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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum magic and computational complexity in the neutrino sector

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for 𝑁 𝜈 ≤ 8 neutrinos. For |𝜈𝑒⟩ ⊗𝑁𝜈 initial states, the magic, as measured by the 𝛼 = 2 stabilizer Renyi entropy ℳ 2 , is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, ℳ 2 /𝑁 𝜈 , decreases with increasing 𝑁 𝜈 . In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic ℳ 2 /𝑁 𝜈 increasing with 𝑁 𝜈 . These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

computational complexity↗
DOE OSTI2025

Sign Problem in Tensor-Network Contraction

We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only positive entries has lower computational complexity as compared to tensor networks with general real or complex entries. This raises the question of how this transition in computational complexity manifests itself in the hardness of different tensor-network-contraction schemes. We pursue this question by studying random tensor networks with varying bias toward positive entries. First, we consider contraction via Monte Carlo sampling and find that the transition from hard to easy occurs when the tensor entries become predominantly positive; this can be understood as a tensor-network manifestation of the well-known negative-sign problem in quantum Monte Carlo. Second, we analyze the commonly used contraction based on boundary tensor networks. The performance of this scheme is governed by the number of correlations in contiguous parts of the tensor network (which by analogy can be thought of as entanglement). Remarkably, we find that the transition from hard to easy—i.e., from a volume-law to a boundary-law scaling of entanglement—already occurs for a slight bias of the tensor entries toward a positive mean, scaling inversely with the bond dimension D , and thus the problem becomes easy the earlier the larger D occurs. This is in contrast both to expectations and to the behavior found in Monte Carlo contraction, where the hardness at fixed bias increases with the bond dimension. To provide insight into this early breakdown of computational hardness and the accompanying entanglement transition, we construct an effective classical statistical-mechanical model that predicts a transition at a bias of the tensor entries of 1 / D , confirming our observations. We conclude by investigating the computational difficulty of computing expectation values of tensor-network wave functions (projected entangled-pair states, PEPSs) and find that in this setting, the complexity of entanglement-based contraction always remains low. We explain this by providing a local transformation that maps PEPS expectation values to a positive-valued tensor network. This not only provides insight into the origin of the observed boundary-law entanglement scaling but also suggests new approaches toward PEPS contraction based on positive decompositions. Published by the American Physical Society 2025

Chen, Jielun (ORCID:0000000178411545)↗
DOE OSTI2025

Leveraging dendritic complexity for neuromorphic computing

Abstract Beyond-von Neumann computing approaches are necessary to sustain the growth of microelectronics and the increasing appetite for artificial intelligence/machine learning algorithms. Neuromorphic computing is an emerging paradigm that takes inspiration from the brain to provide a path forward to improve the computational efficiency and computational density of next-generation computing architectures. In nature, we observe brains performing complex computations with a much smaller energy footprint than conventional computing approaches. Current neuromorphic systems are focused primarily on scalability, namely, increasing the number of computational units (neurons) and connections between units (synapses). However, for brain-like cognition and efficiency in next-generation computing hardware, we need increased complexity in function, as well as improved connection density for scalability. Here, we present our work that aims to incorporate dendrites for ‘compute-on-wire’ in neuromorphic architectures to increase the computational complexity (e.g. number of programmable parameters, nonlinear dynamics) as well as computational efficiency (energy/compute) of artificial neural networks (ANNs). We do this by showcasing neuromorphic dendrite elements that can be leveraged for various applications. We will present examples of neuroscience-inspired direction-selective circuits and an ANN with active dendrites leveraging shunting inhibition. We also demonstrate the benefits of using dendrites in deep neural networks. To conclude, we discuss how we can utilize emerging hardware devices in these systems and design next-generation neuromorphic architectures with dendrites.

Cardwell, Suma G. (ORCID:0000000226575545)↗
DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Experimental Setup and Learning-Based AI Model for Developing Accurate PV Inverter Models

The integration of power electronics-based interfaces presents challenges due to the absence of detailed models and the high computational complexity. Generic models used in system studies lack accuracy in capturing converter dynamics. This paper proposes a data-driven approach developed from experimental setup data. This approach enhances accuracy in photovoltaic inverter modeling. We used two types of PV inverters in the experiment. The recorded experimental data undergo processing through a machine learning model. Results from the model trained through machine learning is also presented.

artificial intelligence↗
DOE OSTI2024

On the hardness of learning ground state entanglement of geometrically local Hamiltonians

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main result is that to show it is cryptographically hard to determine if the ground state of a geometrically local, polynomially gapped Hamiltonian on qudits (d=O(1)) has near-area law vs near-volume law entanglement. This improves prior work of Bouland et al. (arXiv:2311.12017) showing this for non-geometrically local Hamiltonians. In particular we show this problem is roughly factoring-hard in 1D, and LWE-hard in 2D. Our proof works by constructing a novel form of public-key pseudo-entanglement which is highly space-efficient, and combining this with a modification of Gottesman and Irani's quantum Turing machine to Hamiltonian construction. Our work suggests that the problem of learning so-called "gapless" quantum phases of matter might be intractable.

