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At least 775 records · Page 43

Modelling and computational improvements to the simulation of single vector-boson plus jet processes for the ATLAS experiment

This paper presents updated Monte Carlo configurations used to model the production of single electroweak vector bosons (W, Z/γ$^{∗}$) in association with jets in proton-proton collisions for the ATLAS experiment at the Large Hadron Collider. Improvements pertaining to the electroweak input scheme, parton-shower splitting kernels and scale-setting scheme are shown for multi-jet merged configurations accurate to next-to-leading order in the strong and electroweak couplings. The computational resources required for these set-ups are assessed, and approximations are introduced resulting in a factor three reduction of the per-event CPU time without affecting the physics modelling performance. Continuous statistical enhancement techniques are introduced by ATLAS in order to populate low cross-section regions of phase space and are shown to match or exceed the generated effective luminosity. This, together with the lower per-event CPU time, results in a 50% reduction in the required computing resources compared to a legacy set-up previously used by the ATLAS collaboration. The set-ups described in this paper will be used for future ATLAS analyses and lay the foundation for the next generation of Monte Carlo predictions for single vector-boson plus jets production.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The high explosives & affected targets (HEAT) dataset

Artificial Intelligence (AI) surrogate models offer a computationally efficient alternative to full-physics simulations, yet no existing datasets are publicly available for training, testing, and validation of machine learning models of the dynamics of high-explosive driven shocks through multiple materials. Shock propagation through materials is a computationally challenging problem because simulations must include material-specific equations of state (EOS) along with descriptions of other physical processes such as plastic deformation, phase change, damage processes, fluid instabilities, and multi-material interactions. Shocks are typically initiated by high-velocity impacts or explosive loading. The latter case necessitates the addition of models of reactive materials to represent high-explosive (HE) detonation. Here, to address the lack of an expansive dataset for multi-material shock propagation in the AI/ML community, we present the High-Explosives and Affected Targets (HEAT) Dataset. HEAT is a physics-rich collection of two-dimensional, cylindrically symmetric, simulations generated using an Eulerian, multi-material, shock-propagation code developed at Los Alamos National Laboratory. The dataset includes two partitions: (1) the expanding shock-cylinder (CYL) simulations, Figs. 1, and (2) the Perturbed Layered Interface (PLI) simulations, Fig. 2. Entries in both partitions consist of time series of arrays of thermodynamic fields (pressure, density, and temperature), kinematic fields (position and velocity), and additional fields that depend on thermodynamic and/or kinematic fields (e.g., material stress). Materials in the CYL partition include solids (aluminium, copper, depleted uranium, stainless steel, tantalum, and a generic polymer), a liquid (water), gases (air, nitrogen), and a generic detonating material (high explosive, HE). The PLI partition spans a highly varying geometry but consists of fixed materials across entries: Copper, aluminium, stainless steel, generic polymer, and generic HE. HEAT captures critical phenomena such as momentum transfer, shock propagation, plastic deformation, and thermal effects, making HEAT a valuable benchmark for development of AI/ML emulation of multi-material shock propagation.

36 MATERIALS SCIENCE↗

CAFE AU LAIT: Compute-Aware Federated Augmented Low-Rank AI Training

Federated finetuning is crucial for unlocking the knowledge embedded in pretrained Large Language Models (LLMs) when data are geographically distributed across clients. Unlike finetuning with data from a single institution, federated finetuning allows collaboration across multiple institutions, enabling the utilization of diverse and decentralized datasets while preserving data privacy. Given the high computing costs of LLM training and the emphasis on energy efficiency in Federated Learning (FL), Low-Rank Adaptation (LoRA) has emerged as a widely adopted algorithm due to its significantly reduced number of trainable parameters. However, this assumes that all data silos have the necessary computing resources to compute local updates of LLMs. Nevertheless, in practice, the computing resources across clients are highly heterogeneous: while some may have access to hundreds of GPUs, others might have limited or no GPU access. Recently, federated finetuning using synthetic data has been proposed, allowing clients to participate in a collaborative training run without training LLMs locally. However, our experimental results reveal a performance gap between models trained using synthetic data and those trained using local updates. Motivated by the observed heterogeneity in computing resources and the performance gap, we propose a novel two-stage algorithm that leverages the storage and computing capabilities of a strong server. In the first stage, under the coordination of the strong server, clients with limited computing resources collaborate to generate synthetic data, which is transferred to and stored on the strong server. In the second stage, the strong server uses this synthetic data on behalf of the resource-constrained clients to perform federated LoRA finetuning alongside clients with sufficient computing resources. This approach ensures that all clients can participate in the finetuning process. Experimental results demonstrate that incorporating local updates from even a small fraction of clients improves performance compared to using synthetic data for all clients. Furthermore, we incorporate the Gaussian mechanism in both stages to guarantee client-level differential privacy.

