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At least 1,207 records · Page 67

A spectral scheme for Kohn–Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

PATCHY BLAZAR HEATING: DIVERSIFYING THE THERMAL HISTORY OF THE INTERGALACTIC MEDIUM

TeV-blazars potentially heat the intergalactic medium (IGM) as their gamma rays interact with photons of the extragalactic background light to produce electron–positron pairs, which lose their kinetic energy to the surrounding medium through plasma instabilities. This results in a heating mechanism that is only weakly sensitive to the local density, and therefore approximately spatially uniform, naturally producing an inverted temperature–density relation in underdense regions. In this paper we go beyond the approximation of uniform heating and quantify the heating rate fluctuations due to the clustered distribution of blazars and how this impacts the thermal history of the IGM. We analytically compute a filtering function that relates the heating rate fluctuations to the underlying dark matter density field. We implement it in the cosmological code GADGET-3 and perform large-scale simulations to determine the impact of inhomogeneous heating. We show that because of blazar clustering, blazar heating is inhomogeneous for z ≳ 2. At high redshift, the temperature–density relation shows an important scatter and presents a low temperature envelope of unheated regions, in particular at low densities and within voids. However, the median temperature of the IGM is close to that in the uniform case, albeit slightly lower at low redshift. We find that blazar heating is more complex than initially assumed and that the temperature–density relation is not unique. Our analytic model for the heating rate fluctuations couples well with large-scale simulations and provides a cost-effective alternative to subgrid models.

79 ASTRONOMY AND ASTROPHYSICS↗

Spatiotemporal pattern detection, generation, and computation with circuits

Abstract Implementations of neurons, delays, and synapse circuits are presented with simulations. These neural elements are used to create two small spiking neural networks, the Rate-Window and Order-Biased clusters, which are capable of detecting simple two-spike spatiotemporal patterns. A simple pattern detecting network (SPDN) is created by combining the Rate-Window and Order-Biased clusters, where clusters are small spiking neural networks, and its simple pattern detection ability is demonstrated in simulation. The SPDN is used to implement a complex pattern detecting network (CPDN) and its complex pattern detection ability is demonstrated in simulation. Methods for generating arbitrary spatiotemporal patterns are presented. The CPDN and spatiotemporal pattern generation methods are then used to implement a novel spatiotemporal computing paradigm based on detecting and responding to spatiotemporal symbols. A simulation of a spatiotemporal half adder is presented to demonstrate the computing paradigm.

97 - MATHEMATICS AND COMPUTING↗

Tailoring composition and deformation modes at the microstructural level for next generation low-cost high-strength austenitic stainless steels

The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.

08 HYDROGEN↗

Parallel performance of algebraic multigrid domain decomposition

Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This article examines the design, implementation, and parallel performance of a novel algorithm, algebraic multigrid domain decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared with AMG, and speedup over AMG is demonstrated on a large GPU cluster.

97 MATHEMATICS AND COMPUTING↗

Molecular structure determination: Equilibrium structure of pyrimidine (m-C 4 H 4 N 2 ) from rotational spectroscopy (reSE) and high-level ab initio calculation (re) agree within the uncertainty of experimental measurement

The pure rotational spectrum of pyrimidine (m-C 4 H 4 N 2 ), the meta-substituted dinitrogen analog of benzene, has been studied in the millimeter-wave region from 235 GHz to 360 GHz. The rotational spectrum of the ground vibrational state has been assigned and fit to yield accurate rotational and distortion constants. Over 1700 distinct transitions were identified for the normal isotopologue in its ground vibrational state and least-squares fit to a partial sextic S-reduced Hamiltonian. Transitions for all four singly substituted 13 C and 15 N isotopologues were observed at natural abundance and were likewise fit. Deuterium-enriched samples of pyrimidine were synthesized, giving access to all eleven possible deuterium-substituted isotopologues, ten of which were previously unreported. Experimental values of rotational constants and computed values of vibration–rotation interaction constants and electron-mass corrections were used to determine semi-experimental equilibrium structures (r e SE ) of pyrimidine. The r e SE structure obtained using coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] corrections shows exceptional agreement with the re structure computed at the CCSD(T)/cc-pCV5Z level (≤0.0002 Å in bond distance and ≤0.03° in bond angle). Of the various computational methods examined, CCSD(T)/cc-pCV5Z is the only method for which the computed value of each geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The exceptionally high accuracy and precision of the structure determination is a consequence of the large number of isotopologues measured, the precision and extent of the experimental frequency measurements, and the sophisticated theoretical treatment of the effects of vibration–rotation coupling and electron mass. Taken together, these demanding experimental and computational studies establish the capabilities of modern structural analysis for a prototypical monocyclic aromatic compound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Latent code-based fusion: A Volterra neural network approach

