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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Toward computing bounds for Ramsey numbers using quantum annealing

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems, such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum annealing as a tool for use in exploring combinatorial mathematics research problems. We consider the monochromatic triangle problem and the Ramsey number problem, both examples of graph coloring. Conversion to quadratic unconstrained binary optimization (QUBO) form is required to run on quantum hardware. While the monochromatic triangle problem is quadratic by nature, the Ramsey number problem requires the use of order reduction methods for a quadratic formulation. The goal is to provide a method for producing special colorings of graphs which if successful would provide lower bounds for certain Ramsey numbers. We discuss implementations, limitations, and results when running on the D-Wave Advantage quantum annealer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

ON-OFF neuromorphic ISING machines using Fowler-Nordheim annealers

We introduce NeuroSA, a neuromorphic architecture specifically designed to ensure asymptotic convergence to the ground state of an Ising problem using a Fowler-Nordheim quantum mechanical tunneling based threshold-annealing process. The core component of NeuroSA consists of a pair of asynchronous ON-OFF neurons, which effectively map classical simulated annealing dynamics onto a network of integrate-and-fire neurons. The threshold of each ON-OFF neuron pair is adaptively adjusted by an FN annealer and the resulting spiking dynamics replicates the optimal escape mechanism and convergence of SA, particularly at low-temperatures. To validate the effectiveness of our neuromorphic Ising machine, we systematically solved benchmark combinatorial optimization problems such as MAX-CUT and Max Independent Set. Across multiple runs, NeuroSA consistently generates distribution of solutions that are concentrated around the state-of-the-art results (within 99%) or surpass the current state-of-the-art solutions for Max Independent Set benchmarks. Furthermore, NeuroSA is able to achieve these superior distributions without any graph-specific hyperparameter tuning. For practical illustration, we present results from an implementation of NeuroSA on the SpiNNaker2 platform, highlighting the feasibility of mapping our proposed architecture onto a standard neuromorphic accelerator platform.

42 ENGINEERING↗
DOE OSTI2024

Retrieving Top-k Hyperedge Triplets: Models and Applications

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions can- not be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motifs hold promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge inter- sections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding top-k triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least similar with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most similar with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our comprehensive experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.

hypergraphs, motifs, Combinatorial Algorithms↗
DOE OSTI2024

SPARTAN (Scalable Probabilistic Application Reconfigurable Tensor Autonomous Network)

The technical founder of Ludwig Computing Inc has been competitively selected for support by Cyclotron Road, a U.S. Department of Energy (DOE) Advanced Manufacturing Office (AMO) Lab-Embedded Entrepreneurship Program (LEEP) through an approved merit review process. Ludwig Computing Inc, supported by the U.S. Department of Energy's Advanced Manufacturing Office through the Cyclotron Road program, has investigated the advantages of probabilistic computing for real-world compute-intensive applications. This research adds to the understanding of alternative computing paradigms by exploring a unique hardware-software co-design that integrates quantum computing methods with nature-inspired problem-solving techniques. The project's focus on areas such as combinatorial optimization, graph analytics, and machine learning demonstrates the potential for significant advancements in computational efficiency and performance. By harnessing natural randomness to streamline large circuits into fewer devices, Ludwig's approach enables massive parallelism, potentially offering higher throughput, speed, and energy efficiency compared to conventional hardware solutions. This work benefits the public by paving the way for more efficient computing solutions that could address complex real-world problems while potentially reducing energy consumption in data-intensive industries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Near-Term Application Engineering Challenges in Emerging Superconducting Qudit Processors

We review the prospects to build quantum processors based on superconducting transmons and radiofrequency cavities for testing applications in the NISQ era. We identify engineering opportunities and challenges for implementation of algorithms in simulation, combinatorial optimization, and quantum machine learning in qudit-based quantum computers.