Wang, Jiayi [ORNL]↗

Differential cross-section measurements of the production of four charged leptons in association with two jets using the ATLAS detector

Differential cross-sections are measured for the production of four charged leptons in association with two jets. These measurements are sensitive to final states in which the jets are produced via the strong interaction as well as to the purely-electroweak vector boson scattering process. The analysis is performed using proton-proton collision data collected by ATLAS at $\sqrt{s}$ = 13 TeV and with an integrated luminosity of 140 fb –1 . The data are corrected for the effects of detector inefficiency and resolution and are compared to state-of-the-art Monte Carlo event generator predictions. The differential cross-sections are used to search for anomalous weak-boson self-interactions that are induced by dimension-six and dimension-eight operators in Standard Model effective field theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for third-generation vector-like leptons in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for vector-like leptons in multilepton (two, three, or four-or-more electrons plus muons) final states with zero or more hadronic $τ$-lepton decays is presented. The search is performed using a dataset corresponding to an integrated luminosity of 139 fb -1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the LHC. To maximize the separation of signal and background, a machine-learning classifier is used. No excess of events is observed beyond the Standard Model expectation. Using a doublet vector-like lepton model, vector-like leptons coupling to third-generation Standard Model leptons are excluded in the mass range from 130 GeV to 900 GeV at the 95% confidence level, while the highest excluded mass is expected to be 970 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evaluating Acoustic vs. AI-Based Satellite Leak Detection in Aging US Water Infrastructure: A Cost and Energy Savings Analysis

The aging water distribution system in the United States, constructed mainly during the 1970s with some pipes dating back 125 years, is experiencing significant deterioration leading to substantial water losses. Along with the potential for water loss savings, improvements in the distribution system by using leak detection technologies can create net energy and cost savings. In this work, a new framework has been presented to calculate the economic level of leakage within water supply and distribution systems for two primary leak detection technologies (acoustic vs. satellite). In this work, a new framework is presented to calculate the economic level of leakage (ELL) within water supply and distribution systems to support smart infrastructure in smart cities. A case study focused using water audit data from Atlanta, Georgia, compared the costs of two leak mitigation technologies: conventional acoustic leak detection and artificial intelligence–assisted satellite leak detection technology, which employs machine learning algorithms to identify potential leak signatures from satellite imagery. The ELL results revealed that conducting one survey would be optimum for an acoustic survey, whereas the method suggested that it would be expensive to utilize satellite-based leak detection technology. However, results for cumulative financial analysis over a 3-year period for both technologies revealed both to be economically favorable with conventional acoustic leak detection technology generating higher net economic benefits of USD 2.4 million, surpassing satellite detection by 50%. A broader national analysis was conducted to explore the potential benefits of US water infrastructure mirroring the exemplary conditions of Germany and The Netherlands. Achieving similar infrastructure leakage index (ILI) values could result in annual cost savings of $\$4$–$\$4.8$ billion and primary energy savings of 1.6–1.9 TWh. These results demonstrate the value of combining economic modeling with advanced leak detection technologies to support sustainable, cost-efficient water infrastructure strategies in urban environments, contributing to more sustainable smart living outcomes.

acoustic leak detection↗

ZENN: A thermodynamics-inspired computational framework for heterogeneous data–driven modeling

Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.

