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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

SOMAFOAM: An OpenFOAM based solver for continuum simulations of low-temperature plasmas

Here, we report the development of SOMAFOAM, a finite volume framework for performing continuum simulations of low-temperature plasmas. The primary goal of this work is to discuss the features of SOMAFOAM along with representative results provided as examples for a range of operating conditions and geometries. This includes plasma and plasma–dielectric systems operating in direct current, radio frequency, and microwave regimes from pressures as low as 100 mTorr to atmospheric pressure. The code has several useful features including the ability to run massively parallel simulations using arbitrary geometries, structured/unstructured meshes, choice of models such as drift–diffusion/full-momentum at runtime, and species-dependent timesteps to name a few. The verification/validation studies presented include comparison with previously published continuum simulations (low-pressure direct current and radio frequency plasma), with experiments (Gaseous Electronics Conference Reference Cell and microwave microplasma ignited in a split ring resonator), and previously published kinetic simulations (low-pressure radio frequency plasma). Other examples provided include a direct current atmospheric pressure microplasma bounded by dielectric sidewalls and a helium–nitrogen plasma ignited using a needle electrode facing a dielectric. The performance of the code is also discussed with serial and distributed memory parallel runs demonstrated up to 512 cores. The design and implementation of the code in a modular object-oriented framework allows for easy extension and seamless coupling with other codes and can be expected to play an important role in both academia and industry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Beyond the supercomputer

A NASA-directed development of massively parallel processor (MPP) computers is outlined, noting intended applications for data processing for near term earth resource and environment mapping, radar, and television transmissions. The MPP is designed to perform 100 billion operations/sec to obtain satisfactory image processing, while separate processing units correct distortions, register images, calculate correlation functions, and classify multispectral characteristics. Arrays of 1s and 0s will be manipulated in analog-to-digital conversions generating separate planes corresponding to powers of binaries. Data wires are replaced by fiber-optic tubes or thousands of wires, and single logic gates are replaced by thousands of logic gates and every memory element by thousands of memory elements. Features of the interconnections and the images control processor units are detailed, along with implementation of sliders for program flexibility.

Schaefer, D. H.↗
DOE OSTI2020

TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition

With this study, our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100 s of nodes (1,000 s of MPI processes), achieving compression ratios between 100 and 200,000×, which equates to 99--99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗
DOE OSTI2015

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.

36 MATERIALS SCIENCE↗
DOE OSTI2017

SCIDAC Center for simulation of wave particle interactions CompX participation

Harnessing the energy that is released in fusion reactions would provide a safe and abundant source of power to meet the growing energy needs of the world population. The next step toward the development of fusion as a practical energy source is the construction of ITER, a device capable of producing and controlling the high performance plasma required for self-sustaining fusion reactions, or “burning” plasma. The input power required to drive the ITER plasma into the burning regime will be supplied primarily with a combination of external power from radio frequency waves in the ion cyclotron range of frequencies and energetic ions from neutral beam injection sources, in addition to internally generated Ohmic heating from the induced plasma current that also serves to create the magnetic equilibrium for the discharge. The ITER project is a large multi-billion dollar international project in which the US participates. The success of the ITER project depends critically on the ability to create and maintain burning plasma conditions, it is absolutely necessary to have physics-based models that can accurately simulate the RF processes that affect the dynamical evolution of the ITER discharge. The Center for Simulation of WavePlasma Interactions (CSWPI), also known as RF-SciDAC, is a multi-institutional collaboration that has conducted ongoing research aimed at developing: (1) Coupled core-to-edge simulations that will lead to an increased understanding of parasitic losses of the applied RF power in the boundary plasma between the RF antenna and the core plasma; (2) Development of models for core interactions of RF waves with energetic electrons and ions (including fusion alpha particles and fast neutral beam ions) that include a more accurate representation of the particle dynamics in the combined equilibrium and wave fields; and (3) Development of improved algorithms that will take advantage of massively parallel computing platforms at the petascale level and beyond to achieve the needed physics, resolution, and/or statistics to address these issues. CompX provides computer codes and analysis for the calculation of the electron and ion distributions in velocity-space and plasma radius which are necessary for reliable calculations of power deposition and toroidal current drive due to combined radiofrequency and neutral beam at high injected powers. It has also contributed to ray tracing modeling of injected radiofrequency powers, and to coupling between full-wave radiofrequency wave models and the distribution function calculations. In the course of this research, the Fokker-Planck distribution function calculation was made substantially more realistic by inclusion of finite-width drift-orbit effects (FOW). FOW effects were also implemented in a calculation of the phase-space diffusion resulting from radiofrequency full-wave models. Average level of funding for CompX was approximately three man-months per year.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

ATLAS (Automatic Tool for Local Assembly Structures) - A Comprehensive Infrastructure for Assembly, Annotation, and Genomic Binning of Metagenomic and Metaranscripomic Data