Venturelli, Davide [RIACS, Mtn. View] (ORCID:00000↗
DOE OSTI2025

Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over Trotterized adiabatic quantum computation and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critical Hamming radius, or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. This work proposes IST-SAT a new quantum algorithm, which improves upon solutions obtained from initial classical or quantum optimization algorithms. The steering mechanism we introduce through IST-SAT presents a new path toward achieving quantum advantage in optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2025

Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking

Posiform planting is a method for constructing QUBO instances with a unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2025

High-Throughput Microfluidic Electroporation (HTME): A Scalable, 384-Well Platform for Multiplexed Cell Engineering

Electroporation-mediated gene delivery is a cornerstone of synthetic biology, offering several advantages over other methods: higher efficiencies, broader applicability, and simpler sample preparation. Yet, electroporation protocols are often challenging to integrate into highly multiplexed workflows, owing to limitations in their scalability and tunability. These challenges ultimately increase the time and cost per transformation. As a result, rapidly screening genetic libraries, exploring combinatorial designs, or optimizing electroporation parameters requires extensive iterations, consuming large quantities of expensive custom-made DNA and cell lines or primary cells. To address these limitations, we have developed a High-Throughput Microfluidic Electroporation (HTME) platform that includes a 384-well electroporation plate (E-Plate) and control electronics capable of rapidly electroporating all wells in under a minute with individual control of each well. Fabricated using scalable and cost-effective printed-circuit-board (PCB) technology, the E-Plate significantly reduces consumable costs and reagent consumption by operating on nano to microliter volumes. Furthermore, individually addressable wells facilitate rapid exploration of large sets of experimental conditions to optimize electroporation for different cell types and plasmid concentrations/types. Use of the standard 384-well footprint makes the platform easily integrable into automated workflows, thereby enabling end-to-end automation. We demonstrate transformation of E. coli with pUC19 to validate the HTME's core functionality, achieving at least a single colony forming unit in more than 99% of wells and confirming the platform's ability to rapidly perform hundreds of electroporations with customizable conditions. This work highlights the HTME's potential to significantly accelerate synthetic biology Design-Build-Test-Learn (DBTL) cycles by mitigating the transformation/transfection bottleneck.

Gaillard, William R↗
DOE OSTI2025

Quantum Adiabatic Optimization with Rydberg Arrays: Localization Phenomena and Encoding Strategies

Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead associated with such mappings is easily quantifiable and typically polynomial in problem size, it is much harder to quantify their overhead on the quantum algorithm, e.g., the transformation of the adiabatic timescale. In this work, we address this challenge on the concrete example of the encoding scheme proposed in [Nguyen , PRX Quantum , 010316 (2023)], which is designed to map optimization problems on arbitrarily connected graphs into Rydberg atom arrays. We consider the fundamental building blocks underlying this encoding scheme and determine the scaling of the minimum gap with system size along adiabatic protocols. Even when the original problem is trivially solvable, we find that the encoded problem can exhibit an exponentially closing minimum gap. We show that this originates from a quantum coherent effect, which gives rise to an unfavorable localization of the ground-state wave function. On the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose quantum-aware modifications of the encoding scheme that avoid this quantum bottleneck and lead to an exponential improvement in the adiabatic performance. This highlights the crucial importance of accounting for quantum effects when designing strategies to encode classical problems onto quantum platforms. Published by the American Physical Society 2025

Bombieri, Lisa (ORCID:0009000950422897)↗
DOE OSTI2024

Multi-objective optimization of PWR core design using NSGA-II in RAVEN’s optimization framework

Designing an PWR loading pattern is a combinatorial problem challenging to solve by brute force or traditional methods due to the sheer amount of possible combination, and constraints. Nature-inspired algorithms, such as the genetic algorithm, have demonstrated the potential to tackle this problem. The goal of this work was to improve and demonstrate the capabilities for constrained, multi-objective optimization (MOO) of loading patterns using NSGA-II in RAVEN’s optimization framework.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Automated scanning probe microscopy of combinatorial ferroelectric libraries: Gaussian-process-guided exploration and noise-aware experiment planning

