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A formally certified end-to-end implementation of Shor’s factorization algorithm

Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors—“bugs.” Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof’s validity is automatically confirmed—certified—by a “proof assistant.” Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor’s prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way.

Science & Technology - Other Topics↗

ASCR@40: Four Decades of Department of Energy Leadership in Advanced Scientific Computing Research

Throughout its long history, the Office of Advanced Scientific Computing Research (ASCR) has built the critical technologies to ensure U.S. leadership in energy science and national security. It has made its parent agency, the Department of Energy (DOE) and its Office of Science, the world’s recognized leader in computational science. ASCR’s stated mission is “to discover, develop, and deploy computational and networking capabilities to analyze, model, simulate, and predict complex phenomena important to the DOE.” To accomplish this goal, ASCR oversees a large complex of computing and networking facilities and is responsible for procuring, deploying and operating high-performance computing (HPC), networking and storage resources; conducting basic research in mathematics and computer science; developing and sustaining a large body of software; and collaborating with other Office of Science programs, academia and industry. ASCR’s computational science leadership has a long history, predating even DOE’s inception. Applied mathematics and advanced computing were both elements of the Manhattan Project’s Theoretical Division. In the 1950s, DOE’s predecessor, the Atomic Energy Commission, created a mathematics program to develop and apply digital computing by supporting researchers at universities and AEC laboratories. Several organizational and name changes later, this program would grow and become ASCR.

97 MATHEMATICS AND COMPUTING↗

IM3 GO WEST Parameter Search Dataset

GO WEST is an open-source power grid modeling framework for U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It is developed to address weather and water dynamics, and associated vulnerabilities in this bulk power system. It covers 28 balancing authorities (BA) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of U.S. Western Interconnection created by Texas A&M University. Users can try and select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. Therefore, GO WEST can help researchers to strike a balance between model fidelity (i.e. accuracy) and computational complexity (i.e. runtime). This dataset includes model inputs and outputs from 600 model versions for each 2019, 2020, and 2021. The folder naming convention is as follows: Exp{Number of Nodes}_{Mathematical Formulation}_{Transmission Line Limit Scaling Factor in MW}_{Hurdle Rate Scaling Factor in %}_{Year}. Linear programming is designated with "simple" label whereas mixed-integer linear programming is designated with "coal" label. For example, "Exp100_simple_1000_50_2019" folder contains inputs and outputs from 2019 model version with 100 nodes, linear programming, +1000 MW transmission line limit scaling factor, and +50% hurdle rate scaling factor. GO WEST GitHub repository hosts all raw datasets, processing scripts, and model scripts. Please refer to the README file for a detailed description of the included files.

Economics↗

Investing in STEM Benefits Community, Company, and Industry - 20243

Like many organizations and groups, the Department of Energy Environmental Management program and the nuclear industry are facing an aging employee population and record numbers of employee retirements. This 'silver tsunami' of retirees means the industry as a whole is recruiting graduates at a fast pace. So, how do we ensure the nuclear industry has a robust pipeline of graduates with the necessary background? Fluor Idaho's investment in science, technology, engineering, and mathematics (STEM) education programs helps promote the next generation of technical professionals, benefiting both the company and the industry. Through community outreach initiatives and student mentoring programs, Fluor Idaho promotes kids' interest in STEM. The programs are designed to spark STEM interest in grade school and then foster and grow that interest through high school and higher education. After igniting student excitement about STEM topics in school, Fluor Idaho focuses on providing work-specific opportunities including mentoring and intern programs. These programs give students a better look at real-world job opportunities while still stimulating their interest in STEM. These programs ultimately provide career opportunities for the students and a pipeline of workers. Fluor Idaho's strategy for its summer interns has been to place students in a wide variety of projects - from the commissioning of a first-of-a-kind nuclear processing facility, to operating nuclear waste management facilities, to developing computer programs and applications - and give them responsibilities that make them feel like valued contributors. This approach has created a positive and rewarding summer-intern program experience for the students. Fluor Idaho's investment in its future today is reducing the knowledge gap - or cliff - that many contractors in the nuclear industry are facing. It's a worthwhile investment that is readily visible within its many cleanup projects. The next generation of technical professionals is making an impact now - benefiting both the company and the nuclear industry. This paper will review Fluor Idaho's programs, including STEM community outreach and education and mentoring programs. It will also present statistics about the reach of those programs and their successes. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Cooperative Transmission Expansion Planning Experiment Data and Results