ATLAS (Automatic Tool for Local Assembly Structures) is a comprehensive multiomics data analysis pipeline that is massively parallel and scalable. ATLAS contains a modular analysis pipeline for assembly, annotation, quantification and genome binning of metagenomics and metatranscriptomics data and a framework for reference metaproteomic database construction. ATLAS transforms raw sequence data into functional and taxonomic data at the microbial population level and provides genome-centric resolution through genome binning. ATLAS provides robust taxonomy based on majority voting of protein coding open reading frames rolled-up at the contig level using modified lowest common ancestor (LCA) analysis. ATLAS provides robust taxonomy based on majority voting of protein coding open reading frames rolled-up at the contig level using modified lowest common ancestor (LCA) analysis. ATLAS is user-friendly, easy install through bioconda maintained as open-source on GitHub, and is implemented in Snakemake for modular customizable workflows.

genome binning↗
NASA NTRS1994

Using CLIPS in the domain of knowledge-based massively parallel programming

The Program Development Environment (PDE) is a tool for massively parallel programming of distributed-memory architectures. Adopting a knowledge-based approach, the PDE eliminates the complexity introduced by parallel hardware with distributed memory and offers complete transparency in respect of parallelism exploitation. The knowledge-based part of the PDE is realized in CLIPS. Its principal task is to find an efficient parallel realization of the application specified by the user in a comfortable, abstract, domain-oriented formalism. A large collection of fine-grain parallel algorithmic skeletons, represented as COOL objects in a tree hierarchy, contains the algorithmic knowledge. A hybrid knowledge base with rule modules and procedural parts, encoding expertise about application domain, parallel programming, software engineering, and parallel hardware, enables a high degree of automation in the software development process. In this paper, important aspects of the implementation of the PDE using CLIPS and COOL are shown, including the embedding of CLIPS with C++-based parts of the PDE. The appropriateness of the chosen approach and of the CLIPS language for knowledge-based software engineering are discussed.

Dvorak, Jiri J.↗
DOE OSTI2013

Improvements to Nuclear Data and Its Uncertainties by Theoretical Modeling

This project addresses three important gaps in existing evaluated nuclear data libraries that represent a significant hindrance against highly advanced modeling and simulation capabilities for the Advanced Fuel Cycle Initiative (AFCI). This project will: Develop advanced theoretical tools to compute prompt fission neutrons and gamma-ray characteristics well beyond average spectra and multiplicity, and produce new evaluated files of U and Pu isotopes, along with some minor actinides; Perform state-of-the-art fission cross-section modeling and calculations using global and microscopic model input parameters, leading to truly predictive fission cross-sections capabilities. Consistent calculations for a suite of Pu isotopes will be performed; Implement innovative data assimilation tools, which will reflect the nuclear data evaluation process much more accurately, and lead to a new generation of uncertainty quantification files. New covariance matrices will be obtained for Pu isotopes and compared to existing ones. The deployment of a fleet of safe and efficient advanced reactors that minimize radiotoxic waste and are proliferation-resistant is a clear and ambitious goal of AFCI. While in the past the design, construction and operation of a reactor were supported through empirical trials, this new phase in nuclear energy production is expected to rely heavily on advanced modeling and simulation capabilities. To be truly successful, a program for advanced simulations of innovative reactors will have to develop advanced multi-physics capabilities, to be run on massively parallel super- computers, and to incorporate adequate and precise underlying physics. And all these areas have to be developed simultaneously to achieve those ambitious goals. Of particular interest are reliable fission cross-section uncertainty estimates (including important correlations) and evaluations of prompt fission neutrons and gamma-ray spectra and uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Scalable Contour Tree Computation by Data Parallel Peak Pruning

As data sets grow to exascale, automated data analysis and visualization are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. Furthermore, we report the first shared SMP algorithm for fully parallel contour tree computation, with formal guarantees of O(lg V lg t) parallel steps and O(V lg V) work for data with V samples and t contour tree supernodes, and implementations with more than 30× parallel speed up on both CPU using TBB and GPU using Thrust and up 70× speed up compared to the serial sweep and merge algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

Lemke, Max↗
NASA NTRS1994

Automated Performance Prediction of Message Passing Parallel Programs

As the trend toward massively parallel processing continues, the need for tools that can predict scalability trends becomes greater. While high level languages Eke HPF have come into greater use, explicit message-passing programs proliferate, and will probably do so for some time, thanks to the onslaught of standards such as MPI. Much work has been done to create simple models that represent important characteristics of parallel programs, such as latency, network contention, and communication volume. But many of these methods still require a substantial manual effort to represent an application in the model's format. The YAPP ("Yet Another Performance Predictor") tool is an attempt to automate the formation of first-order expressions for completion time, with a minimum of programmer assistance. The content of this paper is as follows: First, we explore the implementation details of YAPP, and illustrate with examples some of the reasons that automatic prediction is difficult. In the following sections, we present the results of four applications, using execution traces on the Intel i860, analyze the error in YAPP's predictions, explain the limitations of our implementation, and mention possible future additions. In particular, we illustrate techniques used to identify pipeline communication patterns, and demonstrate how compiler analysis and regression are combined to automate the prediction process.