Combinatorial materials libraries provide an efficient route for mapping composition–property relationships, but their broader impact depends on rapid, quantitative, and functionally relevant characterization. Scanning Probe Microscopy (SPM), including piezoresponse force microscopy (PFM), offers significant potential for quantitative, functionally relevant combi-library readouts. Here, we implement a fully automated SPM workflow for ferroelectric combinatorial libraries and benchmark Gaussian-process-based Bayesian optimization strategies for autonomous experiment planning. The workflow integrates automated probe motion, contact optimization, imaging, and dual amplitude resonance tracking-PFM spectroscopy, and uses scalarized spectroscopic observables to guide subsequent measurements. Stage motion, probe engagement, in-contact tuning, imaging, spectroscopy, and the choice of the next measurement location all proceed without human input. We demonstrate the approach on Sm-doped BiFeO 3 and Zn x Mg 1−x O libraries. By comparing vanilla Bayesian optimization with a measured-noise variant, we show that explicit treatment of local reproducibility can improve modeling of composition-dependent response when the measured variance is physically meaningful, but can also reduce robustness when variability is dominated by outliers or topographic artifacts. Furthermore, these results establish automated SPM as a bridge between combinatorial synthesis and quantitative functional characterization.

Liu, Yu [University of Tennessee, Knoxville, TN (U↗
DOE OSTI2026

Towards Generalizable and Efficient Circuit Topology Design: A Graph-Transformer-based Surrogate Model with Curriculum Learning

Unlike circuit parameter and sizing optimizations, the automated design of analog circuit topologies poses significant challenges for learning-based approaches. One challenge arises from the combinatorial growth of the topology space with circuit size, which limits the topology optimization efficiency. Moreover, traditional circuit evaluation methods are time-consuming, while the presence of data discontinuity in the topology space makes the accurate prediction of circuit performance exceptionally difficult for unseen topologies. To tackle these challenges, we design a novel Graph-Transformer-based Network (GTN) as the surrogate model for circuit evaluation, offering a substantial acceleration in the speed of circuit topology optimization without sacrificing performance. Our GTN model architecture is designed to embed voltage changes in circuit loops and current flows in connected devices, enabling accurate performance predictions for circuits with unseen topologies. To address the cold start problem when scaling GTN to large-scale circuits, we further introduce a curriculum learning strategy that progressively trains GTN from small-scale to large-scale circuits. This approach enables the model to first learn fundamental physical principles from simpler topologies and gradually adapt to complex configurations, effectively bridging the circuit complexity gap and improving prediction accuracy. Taking the power converter circuit design as an experimental task, our GTN model significantly outperforms an analytical approach and baseline methods directly utilizing graph neural networks. Furthermore, GTN achieves less than 5% relative error and 196× speed-up compared with high-fidelity simulation. Notably, our GTN surrogate model empowers an automatic circuit design framework to discover circuits of comparable quality to those identified through high-fidelity simulation while reducing the time required by up to 98.2%. With curriculum learning, the enhanced GTN achieves a 51% improvement for performance prediction of large-scale circuits compared to the GTN model without this strategy. These advancements establish GTN as a scalable framework for automated analog circuit design across varying circuit complexity levels.

Lu, Haoshu [New Jersey Institute of Technology (NJ↗
DOE OSTI2024

High‐throughput combinatorial approach expedites the synthesis of a lead‐free relaxor ferroelectric system

Abstract Developing novel lead‐free ferroelectric materials is crucial for next‐generation microelectronic technologies that are energy efficient and environment friendly. However, materials discovery and property optimization are typically time‐consuming due to the limited throughput of traditional synthesis methods. In this work, we use a high‐throughput combinatorial synthesis approach to fabricate lead‐free ferroelectric superlattices and solid solutions of (Ba 0.7 Ca 0.3 )TiO 3 (BCT) and Ba(Zr 0.2 Ti 0.8 )O 3 (BZT) phases with continuous variation of composition and layer thickness. High‐resolution x‐ray diffraction (XRD) and analytical scanning transmission electron microscopy (STEM) demonstrate high film quality and well‐controlled compositional gradients. Ferroelectric and dielectric property measurements identify the “optimal property point” achieved at the composition of 48BZT–52BCT. Displacement vector maps reveal that ferroelectric domain sizes are tunable by varying {BCT–BZT} N superlattice geometry. This high‐throughput synthesis approach can be applied to many other material systems to expedite new materials discovery and properties optimization, allowing for the exploration of a large area of phase space within a single growth. image