We propose a deep structure encoder using Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in lieu of generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a robust classification performance.

97 MATHEMATICS AND COMPUTING↗

Stability and mobility of tungsten clusters on tungsten (110) surface: Ab initio and atomistic simulations

Quantifying the surface transport properties of tungsten (W) is of prime importance to understand the formation of nano-fuzz in fusion plasma-facing conditions. The stability and mobility of W adatom clusters (W n , n = 2-9) on the W(110) surface has been investigated by computer simulations, including ab initio calculations using density functional theory (DFT) and molecular statics (MS) simulations with multiple W interatomic potentials. The DFT results demonstrate that the sequential binding energy generally increases with number of W adatoms, except for the 5 th and 7 th W adatoms. The most common elemental migration steps of W n (n>2) clusters are observed to consist of monomer and dimer hops, while larger W n clusters can also diffuse by dissociation and recombination of smaller clusters. The threshold migration energy of W 9 is the highest, then followed by W 8 , W 4 , and W 6 , while W 3 , W 5 , and W 7 have similar migration energies. Compared to DFT, each interatomic potential evaluated overestimates the binding energies of W n clusters. Additionally, the embedded-atom potential developed by Juslin and Wirth adequately predicts the threshold migration energy of W n (n>2) clusters, although it predicts different underlying migration mechanisms. The results show that interaction mechanism between W adatoms controls the stability and mobility of W n clusters on the W(110) surface.

36 MATERIALS SCIENCE↗

Continuous Security and Configuration Monitoring of HPC Clusters

Continuous security and configuration monitoring of information systems has been a time consuming and laborious task for system administrators at the High Performance Computing (HPC) center. Prior to this project, system administrators had to manually check the settings of thousands of nodes, which required a significant number of hours rendering the old process ineffective and inefficient. This paper explains the application of Splunk Enterprise, a software agent, and a reporting tool in the development of a user application interface to track and report on critical system updates and security compliance status of HPC Clusters. In conjunction with other configuration management systems, the reporting tool is to provide continuous situational awareness to system administrators of the compliance state of information systems. Our approach consisted of the development, testing, and deployment of an agent to collect any arbitrary information across a massively distributed computing center, and organize that information into a human-readable format. Using Splunk Enterprise, this raw data was then gathered into a central repository and indexed for search, analysis, and correlation. Following acquisition and accumulation, the reporting tool generated and presented actionable information by filtering the data according to command line parameters passed at run time. Preliminary data showed results for over six thousand nodes. Further research and expansion of this tool could lead to the development of a series of agents to gather and report critical system parameters. However, in order to make use of the flexibility and resourcefulness of the reporting tool the agent must conform to specifications set forth in this paper. This project has simplified the way system administrators gather, analyze, and report on the configuration and security state of HPC clusters, maintaining ongoing situational awareness. Rather than querying each cluster independently, compliance checking can be managed from one central location.

