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At least 163 records · Page 9

Quantum Technologies for UAS (QTech)

Recent advances in small Unmanned Aerial System (sUAS) technologies lower the barriers for use by both private and commercial entities. However, these advances are also likely to lead to greater vehicle densities, a more heterogenous mix of vehicles and equipment and greater levels of vehicle autonomy, which can increase the chance for communications disruptions. For the safe and secure operation of these vehicles, it is essential to have a robust communications network. This work is focused on harnessing the power of quantum technologies to enable this robust communications network by: (1) utilizing quantum optimization algorithms to design robust network with routing redundancy that can respond adaptively to dynamically changing real-time environment and disruptions, (2) utilize quantum optimization algorithms resource allocation for detection, localization, and tracking of mobile communication disruption agents and (3) utilize quantum key distribution (QKD) to execute secure key sharing in anti-jamming protocols for secure radio frequency (RF) communication. Efforts to map these quantum optimization algorithms to commercially available quantum annealers and soon to be available general-purpose gate-model quantum hardware architectures will be reviewed, and plans for testing the solutions to these algorithms through indoor sUAS flight tests will be discussed. Lastly, efforts to miniaturize and practically deploy Quantum Key Distribution (QKD) hardware, which could ultimately be used to securely exchange encryption keys, in sUAS networks will be reviewed.

Quantum Computing↗

Primitive quantum gates for an S U ( 3 ) discrete subgroup: Σ ( 36 × 3 )

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ ( 36 × 3 ) group. This is the first time a non-Abelian crystal-like subgroup of S U ( 3 ) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ ( 36 × 3 ) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

SoS-SDQN: System of Systems Software-defined Quantum Networking

Quantum networks are needed for quantum domain applications that may run across different network deployments - point-to-point, multi-node networks, and possibly across inter-domain quantum networks, like the quantum internet. Unlike classical computing networks, quantum networks involve heterogeneous systems nodes that currently require local and manual control. This needs a unified control approach to help them integrate, work seamlessly, and have global knowledge. Software-defined Networking (SDN) has been successfully leveraged in classical networking for seamless and software-driven control of network infrastructure and packet switching, but not in management of quantum network applications across heterogeneous systems. In this paper, we review the current state of the art and present early developments of a System-of-Systems Software-defined Quantum Networking architecture (SoS-SDQN), a generic architecture that supports software-driven quantum network experiments across heterogeneous quantum systems. The architecture modifies the generic SDN to address the domain requirements of quantum networks and proposes a multilevel SDQN to provide a global view of network status, running applications, and control of incorporated heterogeneous quantum systems. We also design and implement a SoS SouthBound Quantum Interface (SoS-SBQI), a quantum infrastructure protocol that abstracts automation of applications across the network.

Alnajjar, Anees [ORNL] (ORCID:0000000237101601)↗

Hierarchical memories: Simulating quantum LDPC codes with local gates

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to realize these codes. In this paper, we construct a new family of [[N,K,D]] codes, referred to as hierarchical codes, that encode a number of logical qubits K=Ω(N/log(N) 2 ). The N th element of this code family is obtained by concatenating a constant-rate quantum LDPC code with a surface code; nearest-neighbor gates in two dimensions are sufficient to implement the corresponding syndrome-extraction circuit and achieve a threshold. Below threshold the logical failure rate vanishes superpolynomially as a function of the distance D(N). We present a bilayer architecture for implementing the syndrome-extraction circuit, and estimate the logical failure rate for this architecture. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.

Pattison, Christopher A. [California Institute of ↗

Quantum science with arrays of metastable helium-3 atoms

The motion of atoms in programmable optical tweezer arrays offers many new opportunities for neutral atom quantum science. These include inter- and intra-site atom motion for resource-efficient implementations of fermionic and bosonic modes, respectively, as well as tweezer transport for efficient compilation of arbitrary circuits. However, the exploitation of atomic motion for all three purposes and others is limited by the inertia of the atoms. We present a comprehensive architectural blueprint for the use of fermionic metastable helium-3 (He) atoms -- the lightest trappable atomic species -- in programmable optical tweezer arrays. This includes a concrete analysis of atomic structure considerations as well as Rydberg-mediated interactions. We show that inter-tweezer hopping of He atoms can be faster than previous demonstrations with lithium-6. We also demonstrate a new toolbox for encoding and manipulating qubits directly in the tweezer trap potential, uniquely enabled by the light mass of He. Finally, we provide several examples of new opportunities for fermionic quantum simulation and computation that leverage the transport and inter-tweezer hopping of He atom arrays. These tools present new methods to improve the resource efficiency of neutral atom quantum science that may also enable quantum simulations of lattice gauge theories and quantum chemistry outside the Born-Oppenheimer approximation

Li, Zheyuan↗

Teacher-student training improves the accuracy and efficiency of machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) are revolutionizing the field of molecular dynamics (MD) simulations. Recent MLIPs have tended towards more complex architectures trained on larger datasets. The resulting increase in computational and memory costs may prohibit the application of these MLIPs to perform large-scale MD simulations. Herein, we present a teacher-student training framework in which the latent knowledge from the teacher (atomic energies) is used to augment the students' training. We show that the light-weight student MLIPs have faster MD speeds at a fraction of the memory footprint compared to the teacher models. Remarkably, the student models can even surpass the accuracy of the teachers, even though both are trained on the same quantum chemistry dataset. Our work highlights a practical method for MLIPs to reduce the resources required for large-scale MD simulations.

