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At least 991 records · Page 55

Computational projects with the Landau–Zener problem in the quantum mechanics classroom

The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. Additionally, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Is Knowledge about Running Applications Helping Improve Runtime Prediction of HPC Jobs?

High-performance computing systems rely upon scheduling algorithms to achieve high utilization. These schedulers rely upon user estimates of job resource requirements, such as runtime, to determine optimal scheduling of incoming jobs. These user estimates, however, are prone to error. To mitigate this error, significant research has been directed at providing better estimates of job runtime, usually employing machine learning techniques. These techniques are dependent upon the input features selected. Among the possible features is the primary application used by the job. In a survey of more than 20 papers directed at improving runtime prediction, only four included primary application as an input feature. We focus this investigation specifically on the value of adding primary application as an input feature, and find that it does improve model performance, especially for jobs with longer runtimes, though this improvement varies based on the application used. We recommend further research to determine the cause of this variability as well as an optimal strategy for employing a mixture of models both including and not including primary application as a feature.

MATHEMATICS AND COMPUTING↗

Is Knowledge About Running Applications Helping Improve Runtime Prediction of HPC Jobs?

High-performance computing systems rely upon scheduling algorithms to achieve high utilization. These schedulers rely upon user estimates of job resource requirements, such as runtime, to determine optimal scheduling of incoming jobs. These user estimates, however, are prone to error. To mitigate this error, significant research has been directed at providing better estimates of job runtime, usually employing machine learning techniques. These techniques are dependent upon the input features selected. Among the possible features is the primary application used by the job. In a survey of more than 20 papers directed at improving runtime prediction, only four included primary application as an input feature. We focus this investigation specifically on the value of adding primary application as an input feature, and find that it does improve model performance, especially for jobs with longer runtimes, though this improvement varies based on the application used. We recommend further research to determine the cause of this variability as well as an optimal strategy for employing a mixture of models both including and not including primary application as a feature.

feature selection↗

NISQ Benchmarking

Test suite of quantum algorithms for Noisy Intermediate Scale Quantum (NISQ) computers. The test suite includes benchmark-style code for quantum volume circuits (QV), fairness sampling circuits, quantum telecloning circuits, and other NISQ benchmark style algorithms on small problems (i.e., up to 100 qubits), such as Variational Quantum Eigensolver (VQE), Hamiltonian Simulation, and Grover unstructured search example circuits. These benchmark-style applications are implemented in quantum software packages, mostly IBM's QISKIT, but may include vendor-specific frameworks, such as PyQuil (for Rigetti) or Q\# for Microsoft, or CirQ (for Google) as the test suite grows with the vendor sample. The test suite also includes numerical simulation code for Quantum Alternating Operator Ansatz (QAOA) algorithms, VQE, Hamiltonian Simulation and search examples. Numerical simulation code simulates quantum computers on classical computers, which is only possible for small problem instances; the implementation framework of choice is typically within Python, using the numpy/scipy libraries as well as extensions to the Julia language.

Pelofske, Elijah↗

Bias free multiobjective active learning for materials design and discovery

The design rules for materials are clear for applications with a single objective. For most applications, however, there are often multiple, sometimes competing objectives where there is no single best material and the design rules change to finding the set of Pareto optimal materials. In this work, we leverage an active learning algorithm that directly uses the Pareto dominance relation to compute the set of Pareto optimal materials with desirable accuracy. We apply our algorithm to de novo polymer design with a prohibitively large search space. Using molecular simulations, we compute key descriptors for dispersant applications and drastically reduce the number of materials that need to be evaluated to reconstruct the Pareto front with a desired confidence. This work showcases how simulation and machine learning techniques can be coupled to discover materials within a design space that would be intractable using conventional screening approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation

Here, we adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum algorithmic measurement

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system’s Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. Here, in this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Luo, Ye [Argonne National Laboratory (ANL), Argonn↗

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗

Validation of time-dependent shift using the pulsed sphere benchmarks

The detailed behavior of neutrons in a rapidly changing time-dependent physical system is a challenging computational physics problem, particularly when using Monte Carlo methods on heterogeneous high-performance computing architectures. A small number of algorithms and code implementations have been shown to be performant for time-independent (fixed source and k-eigenvalue) Monte Carlo, and there are existing simulation tools that successfully solve the time-dependent Monte Carlo problem on smaller computing platforms. To bridge this gap, a time-dependent version of ORNL’s Shift code has been recently developed. Shift’s history-based algorithm on CPUs, and its event-based algorithm on GPUs, have both been observed to scale well to very large numbers of processors, which motivated the extension of this code to solve time-dependent problems. The validation of this new capability requires a comparison with time-dependent neutron experiments. Lawrence Livermore National Laboratory’s (LLNL) pulsed sphere benchmark experiments were simulated in Shift to validate both the time-independent as well as new time-dependent features recently incorporated into Shift. A suite of pulsed-sphere models was simulated using Shift and compared to the available experimental data and simulations with MCNP. Overall results indicate that Shift accurately simulates the pulsed sphere benchmarks, and that the new time-dependent modifications of Shift are working as intended. Validated exascale neutron transport codes are essential for a wide variety of future multiphysics applications.