97 MATHEMATICS AND COMPUTING↗

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluation of advanced automatic PET segmentation methods using nonspherical thin-wall inserts

Purpose: The use of positron emission tomography (PET) within radiotherapy treatment planning requires the availability of reliable and accurate segmentation tools. PET automatic segmentation (PET-AS) methods have been recommended for the delineation of tumors, but there is still a lack of thorough validation and cross-comparison of such methods using clinically relevant data. In particular, studies validating PET segmentation tools mainly use phantoms with thick plastic walls inserts of simple spherical geometry and have not specifically investigated the effect of the target object geometry on the delineation accuracy. Our work therefore aimed at generating clinically realistic data using nonspherical thin-wall plastic inserts, for the evaluation and comparison of a set of eight promising PET-AS approaches. Methods: Sixteen nonspherical inserts were manufactured with a plastic wall of 0.18 mm and scanned within a custom plastic phantom. These included ellipsoids and toroids derived with different volumes, as well as tubes, pear- and drop-shaped inserts with different aspect ratios. A set of six spheres of volumes ranging from 0.5 to 102 ml was used for a baseline study. A selection of eight PET-AS methods, written in house, was applied to the images obtained. The methods represented promising segmentation approaches such as adaptive iterative thresholding, region-growing, clustering and gradient-based schemes. The delineation accuracy was measured in terms of overlap with the computed tomography reference contour, using the dice similarity coefficient (DSC), and error in dimensions. Results: The delineation accuracy was lower for nonspherical inserts than for spheres of the same volume in 88% cases. Slice-by-slice gradient-based methods, showed particularly lower DSC for tori (DSC < 0.5), caused by a failure to recover the object geometry. The region-growing method reached high levels of accuracy for most inserts (DSC > 0.76 except for tori) but showed the largest errors in the recovery of pears and drops dimensions (higher than 10% and 30% of the true length, respectively). Large errors were visible for one of the gradient-based contouring methods when delineating drop-shaped inserts. Low DSC due to systematic underestimation of the volumes was observed for our fuzzy clustering method when using nonspherical inserts. The adaptive iterative thresholding method produced the highest DSC score on our nonspherical dataset (DSC > 0.83, except for tori) and showed robustness to the insert geometry. Conclusions: This study investigated the accuracy of eight PET-AS methods for the delineation of objects with a range of nonspherical geometries. The authors’ results confirmed the robustness of some segmentation approaches, but also showed the weaknesses of some of the other methods implemented, which were not observed with spherical inserts. This work therefore highlights the importance of using a variety of thin-wall inserts with complex geometries for the validation of PET-AS methods and provided useful information for further development of the methods tested.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Avoiding Excess Computation in Asynchronous Evolutionary Algorithms

Asynchronous evolutionary algorithms are becoming increasingly popular as a means of making full use of many processors while solving computationally expensive search and optimization problems. These algorithms excel at keeping large clusters fully utilized, but may sometimes inefficiently sample an excess of fast-evaluating solutions at the expense of higher-quality, slow-evaluating ones. We introduce a steady-state parent selection strategy, SWEET (“Selection whilE EvaluaTing”), that sometimes selects individuals that are still being evaluated and allows them to reproduce early. This gives slow-evaluating individuals that have higher fitnesses an increased ability to multiply in the population. We find that SWEET appears effective in simulated take-over time analysis, but that its benefit is confined mostly to early in the run, and our preliminary study on an autonomous vehicle controller problem that involves tuning a spiking neural network proves inconclusive.

Scott, Eric↗

SHAPER: can you hear the shape of a jet?

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover’s Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Cluster truncated Wigner approximation in strongly interacting systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method

Heterogeneous materials are ubiquitous in nature and synthetic situations and have a wide range of important engineering applications. Accurate modeling and reconstructing three-dimensional (3D) microstructure of topologically complex materials from limited morphological information such as a two-dimensional (2D) micrograph is crucial to the assessment and prediction of effective material properties and performance under extreme conditions. Here, we extend a recently developed dilation–erosion method and employ the Yeong–Torquato stochastic reconstruction procedure to model and generate 3D austenitic–ferritic cast duplex stainless steel microstructure containing percolating filamentary ferrite phase from 2D optical micrographs of the material sample. Specifically, the ferrite phase is dilated to produce a modified target 2D microstructure and the resulting 3D reconstruction is eroded to recover the percolating ferrite filaments. The dilation–erosion reconstruction is compared with the actual 3D microstructure, obtained from serial sectioning (polishing), as well as the standard stochastic reconstructions incorporating topological connectedness information. The fact that the former can achieve the same level of accuracy as the latter suggests that the dilation–erosion procedure is tantamount to incorporating appreciably more topological and geometrical information into the reconstruction while being much more computationally efficient. - Highlights: • Spatial correlation functions used to characterize filamentary ferrite phase • Clustering information assessed from 3D experimental structure via serial sectioning • Stochastic reconstruction used to generate 3D virtual structure 2D micrograph • Dilation–erosion method to improve accuracy of 3D reconstruction.

