otherwise inaccessible with macroscale methods. This review summarizes recent progress in applying techniques of scanning EC microscopy (SECM) and scanning EC cell microscopy (SECCM) to obtain distinctive insights into the fundamentals of 2D electrodes. We showcase the capabilities of EC microscopies in addressing the roles of defects, thickness, environments, strain, phase, stacking, and many other aspects in the heterogeneous electron transfer, ion transport, electrocatalysis, and photoelectrochemistry of representative 2D materials and their derivatives. Perspectives for the advantages, challenges, and future opportunities of scanning EC probe microscopy investigation of 2D structures are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamical edge modes and entanglement in Maxwell theory

Abstract Previous work on black hole partition functions and entanglement entropy suggests the existence of “edge” degrees of freedom living on the (stretched) horizon. We identify a local and “shrinkable” boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D entanglement entropy consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.

Physics↗
DOE OSTI2014

An NCN-pincer ligand dysprosium single-ion magnet showing magnetic relaxation via the second excited state

Single-molecule magnets are compounds that exhibit magnetic bistability purely of molecular origin. The control of anisotropy and suppression of quantum tunneling to obtain a comprehensive picture of the relaxation pathway manifold, is of utmost importance with the ultimate goal of slowing the relaxation dynamics within single-molecule magnets to facilitate their potential applications. Combined ab initio calculations and detailed magnetization dynamics studies reveal the unprecedented relaxation mediated via the second excited state within a new DyNCN system comprising a valence-localized carbon coordinated to a single dysprosium(III) ion. The essentially $C_{2v}$ symmetry of the Dy III ion results in a new relaxation mechanism, hitherto unknown for mononuclear Dy III complexes, opening new perspectives for means of enhancing the anisotropy contribution to the spin-relaxation barrier.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Dynamical system analysis of Einstein–Skyrme model in a Kantowski–Sachs spacetime

The present work deals with anisotropic (but zero heat flux) Skyrme fluid with a constant radial profile in locally rotational Kantowski–Sachs spacetime in the background of Einstein gravity. By suitably change of variables the field equations are transformed to an autonomous system. To examine the stability of the system critical points are determined. For hyperbolic critical points the analysis of the system is done using Hartman–Grobman theorem, while center manifold theory is used to analyze non-hyperbolic critical points. Also stability at infinity is analyzed to visualize the global evolution of the Universe. As a result the 3D-phase space is identified with the Poincaré 3-sphere embedded in R{sup 4}. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally possible bifurcation scenarios are discussed to identify the point of phase transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Interactive prostate segmentation using atlas-guided semi-supervised learning and adaptive feature selection

Purpose: Accurate prostate segmentation is necessary for maximizing the effectiveness of radiation therapy of prostate cancer. However, manual segmentation from 3D CT images is very time-consuming and often causes large intra- and interobserver variations across clinicians. Many segmentation methods have been proposed to automate this labor-intensive process, but tedious manual editing is still required due to the limited performance. In this paper, the authors propose a new interactive segmentation method that can (1) flexibly generate the editing result with a few scribbles or dots provided by a clinician, (2) fast deliver intermediate results to the clinician, and (3) sequentially correct the segmentations from any type of automatic or interactive segmentation methods. Methods: The authors formulate the editing problem as a semisupervised learning problem which can utilize a priori knowledge of training data and also the valuable information from user interactions. Specifically, from a region of interest near the given user interactions, the appropriate training labels, which are well matched with the user interactions, can be locally searched from a training set. With voting from the selected training labels, both confident prostate and background voxels, as well as unconfident voxels can be estimated. To reflect informative relationship between voxels, location-adaptive features are selected from the confident voxels by using regression forest and Fisher separation criterion. Then, the manifold configuration computed in the derived feature space is enforced into the semisupervised learning algorithm. The labels of unconfident voxels are then predicted by regularizing semisupervised learning algorithm. Results: The proposed interactive segmentation method was applied to correct automatic segmentation results of 30 challenging CT images. The correction was conducted three times with different user interactions performed at different time periods, in order to evaluate both the efficiency and the robustness. The automatic segmentation results with the original average Dice similarity coefficient of 0.78 were improved to 0.865–0.872 after conducting 55–59 interactions by using the proposed method, where each editing procedure took less than 3 s. In addition, the proposed method obtained the most consistent editing results with respect to different user interactions, compared to other methods. Conclusions: The proposed method obtains robust editing results with few interactions for various wrong segmentation cases, by selecting the location-adaptive features and further imposing the manifold regularization. The authors expect the proposed method to largely reduce the laborious burdens of manual editing, as well as both the intra- and interobserver variability across clinicians.

07 ISOTOPE AND RADIATION SOURCES↗