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Large Scale Neuromorphic Computing at Sandia National Labs from Algorithms to Architectures
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Advances in Image-Domain Multi-Resolution and Super-Resolution Algorithms for Industrial X-Ray Computed Tomography: A Literature Survey and New Insights
Industrial X-ray Computed Tomography (XCT) is a nondestructive method for inspection and character ization of materials and parts. XCT captures images of a part from various angles, and these images are then used to construct Three-Dimensional (3D) representations of that part. This method enables assessing the quality of the parts, identifying defects and understanding their physical properties without damaging them.
Novel Algorithms for Beyond-von-Neumann Computing
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Computational Sciences and Math at Sandia -- Algorithms Software and Applications.
Abstract not provided.
Quantum Computing for Theoretical Nuclear Physics, A White Paper prepared for the U.S. Department of Energy, Office of Science, Office of Nuclear Physics
Tremendous excitement exists among quantum computing enthusiasts as we witness the rapid evolution of quantum computing devices toward early practical implementation. Importantly, algorithm developments suggest that qubit devices have the potential to solve quantum many-body and quantum field theory problems of relevance to various research directions within the Department of Energy Office of Science and National Science Foundation. While exascale platforms represent the current horizon of excellence in computing, quantum computing provides the technology that lies beyond this horizon and opens the door to new vistas of theoretical endeavor. During a recent workshop at the Institute for Nuclear Theory, a group of 39 scientists from academia, government, national laboratories, and industry gathered to discuss the future of quantum computing for nuclear physics. Researchers described the basic scientific challenges in quantum chromodynamics and quantum many-body problems that could be addressed utilizing the power of quantum computing in the future. The group also discussed mechanisms for developing quantum-computing algorithms specifically for nuclear physics applications. This White Paper provides a synopsis of the workshop discussions, and suggests possible activities that might be supported as part of a vibrant pilot program of nuclear physics research in this area.
True Load Balancing for Matricized Tensor Times Khatri-Rao Product
MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. In conclusion, parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.
A Solution Method for the Filtered Lifting Line Theory
The filtered lifting line theory presents a continuous form of the inviscid momentum equations of flow over a lifting device, such as a wing or rotor blade, using body forces without mathematical singularities. This theory is also consistent with an actuator line representation of a lifting device. In this work, we present a reformulation of the equations in terms of the local flow angle along the line, which allows solving the stand-alone equations using multivariate root-finding algorithms. This approach can be used to obtain a fast, computationally inexpensive solution of the loading distribution along a wing without the need to perform computational fluid dynamic simulations. We study the requirements in terms of resolution in the spanwise direction and establish the criteria for spacing and minimum amount of points required along the blade to obtain converged solutions. The solutions are compared to results from large-eddy simulations, and we observed excellent agreement with less than a percent difference in quantities along the blade between the methods.
A 3D Parallel Algorithm for QR Decomposition
Interprocessor communication often dominates the runtime of large matrix computations. Here, we present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing its latency cost (number of messages). By varying a parameter to navigate the bandwidth/latency tradeoff, we can tune this algorithm for machines with different communication costs.
An Integral-based Technique to Accelerate the Monte Carlo Radiative Transfer Computation for Supernovae
We present an integral-based technique (IBT) algorithm to accelerate supernova (SN) radiative transfer calculations. The algorithm utilizes “integral packets,” which are calculated by the path integral of the Monte Carlo (MC) energy packets, to synthesize the observed spectropolarimetric signal at a given viewing direction in a 3D time-dependent radiative transfer program. Compared to the event-based technique (EBT) proposed by M. Bulla et al., our algorithm significantly reduces the computation time and increases the MC signal-to-noise ratio (S/N). Using a 1D spherical symmetric Type Ia SN ejecta model DDC10 and its derived 3D model, the IBT algorithm has successfully passed the verification of spherical symmetry and cross comparison on a 3D SN model with the direct-counting technique and EBT. Notably, with our algorithm implemented in the 3D MC radiative transfer code SEDONA, the computation time is faster than EBT by a factor of 10−30, and the S/N is better by a factor of 1.5−3, with the same number of MC quanta.