36 MATERIALS SCIENCE↗

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗

Barriers to adopting artificial intelligence and machine learning technologies in nuclear power

Artificial intelligence and machine learning (AI/ML) technologies offer unique opportunities to transform nuclear plant operations and power generation. Benefits will be felt not only within existing analog and digital instrumentation and control, but also within work processes, the integration of people with technology and most importantly, the business case. The application of this new technology can help simplify complex problems and produce more effective decision-making, making nuclear power safer, more efficient, and more economically viable in the current energy market. Nonetheless, there are potential barriers to its adoption that must be overcome. The purpose of this paper is to categorize, review, and discuss barriers to AI/ML adoption within the nuclear power industry, with a focus on existing commercial reactors. Unique considerations for advanced reactors are also offered. Here we provide a comprehensive overview of the historical, technical, and business barriers that the industry faces, as well as stakeholder readiness, and end-user acceptance. We underscore the importance of user experience and offer potential solutions in overcoming each barrier. These include provisions for easier plant data access, a friendly regulatory environment, and investment in user trust and explainable AI.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Measurement of the Z boson invisible width at $\sqrt{s}=13$ TeV with the ATLAS detector

A measurement of the invisible width of the Z boson using events with jets and missing transverse momentum is presented using 37 fb -1 of 13 TeV proton–proton data collected by the ATLAS detector in 2015 and 2016. The ratio of Z → inv to Z → ℓℓ events, where inv refers to non-detected particles and ℓ is either an electron or a muon, is measured and corrected for detector effects. Events with at least one energetic central jet with p T ≥ 110 GeV are selected for both the Z → inv and Z → ℓℓ final states to obtain a similar phase space in the ratio. The invisible width is measured to be 506 ± 2 (stat.) ± 12 (syst.) MeV and is the single most precise recoil-based measurement. The result is in agreement with the most precise determination from LEP and the Standard Model prediction based on three neutrino generations.

13000 GeV-cms↗

Neural networks for modeling and control of particle accelerators

Charged particle accelerators support a wide variety of scientific, industrial, and medical applications. They range in scale and complexity from systems with just a few components for beam acceleration and manipulation, to large scientific user facilities that span many kilometers and have hundreds-to-thousands of individually-controllable components. Specific operational requirements must be met by adjusting the many controllable variables of the accelerator. Meeting these requirements can be challenging, both in terms of the ability to achieve specific beam quality metrics in a reliable fashion and in terms of the time needed to set up and maintain the optimal operating conditions. One avenue toward addressing this challenge is to incorporate techniques from the fields of machine learning (ML) and artificial intelligence (AI) into the way particle accelerators are modeled and controlled. While many promising approaches within AI/ML could be used for particle accelerators, this dissertation focuses on approaches based on neural networks. Neural networks are particularly well-suited to modeling, control, and diagnostic analysis of nonlinear systems, as well as systems with large parameter spaces. They are also very appealing for their ability to process high-dimensional data types, such as images and time series (both of which are ubiquitous in particle accelerators). In this work, key studies that demonstrated the potential utility of modern neural network-based approaches to modeling and control of particle accelerators are presented. The context for this work is important: at the start of this work in 2012, there was little interest in AI/ML in the particle accelerator community, and many of the advances in neural networks and deep learning that enabled its present success had not yet been made at that time. As such, this work was both an exploration of possible application areas and a generator of proof-of-concept demonstrations in these areas.

43 PARTICLE ACCELERATORS↗

A Transdisciplinary Review of Deep Learning Research and Its Relevance for Water Resources Scientists

Deep learning (DL), a new generation of artificial neural network research, has transformed industries, daily lives, and various scientific disciplines in recent years. DL represents significant progress in the ability of neural networks to automatically engineer problem-relevant features and capture highly complex data distributions. I argue that DL can help address several major new and old challenges facing research in water sciences such as interdisciplinarity, data discoverability, hydrologic scaling, equifinality, and needs for parameter regionalization. This review paper is intended to provide water resources scientists and hydrologists in particular with a simple technical overview, transdisciplinary progress update, and a source of inspiration about the relevance of DL to water. The review reveals that various physical and geoscientific disciplines have utilized DL to address data challenges, improve efficiency, and gain scientific insights. DL is especially suited for information extraction from image-like data and sequential data. Techniques and experiences presented in other disciplines are of high relevance to water research. Meanwhile, less noticed is that DL may also serve as a scientific exploratory tool. A new area termed AI neuroscience , where scientists interpret the decision process of deep networks and derive insights, has been born. This budding subdiscipline has demonstrated methods including correlation-based analysis, inversion of network-extracted features, reduced-order approximations by interpretable models, and attribution of network decisions to inputs. Moreover, DL can also use data to condition neurons that mimic problem-specific fundamental organizing units, thus revealing emergent behaviors of these units. Vast opportunities exist for DL to propel advances in water sciences.