36 MATERIALS SCIENCE↗

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗

Modeling the Flow of Rarefied Gases at NASA

At modest temperatures, the thermal energy of atmospheric diatomic gases such as nitrogen is primarily distributed between only translational and rotational energy modes. Furthermore, these energy modes are fully excited such that the specific heat at constant volume is well approximated by the simple expression C(sub v) = 5/2 R. As a result, classical mechanics provides a suitable approximation at such temperatures of the true quantum mechanical behavior of the inter-molecular collisions of such molecules. Using classical mechanics, the transfer of energy between rotational and translation energy modes is studied. The approach of Lordi and Mates is adopted to compute the trajectories and time dependent rotational orientations and energies during the collision of two non-polar diatomic molecules. A Monte-Carlo analysis is performed collecting data from the results of many such simulations in order to estimate the rotational relaxation time. A Graphical Processing Unit (GPU) is employed to improve the performance of the Monte-Carlo analysis. A comparison of the performance of the GPU implementation to an implementation on traditional computer architecture is made. Effects of the assumed inter-molecular potential on the relaxation time are studied. The seminar will also present highlights of computational analyses performed at NASA Johnson Space Center of heat transfer in rarefied gases.

Forrest E. Lumpkin, III↗

Computational Power of Random Quantum Circuits in Arbitrary Geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of approximately 50 qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and, therefore, how much infidelity is suffered) in generating highly entangled states. Here, we describe recent hardware upgrades to Quantinuum’s H2 quantum computer, enabling it to operate on up to 56 qubits with arbitrary connectivity and 99.843(5)% two-qubit gate fidelity. We define a class of circuits with random geometries that become hard to classically simulate in very low depth and implement them utilizing the flexible connectivity of H2. A careful analysis demonstrating the fast saturation of classical simulation complexity with depth indicates that H2 can yield data well beyond the reach of state-of-the art classical simulation methods at unprecedented fidelities. We find that the considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the quantum charge-coupled device architecture as continued progress is made toward building larger machines. Published by the American Physical Society 2025

DeCross, M.↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗

Machine Phase Fullerene Nanotechnology: 1996

NASA has used exotic materials for spacecraft and experimental aircraft to good effect for many decades. In spite of many advances, transportation to space still costs about $10,000 per pound. Drexler has proposed a hypothetical nanotechnology based on diamond and investigated the properties of such molecular systems. These studies and others suggest enormous potential for aerospace systems. Unfortunately, methods to realize diamonoid nanotechnology are at best highly speculative. Recent computational efforts at NASA Ames Research Center and computation and experiment elsewhere suggest that a nanotechnology of machine phase functionalized fullerenes may be synthetically relatively accessible and of great aerospace interest. Machine phase materials are (hypothetical) materials consisting entirely or in large part of microscopic machines. In a sense, most living matter fits this definition. To begin investigation of fullerene nanotechnology, we used molecular dynamics to study the properties of carbon nanotube based gears and gear/shaft configurations. Experiments on C60 and quantum calculations suggest that benzyne may react with carbon nanotubes to form gear teeth. Han has computationally demonstrated that molecular gears fashioned from (14,0) single-walled carbon nanotubes and benzyne teeth should operate well at 50-100 gigahertz. Results suggest that rotation can be converted to rotating or linear motion, and linear motion may be converted into rotation. Preliminary results suggest that these mechanical systems can be cooled by a helium atmosphere. Furthermore, Deepak has successfully simulated using helical electric fields generated by a laser to power fullerene gears once a positive and negative charge have been added to form a dipole. Even with mechanical motion, cooling, and power; creating a viable nanotechnology requires support structures, computer control, a system architecture, a variety of components, and some approach to manufacture. Additional information is contained within the original extended abstract.