A modified formula for dose calculations of stereotactic ablative body radiotherapy for non–small cell lung cancer
To provide a modified formula consistent with the Monte Carlo (MC) algorithm for dose calculations during stereotactic ablative body radiotherapy for non–small cell lung cancer. Seventy CyberKnife treatment plans were calculated and analyzed by MC and ray-tracing (RT) algorithms, separately. Parameters of treatment plans were compared, and those associated with differences of dose distributions were analyzed to establish a modified formula. Gross tumor volume and tumor tracking volume (TTV) were defined as the evident disease on the sequences of the window width and level of the lung and the mediastinum. Additionally, the formula was validated by another 20 plans. The prescription dose of the 90 patients was 60 Gy/5f. The RT algorithm overestimated the planning target volume (PTV) D{sub 95} by an average of 8.59 Gy and the gross tumor volume D{sub 99} by an average of 5.84 Gy. The homogeneity index of PTV was underestimated by 0.11 on average, whereas the conformity index and new conformity index was underestimated by 0.05. The RT algorithm overestimated the dose distribution to the spinal cord by 2.23 Gy, the esophagus by 1.96 Gy, the trachea by 1.89 Gy, the left-sided bronchus by 1.77 Gy, the right-sided bronchus by 1.64 Gy, and the heart by 2.16 Gy. The average whole-lung dose volumes of lung tissues and dose volumes of V{sub 5} were overestimated by 2.69 Gy and 7.52%, respectively. A power function distribution (R{sup 2} = 0.8626) was confirmed between PTV D{sub 95} and TTV volumes. PTV D{sub 95} calculated by the MC algorithm could be computed easily with TTV and PTV D{sub 95} calculated by the RT algorithm based on the formula. The modified equation was more consistent with MC algorithm than with other formula, which could be a reference to those not accessible to the MC algorithm.
Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model
The variational quantum eigensolver is a promising algorithm for noisy intermediate scale quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. Here, we consider the exactly diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe Ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}$(N) and $\mathcal{O}$(log 2 N) that can prepare any trigonometric LMG eigenstate of N particles. The number of gates required for both circuits is $\mathcal{O}$(N). The energies of the eigenstates can then be measured and compared to the exactly known answers.
Radioactive Decay Computation with a Graph Approach for Solving a Linear Dynamic System
ABSTRACT: This article gives two graph-based algorithms for radioactive decay computation. The first algorithm identifies the connected components of the graph induced from the given radioactive decay dynamics to reduce the size of the problem. The solutions are derived over the precalculated connected components, respectively and independently. The second algorithm utilizes acyclic structure of radioactive decay dynamics. The algorithm evaluates the reachable vertices of the induced system graph from the initially activated vertices and finds the minimal set of starting vertices populating the entire reachable vertices. Then, the decay calculations are performed over the reachable vertices from the identified minimal starting vertices, respectively, with the partitioned initial value over the reachable vertices. A formal argument is given to show that the proposed graph inspired divide and conquer calculation methods perform the intended radioactive decay calculation. Empirical efforts comparing the proposed radioactive decay calculation algorithms are presented.
Investigating power capping toward energy-efficient scientific applications: Investigating Power Capping toward Energy-Efficient Scientific Applications
The emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale-level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore how different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. Lastly, we quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.
Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂(𝑁log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.
Parallel-in-time quantum simulation via Page and Wootters quantum time
In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪(log(𝑁)𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.
Algorithms in Diffraction Profile Analysis
This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.
Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization in the presence of noise. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in Motta et al. (2020) eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to challenging quantum computations of relevance for chemistry and nuclear physics, using the deuteron-binding energy and molecular hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of timesteps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.