Palmer, Camille J.↗

ECP ST Capability Assessment Report (CAR) for VTK-m (FY20)

The ECP/VTK-m project is providing the core capabilities to perform scientific visualization on Exascale architectures. The ECP/VTK-m project fills the critical feature gap of performing visualization and analysis on processors like graphics-based processors. The results of this project will be delivered in tools like ParaView, Vislt, and Ascent as well as in stand-alone form. Moreover, these projects are depending on this ECP effort to be able to make effective use of ECP architectures. One of the biggest recent changes in high-performance computing is the increasing use of accelerators. Accelerators contain processing cores that independently are inferior to a core in a typical CPU, but these cores are replicated and grouped such that their aggregate execution provides a very high computation rate at a much lower power. Current and future CPU processors also require much more explicit parallelism. Each successive version of the hardware packs more cores into each processor, and technologies like hyper threading and vector operations require even more parallel processing to leverage each core's full potential. VTK-m is a toolkit of scientific visualization algorithms for emerging processor architectures. VTK-m supports the fine-grained concurrency for data analysis and visualization algorithms required to drive extreme scale computing by providing abstract models for data and execution that can be applied to a variety of algorithms across many different processor architectures. The ECP/VTK-m project is building up the VTK-m codebase with the necessary visualization algorithm implementations that run across the varied hardware platforms to be leveraged at the Exascale. We will be working with other ECP projects, such as ALPINE, to integrate the new VTK-m code into production software to enable visualization on our HPC systems.

97 MATHEMATICS AND COMPUTING↗

Chemical applications of variational quantum eigenvalue-based quantum algorithms: Perspective and survey

Exploring many-body chemical systems on classical computers often involves solving the Schrödinger equation. However, this approach is frequently limited by the exponential increase in the dimensionality of the Hamiltonian as the number of degrees of freedom increases. In contrast, quantum computing, specifically through the variational quantum eigensolver (VQE) framework, shows promise in overcoming this exponential cost. VQE can utilize the collective properties of quantum states to model the wavefunction in polynomial time. Despite the current limitations of quantum hardware, significant advances have been made in the development of VQE-based algorithms. Here, in this review, we provide an overview of emerging protocols, focusing on their applications in simulating the ground state, excited state, and vibrational properties of chemical systems. By examining notable algorithmic advancements and applications, this review aims to shed light on the challenges and potential of VQE-based algorithms in addressing relevant chemical problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Progress in Modeling the 2019 Extended Magnetically Insulated Transmission Line (MITL) and Courtyard Environment Trial at HERMES-III

This report documents the progress made in simulating the HERMES-III Magnetically Insulated Transmission Line (MITL) and courtyard with EMPIRE and ITS. This study focuses on the shots that were taken during the months of June and July of 2019 performed with the new MITL extension. There were a few shots where there was dose mapping of the courtyard, 11132, 11133, 11134, 11135, 11136, and 11146. This report focuses on these shots because there was full data return from the MITL electrical diagnostics and the radiation dose sensors in the courtyard. The comparison starts with improving the processing of the incoming voltage into the EMPIRE simulation from the experiment. The currents are then compared at several location along the MITL. The simulation results of the electrons impacting the anode are shown. The electron impact energy and angle is then handed off to ITS which calculates the dose on the faceplate and locations in the courtyard and they are compared to experimental measurements. ITS also calculates the photons and electrons that are injected into the courtyard, these quantities are then used by EMPIRE to calculated the photon and electron transport in the courtyard. The details for the algorithms used to perform the courtyard simulations are presented as well as qualitative comparisons of the electric field, magnetic field, and the conductivity in the courtyard. Because of the computational burden of these calculations the pressure was reduce in the courtyard to reduce the computational load. The computation performance is presented along with suggestion on how to improve both the computational performance as well as the algorithmic performance. Some of the algorithmic changed would reduce the accuracy of the models and detail comparison of these changes are left for a future study. As well as, list of code improvements there is also a list of suggested experimental improvements to improve the quality of the data return.

47 OTHER INSTRUMENTATION↗

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗

Generic Spiking Architecture (GenSA)

Neuromorphic devices are a rapidly growing area of interest in industry, with machines in production by IBM and Intel, among others. These devices promise to reduce size, weight and power (SWaP) costs while increasing resilience and facilitating high- performance computing (HPC). Each device will favor some set of algorithms, but this relationship has not been thoroughly studied. The field of neuromorphic computing is so new that existing devices were designed with merely estimated use-cases in mind. To better understand the fit between neuromorphic algorithms and machines, a simulated machine can be configured to any point in the design space. This will identify better choices of devices, and perhaps guide the market in new directions. The design of a generic spiking machine generalizes existing examples while also looking forward to devices that haven't been built yet. Each parameter is specified, along the approach/mechanism by which the relevant component is implemented in the simulator.

97 MATHEMATICS AND COMPUTING↗

New technologies as decision aids for the advancement of ecological risk assessment

Moore's law states that the number of transistors that can be placed on an integrated circuit doubles every two years (Moore, 1975). This has led to a steady increase in the processing power of computers over time, and technology is now enhancing and advancing software and scientific applications, which has enabled computationally intensive methods such as machine learning, data science, modeling, and simulation. The advancement of computers and data-driven algorithms is profoundly impacting people's lives. It is changing the way we work, the way we learn, and the way we interact with the world around us. Here, this editorial will discuss how scientists can benefit from the latest technology advancements and related tools by incorporating them into the ecological risk assessment (ERA) to study ecosystems as a way to create refined assessments and accelerate the turnaround times.

54 ENVIRONMENTAL SCIENCES↗