54 ENVIRONMENTAL SCIENCES↗

Glovebox Handling of High-Consequence Materials with Super Baxter and Gesture-Based Programming - 18598

The handling of high-consequence materials is a difficult task requiring safe object manipulation while avoiding the risk of contamination or spillage. Specific operations including opening containers, segregating the wastes, and repackaging are required to be safely executed inside contained spaces such as gloveboxes. However, the workers' ability and dexterity to manipulate objects through thick protective gloves are compromised in many aspects. The fixed position of the glovebox arm ports restricts the movements of the workers' arms, which also makes it hard to lift heavy objects. Further, the operational workspace inside the glovebox is restricted by the gloves' reachability. Safety of workers is the paramount concern in glovebox operations and the very reason for their existence. Sharp edges and tools increases the risk of glove punctures, which may expose the operator to chemicals and radiation and risks contamination in the vicinity outside the glovebox. The operators are also affected by ergonomic stressors due to prolonged and repetitive operations. To achieve a high degree of human safety, robotic solutions to handle high-consequence materials inside the glovebox are desirable, as they remove the operators from the hazards listed above. However, robots, in general, lack the degree of adaptability necessary for most high-consequence material handling tasks as these tasks are often unstructured or highly variable. Likewise, most human operators, while highly skilled in the tasks at hand (task expertise), lack the robot programming skills necessary to adapt the robot's motions to the variations (programming expertise). A way to bridge this divide is to make robot programming more intuitive to human operators. Since humans naturally teach one another through demonstration and learning, robotic 'programming by demonstration' paradigms have begun to appear to reduce the burden of robot reprogramming. Gesture-Based Programming attempts to achieve that by enabling a robot to observe the normal actions and affordances of a human performing a task to learn to map those onto the skills of the robot. In the end, this approach permits benefits from both the human and the robot: the human's adaptive decision making and the robot's resilience to high-consequence material. Robotic solutions assuringly provide protection for the operators, however their autonomy brings about other potential risks. Artificial Intelligence is not perfect; it is a black box, which can produce results, but the full extent of those results may not be known precisely. In self-driving cars, a hypothetical AI problem is the 'green man detector'. Since self-driving cars have presumably never seen a green man, how can we know it won't veer toward him the first time it sees a green man? Likewise, even though GbP provides an open method for safe task execution replicating a human, incorrect task inferences can lead to potential collisions or unintended operations. Thus, a hardware safety measure is proposed to provide reliable operation inside the glovebox, and true safe operations are achieved by mechanically limiting the operational range of each arm link. The operational range is computed and validated through exhaustive offline simulations, which can be streamlined by affordable computing power. Super Baxter is one such robot which incorporates these capabilities. It is a human-like, bimanual robot, being developed at the Collaborative Robotics Lab (CRL) in conjunction with the Dept. of Energy/Environmental Management, Rethink Robotics, Barrett Technology, and the NSF Center for Robots and Sensors for the Human Well-Being (RoSe-HUB). Super Baxter is envisioned to represent the next generation of collaborative robots that will be intrinsically human-safe, as well as exceptionally human-intuitive. In summary, Super Baxter will enable safe glovebox operations through low-shot Gesture based Programming incorporated with hardware safety measures. Two aspects of safety will be discussed in the paper. First, the safety of the operator achieved by allowing him to program Super Baxter remotely through Gesture based Programming. Second, the safety of the glovebox, achieved by incorporating hardware safety measures using joint limits. Further, the capability of Super Baxter on Gesture based Programming is demonstrated through typical object manipulation tasks in glovebox operations. (authors)

42 ENGINEERING↗

Classification of Cloud Particle Imagery and Thermodynamics (COCPIT): A New Databasing Tool for the Characterization of Cloud Particle Images Captured During DOE Field Campaigns

The Department of Energy for decades has explored the earth system and atmosphere through research and deployment of in-situ and remote sensing platforms during field campaigns. Among these datasets exists a vast supply of cloud particle images that provide visual insight into the complex microphysics in the clouds that span our globe. The millions of images collected over decades of deployments provides a unique opportunity to further our understanding of our atmosphere down to the crystal size. This work over the past 5 years has sought to organize these images into digestible datasets that can then be used by scientists to further our understanding of microphysics. A machine learning model was developed that categorizes over 1.5 million images across 11 weather events with over 90% accuracy according to particle type. The database was then extended to include dimensional characteristics of the particle as well as co-location of environmental properties, such as temperature and water content. Then, to initialize the connection between these data and our understanding of how crystals form and grow, weather research and forecasting simulations were run to generate the growth histories of the classified crystals. This research culminates with 2 databases per event: (1) a database of all classified crystals and their dimensional and environmental properties and (2) simulated growth histories of each crystal. Finally, a user interface was created to allow researchers to explore data statistics.