Globus, Al↗

Exact and Fixed-Point Grover Search with Qudits

Grover's algorithm provides a quadratic speedup for searching unstructured databases and is traditionally implemented with qubits in Hilbert spaces whose dimensions are powers of two. With the advent of quantum platforms utilizing qudits---quantum systems with more than two levels---there is a need to generalize Grover search to these architectures, including heterogeneous systems with qudits of varying dimensions. Here, we present a unified framework for qudit-based Grover search, detailing the construction of oracles and diffusion operators with and without ancilla qubits and generalizing deterministic and fixed-point search variants that ensure exact or bounded success probabilities. We analyze phase-matching techniques and provide explicit circuit decompositions suitable for diverse hardware platforms. We also compare the corresponding trajectories on the Bloch sphere to provide an intuitive visualization of how the different phase choices amplify the target state. These results facilitate flexible, hardware-oriented protocols for implementing Grover search on qudit processors, potentially reducing circuit depth and enhancing success probabilities, thereby offering a practical toolkit for quantum computation and sensing applications leveraging multilevel quantum systems.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

Impact of Emerging Computing Architectures and Opportunities for Process Systems Engineering Applications

Moore’s “law” was the observation that the number of transistors in an integrated circuit doubled approximately every two years. This trend has distinctly failed to hold in recent years. The death of Moore’s law has left researchers and practitioners in the computational sciences searching for technologies to provide the speedups formerly supported by Moore’s law. Previously overlooked chip architectures and other computing technologies are now receiving more development resources. Critically, these technologies are gaining more mature software support, opening their adoption by researchers in algorithms and applications. In this article, we review some of these computing technologies, their relationship with various algorithms and applications, and their potential benefits (or pitfalls). We close with recommendations for future work by the process systems engineering community specifically.

Emerging hardware↗

NASA Tech Briefs, October 2006

Topics covered include: Protein Sensors Based on Optical Ring Resonators; Phase Sensor for Aligning a Segmented Telescope Mirror; Control Software for Advanced Video Guidance Sensor; Generating Control Commands From Gestures Sensed by EMG; Multiple-Flat-Panel System Displays Multidimensional Data; 3D X-Ray Luggage-Screening System; Probe Station and Near-Field Scanner for Testing Antennas; Photodetector Arrays for Multicolor Visible/Infrared Imaging; Semiconductor Bolometers Give Background-Limited Performance; Multichannel X-Band Dielectric-Resonator Oscillator; Automatic Alignment of Displacement-Measuring Interferometer; Earth Observing System Data Gateway; Power User Interface; Mercury Shopping Cart Interface; Cassini Archive Tracking System; Architecture Adaptive Computing Environment; Computing Fault Displacements from Surface Deformations; Oxygen-Permeable, Hydrophobic Membranes of Silanized alpha-Al2O3; SiC Composite Turbine Vanes; Retaining Device for the Interior Structure of a Spacecraft Payload; Tool for Torquing Circular Electrical-Connector Collars; System for Continuous Deaeration of Hydraulic Oil; Solar-Powered Cooler and Heater for an Automobile Interior; Improved Oxygen-Beam Texturing of Glucose-Monitoring Optics; Tool for Two Types of Friction Stir Welding; Stationary Apparatus Would Apply Forces of Walking to Feet; Instrument Would Detect and Collect Biological Aerosols; Boundary Condition for Modeling Semiconductor Nanostructures; Miniature Distillation Column for Producing LOX From Air; Even Illumination from Fiber-Optic-Coupled Laser Diodes; Optically Driven Deformable Mirrors; Algorithm for Automated Detection of Edges of Clouds; Exploiting Quantum Resonance to Solve Combinatorial Problems; Hybrid Terrain Database; On Release of Microbe-Laden Particles from Mars Landers; A Concept for Run-Time Support of the Chapel Language; Thermoelectric Inhomogeneities in (Ag(sub 1-y)SbTe2)(sub x)(PbTe)(sub 1-x); and Spacecraft Escape Capsule.

Source record↗

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

AladynPi – Adaptive Neural Network Molecular Dynamics Simulation Code with Physically Informed Potential: Computational Materials Mini-Application

This report provides an overview and description of commands used in the Computational Materials mini-application, AladynPi. AladynPi is an extension of a previously released mini-application, Aladyn (https://github.com/nasa/aladyn; Yamakov, V.I., and Glaessgen, E.H., NASA/TM-2018-220104). Aladyn and AladynPi are basic molecular dynamics codes written in FORTRAN 2003, which are designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory method. An input for the ANN is a set of structure coefficients, characterizing the local atomic environment of each atom, for which the atomic energy is obtained in the ANN inference process. In Aladyn, the ANN gives directly the energy of interatomic interactions. In AladynPi, the ANN gives optimized parameters for a predefined empirical function, known as bond-order-potential (BOP). The parameterized BOP function is then used to calculate the energy. AladynPi code is being released to serve as a training testbed for students and professors in academia to explore possible optimization algorithms for parallel computing on multicore central processing unit (CPU) computers or computers utilizing manycore architectures based on graphic processing units (GPUs). The effort is supported by the High Performance Computing incubator (HPCi) project at NASA Langley Research Center.

Yamakov, Vesselin I.↗

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