Computational Complexity (cs.CC)↗
DOE OSTI2024

Learning of networked spreading models from noisy and incomplete data

Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure, noisy data, missing observations in time, as well as an efficient incorporation of prior information to minimize the number of samples required for an accurate learning. Here, in this work, we introduce a universal learning method based on a scalable dynamic message-passing technique that addresses these challenges often encountered in real data. The algorithm leverages available prior knowledge on the model and on the data, and reconstructs both network structure and parameters of a spreading model. We show that a linear computational complexity of the method with the key model parameters makes the algorithm scalable to large network instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

VAN-DAMME: GPU-accelerated and symmetry-assisted quantum optimal control of multi-qubit systems

We present an open-source software package, VAN-DAMME (Versatile Approaches to Numerically Design, Accelerate, and Manipulate Magnetic Excitations), for massively-parallelized quantum optimal control (QOC) calculations of multi-qubit systems. To enable large QOC calculations, the VAN-DAMME software package utilizes symmetry-based techniques with custom GPU-enhanced algorithms. This combined approach allows for the simultaneous computation of hundreds of matrix exponential propagators that efficiently leverage the intra-GPU parallelism found in high-performance GPUs. In addition, to maximize the computational efficiency of the VAN-DAMME code, we carried out several extensive tests on data layout, computational complexity, memory requirements, and performance. These extensive analyses allowed us to develop computationally efficient approaches for evaluating complex-valued matrix exponential propagators based on Padé approximants. To assess the computational performance of our GPU-accelerated VAN-DAMME code, we carried out QOC calculations of systems containing 10 - 15 qubits, which showed that our GPU implementation is 18.4× faster than the corresponding CPU implementation. Our GPU-accelerated enhancements allow efficient calculations of multi-qubit systems, which can be used for the efficient implementation of QOC applications across multiple domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Kolmogorov-Arnold networks↗
DOE OSTI2025

Accelerating resonant spectroscopy simulations using multishifted biconjugate gradient

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide important insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum Algorithms for Representation-Theoretic Multiplicities

Kostka, Littlewood-Richardson, Plethysm, and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory, geometric complexity, and algebraic combinatorics. We give quantum algorithms for computing these coefficients whenever the ratio of dimensions of the representations is polynomial. We show that there is an efficient classical algorithm for computing the Kostka numbers under this restriction and conjecture the existence of an analogous algorithm for the Littlewood-Richardson coefficients. We argue why such classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients and conjecture that our quantum algorithms lead to superpolynomial speedups. The conjecture about Kronecker coefficients was disproved by Panova [Polynomial time classical versus quantum algorithms for representation theoretic multiplicities, arXiv:2502.20253] with a classical algorithm which, if optimal, points to a 𝒪⁡(𝑛 4+2⁢𝑘 ) vs $\tilde{Ω}$⁡(𝑛 4⁢𝑘 2 +1 ) polynomial gap in quantum vs classical computational complexity for an integer parameter 𝑘.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Enhancing EV Motor Design Through Knowledge-Based AI and Hierarchical Fuzzy Logic Model

This work presents a novel approach to optimizing electric vehicle motor design through the integration of Knowledge-Based Artificial Intelligence (KB-AI) and Hierarchical Fuzzy Logic. Traditional motor design processes are time-intensive, relying heavily on iterative simulations and domain-specific expertise. These processes are further complicated by the nonlinear relationships between key design parameters. The proposed framework addresses these challenges by systematically encoding expert knowledge from scientific literature into a fuzzy logic system, allowing for the efficient handling of complex design variables. The hierarchical fuzzy logic model reduces computational complexity by decomposing the nonlinear relationships into manageable rule sets while maintaining design accuracy. The proposed methodology was applied to the design of a 100 kW motor, yielding optimal values for key parameters. This resulted in a compact motor design with a volume of 2.2 liters, showcasing the framework’s ability to deliver high-performance, application-specific motor configurations.