54 ENVIRONMENTAL SCIENCES↗

Profiles of upcoming HPC Applications and their Impact on Reservation Strategies

With the expected convergence between HPC, BigData and AI, new applications with different profiles are coming to HPC infrastructures. Here, we aim at better understanding the features and needs of these applications in order to be able to run them efficiently on HPC platforms. The approach followed is bottom-up: we study thoroughly an emerging application from the neuroscience community (SLANT) to understand its behavior. Based on these observations, we derive a generic, yet simple, application model (namely, a linear sequence of stochastic jobs). We expect this model to be representative for a large set of upcoming applications that require the computational power of HPC clusters without fitting the typical behavior of large-scale traditional applications. In a second step, we show how one can manipulate this generic model in a scheduling framework. Specifically we consider the problem of making reservations (both time and memory) for an execution on an HPC platform. We derive solutions using the model of the first step of this work. We experimentally show the robustness of the model, even with very few data or with another application, to generate the model, and provide performance gains with regards to standard and more recent approaches used in the neuroscience community.

97 MATHEMATICS AND COMPUTING↗

Measurements of top-quark pair single- and double-differential cross-sections in the all-hadronic channel in pp collisions at $ \sqrt{\mathrm{s}} $ = 13 TeV using the ATLAS detector

Differential cross-sections are measured for top-quark pair production in the all-hadronic decay mode, using proton-proton collision events collected by the ATLAS experiment in which all six decay jets are separately resolved. Absolute and normalised single- and double-differential cross-sections are measured at particle and parton level as a function of various kinematic variables. Emphasis is placed on well-measured observables in fully reconstructed final states, as well as on the study of correlations between the top-quark pair system and additional jet radiation identified in the event. The study is performed using data from proton-proton collisions at s = 13 TeV collected by the ATLAS detector at CERN’s Large Hadron Collider in 2015 and 2016, corresponding to an integrated luminosity of 36.1 fb - 1 . The rapidities of the individual top quarks and of the top-quark pair are well modelled by several independent event generators. Significant mismodelling is observed in the transverse momenta of the leading three jet emissions, while the leading top-quark transverse momentum and top-quark pair transverse momentum are both found to be incompatible with several theoretical predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data-driven design of electrolyte additives supporting high-performance 5 V LiNi 0.5 Mn 1.5 O 4 positive electrodes

LiNi 0.5 Mn 1.5 O 4 (LNMO) is a high-capacity spinel-structured material with an average lithiation/de-lithiation potential at ca. 4.6–4.7 V vs Li + /Li, far exceeding the stability limits of electrolytes. An efficient way to enable LNMO in lithium-ion batteries is to reformulate an electrolyte composition that stabilizes both graphitic (Gr) negative electrode with solid-electrolyte-interphase and LNMO with cathode-electrolyte-interphase. In this study, we select and test a diverse collection of 28 single and dual additives for the Gr||LNMO battery system. Subsequently, we train machine learning models on this dataset and employ the trained models to suggest 6 binary compositions out of 125, based on predicted final area-specific-impedance, impedance rise, and final specific-capacity. Such machine learning-generated new additives outperform the initial dataset. This finding not only underscores the efficacy of machine learning in identifying materials in a highly complicated application space but also showcases an accelerated material discovery workflow that directly integrates data-driven methods with battery testing experiments.

batteries↗

Heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides

We propose a heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides. We show the details by implementing nonlocal entanglement generation, entanglement swapping, and entanglement purification modules with atoms in waveguides, and discuss the feasibility of the repeater with currently achievable technology. In our scheme, the faulty events can be discarded by detecting the polarization of the photons. That is, our protocols are accomplished with a fidelity of 100% in principle, which is advantageous for implementing realistic long-distance quantum communication. Moreover, additional atomic qubits are not required, but only a single-photon medium. Our scheme is scalable and attractive since it can be realized in solid-state quantum systems. With the great progress on controlling atom-waveguide systems, the repeater may be very useful in quantum information processing in the future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