36 MATERIALS SCIENCE↗

Fe Protein-Independent Substrate Reduction by Nitrogenase MoFe Protein Variants

The reduction of substrates catalyzed by nitrogenase normally requires nucleotide-dependent Fe protein delivery of electrons to the MoFe protein, which contains the active site FeMo-cofactor. Here, it is reported that independent substitution of three amino acids (ß-98Tyr→His, α-64Tyr→His, and ß-99Phe→His) located between the P cluster and FeMo-cofactor within the MoFe protein endows it with the ability to reduce protons to H2, azide to ammonia, and hydrazine to ammonia without the need for Fe protein or ATP. Instead, electrons can be provided by the low potential reductant polyaminocarboxylate ligated Eu(II) (Em -1.1 to -0.84 V vs NHE). The crystal structure of the ß-98Tyr→His variant MoFe protein was determined, revealing only small changes near the amino acid substitution that affect the solvent structure and immediate vicinity between the P cluster and the FeMo-cofactor, with no global conformational changes observed. Computational normal mode analysis on the nitrogenase complex reveal coupling in the motions of the Fe protein and the region of the MoFe protein with these three amino acids, which suggests a possible mechanism for how Fe protein might communicate deep within the MoFe protein subtle changes that profoundly affect intramolecular electron transfer and substrate reduction. This work was supported by a grant from the National Science Foundation (MCB-1330807) to JWP and LCS. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0010687 and DE-SC0010834 to LCS and DRD) and the Division of Chemical Sciences, Geosciences, and Bio-Sciences (SR). The coordinates for the ß-98His MoFe protein were deposited with the Protein Data Bank (PDB 4XPI).

Danyal, Karamatullah↗

Fission and fusion scenarios for magnetic microswimmer clusters

Fission and fusion processes of particle clusters occur in many areas of physics and chemistry from subnuclear to astronomic length scales. Here we study fission and fusion of magnetic microswimmer clusters as governed by their hydrodynamic and dipolar interactions. Rich scenarios are found that depend crucially on whether the swimmer is a pusher or a puller. In particular a linear magnetic chain of pullers is stable while a pusher chain shows a cascade of fission (or disassembly) processes as the self-propulsion velocity is increased. Contrarily, magnetic ring clusters show fission for any type of swimmer. Moreover, we find a plethora of possible fusion (or assembly) scenarios if a single swimmer collides with a ringlike cluster and two rings spontaneously collide. Lastly, our predictions are obtained by computer simulations and verifiable in experiments on active colloidal Janus particles and magnetotactic bacteria.

36 MATERIALS SCIENCE↗

Many-body entanglement in solid-state emitters

The preparation and control of quantum states lie at the heart of quantum information science. Recent advances in solid-state quantum emitters (QEs) and nanophotonics have transformed the landscape of quantum photonic technologies, enabling scalable generation of quantum states of light and matter. A new frontier in solid-state quantum photonics is the engineering of many-body interactions between QEs and photons to achieve robust coherence and controllable many-body entanglement. These entangled states, including photonic graph and cluster states, superradiant emission and emergent quantum phases, are promising for quantum computation, sensing and simulation. However, intrinsic inhomogeneities and decoherence in solid-state platforms pose considerable challenges in realizing such complex entangled states. This Review provides an overview of fundamental many-body interactions and dynamics at the light–matter interfaces of solid-state QEs and discusses recent advances in mitigating decoherence and harnessing robust many-body coherence.

36 MATERIALS SCIENCE↗