Kumar, Praveen [ORNL] (ORCID:0000000291877857)↗
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2024

2019 Budget Request for the DOE Computational Science Graduate Fellowship (CSGF) Grant

The Department of Energy Computational Science Graduate Fellowship (DOE CSGF) is necessary to meet the continual challenging national workforce needs that arise as computational science and engineering problems continue to grow in scope and complexity. Computational science and engineering (CSE) is a multidisciplinary approach that uses scientific computing to solve practical problems methods and to supply technical tools across the scientific discovery spectrum. In particular, the DOE CSGF emphasizes high-performance computing (HPC) that enables CSE that advances science and engineering in directions important to the DOE and the economy in general. Over the past half-century, HPC has been an essential tool for DOE’s success. During this period, important missions, such as nuclear stockpile stewardship, have turned to HPC as an essential technology. Entire science disciplines, such as biology and cosmology, have been transformed through the augmentation of scientific observation via HPC. At government laboratories and in industry, DOE CSGF alumni are helping push traditional HPC boundaries while contributing to discoveries in high-energy physics, renewable energy, fusion-reactor design, additive manufacturing, nanomaterials for next-generation batteries and transistors, and turbine and advanced nuclear reactor modeling. In addition, HPC is used to address national health needs that will eventually point to cures both by helping cancer researchers manage and analyze huge troves of data, by simulating biological mechanisms, and by accelerating drug development — including continuing to rise to the challenge of pandemic-related research. A 2023 report from the ASCAC Subcommittee on American Competitiveness and Innovation to the ASCR office, “Can the United States Maintain Its Leadership in High-Performance Computing?” says of the Program, “The CSGF program provides a barometer for disciplines that will be of interest to future DOE computing.” An explosion in scientific and technological data has driven the need for increasingly sophisticated HPC to transform those data into scientific understanding. With access to more and more data and the proliferation of HPC, Machine Learning and Artificial Intelligence are experiencing a renaissance, complementing the now well-established use of computational simulation. Indeed, in its September 2020 subcommittee report on “AI/ML, Data Intensive Science and High-Performance Computing”, the DOE Advanced Scientific Computing Advisory Committee (ASCAC) explicitly called for a fellowship program to train computational and data scientists to tackle exascale and data-intensive computing challenges. This collaboration of empirical and theory-based modeling will increasingly inform federal policymakers whose decisions affect American society and future generations, and it requires highly skilled and intellectually agile computational scientists who can support the fast-moving DOE National Laboratory research environment. In fact, the DOE CSGF program has explicitly and consistently addressed this need.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Defining quantum-ready primitives for hybrid HPC-QC supercomputing: a case study in Hamiltonian simulation

As computational demands in scientific applications continue to rise, hybrid high-performance computing (HPC) systems integrating classical and quantum computers (HPC-QC) are emerging as a promising approach to tackling complex computational challenges. One critical area of application is Hamiltonian simulation, a fundamental task in quantum physics and other large-scale scientific domains. This paper investigates strategies for quantum-classical integration to enhance Hamiltonian simulation within hybrid supercomputing environments. By analyzing computational primitives in HPC allocations dedicated to these tasks, we identify key components in Hamiltonian simulation workflows that stand to benefit from quantum acceleration. To this end, we systematically break down the Hamiltonian simulation process into discrete computational phases, highlighting specific primitives that could be effectively offloaded to quantum processors for improved efficiency. Our empirical findings provide insights into system integration, potential offloading techniques, and the challenges of achieving seamless quantum-classical interoperability. We assess the feasibility of quantum-ready primitives within HPC workflows and discuss key barriers such as synchronization, data transfer latency, and algorithmic adaptability. These results contribute to the ongoing development of optimized hybrid solutions, advancing the role of quantum-enhanced computing in scientific research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ensemble Simulations on Leadership Computing Systems

Scientific productivity can be enhanced through workflow management tools, relieving large High Performance Computing (HPC) system users from the tedious tasks of scheduling and designing the complex computational execution of scientific applications. This paper presents a study on the usage of ensemble workflow tools to accelerate science using the Summit and Frontier supercomputing systems. The research aims to connect science domain simulations using Oak Ridge Leadership Computing Facility (OLCF) supercomputing platforms with ensemble workflow methods in order to accelerate HPC-enabled discovery and boost scientific impact. We present the coupling, porting and optimization of Radical-Cybertools on three applications: Chroma, NAMD and LAMMPS. The tools augment traditional HPC monolithic runs with a pilot scheduler. Lessons-learned are discussed for physics, biology and materials science applications. We discuss intrinsic limitations of coupling and porting ensemble workflow tools to applications that run on large HPC systems. The origins of technical challenges and their solutions developed during the implementation process are discussed. Data management strategies, OLCF’s policies for ensembles, and natively supported workflow tools are also summarized.

Georgiadou, Antigoni [ORNL] (ORCID:000000020977631↗