Block, Robert J.↗
DOE OSTI2014

Automated Algorithms for Quantum-Level Accuracy in Atomistic Simulations: LDRD Final Report.

This report summarizes the result of LDRD project 12-0395, titled "Automated Algorithms for Quantum-level Accuracy in Atomistic Simulations." During the course of this LDRD, we have developed an interatomic potential for solids and liquids called Spectral Neighbor Analysis Poten- tial (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected on to a basis of hyperspherical harmonics in four dimensions. The SNAP coef- ficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. Global optimization methods in the DAKOTA software package are used to seek out good choices of hyperparameters that define the overall structure of the SNAP potential. FitSnap.py, a Python-based software pack- age interfacing to both LAMMPS and DAKOTA is used to formulate the linear regression problem, solve it, and analyze the accuracy of the resultant SNAP potential. We describe a SNAP potential for tantalum that accurately reproduces a variety of solid and liquid properties. Most significantly, in contrast to existing tantalum potentials, SNAP correctly predicts the Peierls barrier for screw dislocation motion. We also present results from SNAP potentials generated for indium phosphide (InP) and silica (SiO 2 ). We describe efficient algorithms for calculating SNAP forces and energies in molecular dynamics simulations using massively parallel computers and advanced processor ar- chitectures. Finally, we briefly describe the MSM method for efficient calculation of electrostatic interactions on massively parallel computers.

Thompson, Aidan Patrick↗
DOE OSTI2015

Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU’s) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH{sub 3}, CO{sub 2}, formic acid, and benzene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Modular Spiking Neural Circuits for Mapping Long Short-Term Memory on a Neurosynaptic Processor

Due to the distributed and asynchronous nature of neural computation through low-energy spikes, brain-inspired hardware systems offer high energy efficiency and massive parallelism. One such platform is the IBM TrueNorth neurosynaptic system. Recently, TrueNorth compatible representation learning algorithms have emerged, achieving close to the state-of-the-art performance in various data sets. However, its application in temporal sequence processing models, such as recurrent neural networks (RNNs), is still only at the proof of concept level. There is an inherent difficulty in capturing temporal dynamics of an RNN using spiking neurons, which is only exasperated by the hardware constraints in connectivity and synaptic weight resolution. This paper presents a design flow that overcomes these difficulties and maps a special case of recurrent networks called long short-term memory (LSTM) onto a spike-based platform. The framework utilizes various approximation techniques, such as activation discretization, weight quantization, and scaling and rounding, spiking neural circuits that implement the complex gating mechanisms, and a store-and-release technique to enable neuron synchronization and faithful storage. While the presented techniques can be applied to map LSTM to any spiking neural network (SNN) simulator/emulator, here we choose the TrueNorth chip as the target platform by adhering to its hardware constraints. Three LSTM applications, parity check, extended Reber grammar, and question classification, are evaluated. The tradeoffs among accuracy, performance, and energy tradeoffs achieved on TrueNorth are demonstrated. Finally, this is compared with the performance on an SNN platform without hardware constraints, which represents the upper bound of the achievable accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

MemXCT: Design, Optimization, Scaling, and Reproducibility of X-Ray Tomography Imaging

Here, this work extends our previous research entitled "MemXCT: Memory-centric X-ray CT Reconstruction with Massive Parallelization" that was originally published at SC19 conference (Hidayetoglu et al., 2019) with reproducibility of the computational imaging performance. X-ray computed tomography (XCT) is regularly used at synchrotron light sources to study the internal morphology of materials at high resolution. However, experimental constraints, such as radiation sensitivity, can result in noisy or undersampled measurements. Further, depending on the resolution, sample size and data acquisition rates, the resulting noisy dataset can be in the order of terabytes. Advanced iterative reconstruction techniques can produce high-quality images from noisy measurements, but their computational requirements have made their use an exception rather than the rule. We propose a novel memory-centric approach that avoids redundant computations at the expense of additional memory complexity. We develop a memory-centric iterative reconstruction system, MemXCT, that uses an optimized SpMV implementation with two-level pseudo-Hilbert ordering and multi-stage input buffering. We evaluate MemXCT on various supercomputer architectures involving KNL and GPU. MemXCT can reconstruct a large (11Kx11K) mouse brain tomogram in 10 seconds using 4096 KNL nodes (256K cores). The results presented in our original article at the SC19 were based on large-scale supercomputing resources. The MemXCT application was selected for the Student Cluster Competition (SCC) Reproducibility Challenge and evaluated on a variety of cloud computing resources by universities around the world in the SC20 conference. We summarize the results of the top-ranked SCC Reproducibility Challenge teams and identify the most pertinent measures for ensuring the reproducibility of our experiments in this article.

47 OTHER INSTRUMENTATION↗
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↗