36 MATERIALS SCIENCE↗
DOE OSTI2026

Self-driving thin film laboratory: autonomous epitaxial atomic-layer synthesis via real-time computer vision analysis of electron diffraction

Emerging materials science platforms with the ability to make autonomous decisions on the fly are fundamentally changing the outlook and protocols for materials optimization and discovery. Because AI-driven self-navigating schemes can effectively reduce the total number of iterations needed to arrive at the "answer" (i.e. the best stochiometric composition for a desired physical property, optimum materials processing parameters, etc.) by significant margins, they have the potential to revolutionize materials and chemical manufacturing processes at large in research laboratory settings as well as in industrial plants. Here, we demonstrate a successful implementation of real-time closed-loop autonomous navigation of a multi-dimensional materials synthesis parameter space for fabricating phase-pure epitaxial films of a metastable phase of a functional oxide in a combinatorial pulsed laser deposition chamber. Sequential epitaxial growth iterations in search of the optimized recipe to stabilize the desired crystal phase were performed using frame-by-frame quantitative computer vision analysis of reflection high-energy electron diffraction (RHEED) images of the unit-cell level film being deposited. The autonomous scheme regularly resulted in > 30-fold reduction in the number of required experiments compared to a comprehensive mapping of the parameter space. The real-time workflow developed here can be readily extended to a variety of thin film synthesis platforms opening the door for self-driving atomic-level materials design as well as autonomous optimization of semiconductor manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Enhanced Power Grid Maintenance Planning and Quantum-Inspired Combinatorial Prospects

Efficient and reliable scheduling of maintenance for power generation and transmission infrastructure is essential for minimizing operational costs and ensuring grid stability. This paper introduces an integrated optimization framework for coordinated maintenance scheduling of generators and transmission lines under resource and reliability constraints. The model minimizes a composite cost function including maintenance and generation costs, as well as penalties for delayed maintenance, while satisfying N−1 security constraints, operational limits, and crew availability. Case studies on the IEEE 300-bus test system demonstrate the effectiveness of the proposed approach in producing feasible and cost-effective maintenance schedules. To address scalability and combinatorial complexity, the model is mapped into a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling exploration of solution approaches based on Quantum Imaginary Time Evolution (QITE). While the QUBO reformulation provides a foundation for future quantum-inspired optimization, this study focuses primarily on the development and demonstration of the classical optimization framework and illustrates the potential applicability of QITE in large-scale maintenance scheduling.

Chen, Yang [ORNL] (ORCID:0000000271693874)↗
DOE OSTI2024

High-throughput combinatorial approach expedites the synthesis of a lead-free relaxor ferroelectric system

Developing novel lead-free ferroelectric materials is crucial for next-generation microelectronic technologies that are energy efficient and environment friendly. However, materials discovery and property optimization are typically time-consuming due to the limited throughput of traditional synthesis methods. In this work, we use a high-throughput combinatorial synthesis approach to fabricate lead-free ferroelectric superlattices and solid solutions of (Ba 0.7 Ca 0.3 )TiO 3 (BCT) and Ba(Zr 0.2 Ti 0.8 )O 3 (BZT) phases with continuous variation of composition and layer thickness. High-resolution x-ray diffraction (XRD) and analytical scanning transmission electron microscopy (STEM) demonstrate high film quality and well-controlled compositional gradients. Ferroelectric and dielectric property measurements identify the “optimal property point” achieved at the composition of 48BZT–52BCT. Displacement vector maps reveal that ferroelectric domain sizes are tunable by varying {BCT–BZT} N superlattice geometry. This high-throughput synthesis approach can be applied to many other material systems to expedite new materials discovery and properties optimization, allowing for the exploration of a large area of phase space within a single growth.

36 MATERIALS SCIENCE↗