GO WEST is an open-source power grid modeling framework for U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BA) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of U.S. Western Interconnection created by Texas A&M University. Users can try and select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within GO WEST framework. In this sense, TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. TEP minimizes the total cost of the system which comprises the operational cost of satisfying electricity demand (i.e., generation cost), cost of loss of load (i.e., unserved energy), cost of power flow, and cost of new transmission capacity additions (i.e., investment cost). In order to use TEP model, users need to create scenarios with GO WEST framework. In this analysis, outputs from several models are used to create future inputs to GO WEST and TEP models, including GCAM-USA, TELL, CERF and reV. This dataset includes experiment inputs and outputs from three different transmission expansion scenarios (cooperative, intermediate, and individual) for 2019 and 2059. For 2019, a base scenario to illustrate the default (i.e., historical) power grid operations is also included. This study utilizes rcp45hotter_ssp3 scenario from a previous version of GCAM-USA simulations. Sources of the shapefiles in supplementary data are HIFLD Open and U.S. Energy Atlas. Please see the README file for a detailed description of the main and supplementary data.

Capacity Expansion Model↗

IM3 Projected U.S. Western Interconnection Grid Stress Dataset

This dataset provides projected grid stress and reliability results (including all model inputs and outputs from GO WEST and TEP) for Integrated Multisector, Multiscale Modeling (IM3) Phase 2 simulations across eight different scenarios for the U.S. Western Interconnection through 2055. The scenarios include combinations of two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States from a set of Thermodynamic Global Warming (TGW) simulations. These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight simulations are: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 GO WEST is an open-source power grid modeling framework for the U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BAs) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of the U.S. Western Interconnection (ACTIVSg10k). Users can select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on the GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within the GO WEST framework. The TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. In order to use TEP model, users need to create scenarios with the GO WEST framework. Please refer to README file for a detailed description of the dataset including individual files and references.

Capacity Expansion Model↗

The Kokkos Ecosystem [Brief]

In 2016/2017, the field of High-Performance Computing (HPC) entered a new era driven by fundamental physics challenges to produce ever more energy and cost-efficient processors. Since the convergence on the Message-Passing Interface (MPI) standard in the mid-1990s, application developers enjoyed a seemingly static view of the underlying machine — that of a distributed collection of homogeneous nodes executing in collaboration. However, after almost two decades of dominance, the sole use of MPI to derive parallelism acted as a limiter to improved future performance. While MPI is widely expected to continue to function as the basic mechanism for communication between compute nodes for the immediate future, additional parallelism is required on the computing node itself if high performance and efficiency goals are to be realized. When reviewing the architectures of the top HPC systems today, the change in paradigm is clear: the compute nodes of the leading machines in the world are either powered by many-core chips with a few dozen cores each, or use heterogeneous designs, where traditional CPUs marshal work to massively parallel compute accelerators which has as many as 200,000 processing threads in flight simultaneously. Complicating matters further for application developers, each processor vendor has its own preferred way of writing code for their architecture.The Kokkos EcoSystem was released by Sandia in 2017 to address this new era in HPC system design by providing a vendor independent performance portable programming system for scientific, engineering, and mathematical software applications written in the C++ programming language. Using Kokkos, application developers can be more productive because they will not have to create and maintain separate versions of their software for each architecture, nor will they have to be experts in each architecture's peculiar requirements. Instead, they will have a single method of programming for the diverse set of modern HPC architectures. While Kokkos started in 2011 as a programming model only, it soon became clear that complex applications needed more. It is also critical to have a portable mathematical functions and developers need tools to debug their applications, gain insight into the performance characteristics of their codes and tune algorithm performance parameters through automated processes. The Kokkos EcoSystem addresses those needs through its three main components: the Kokkos Core programming model, the Kokkos Kernels math library, and the Kokkos Tools project.

97 MATHEMATICS AND COMPUTING↗

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

Bootstrap and amplitudes: a hike in the landscape of quantum field theory

This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories. We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic quantum field theories. Here, the first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the CP 1 model with the Fubini-Study metric arising from re-summation of the n-point interaction terms derived from amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Topological aspects of matters and Langlands program

The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal nature of the energy spectrum of two-dimensional Bloch electrons, statistical physics, and quantum computation. The new unified view of existing dualism presented in this paper raises the entirely new question of how each theory of physics is connected as a piece of the Langlands program.

Physics↗

Taming nuclear mass models with Gaussian processes

We propose a new set of nuclear mass predictions based on multiple theoretical mass models. By employing Gaussian process regression with the Matérn kernel, we achieved root-mean-square (rms) deviations below 100 keV for the training dataset. The best-performing mass models achieved rms deviations below 150 keV for the new precise mass data from AME2020, whereas the ensemble average showed robust performance across the nuclear chart. Our approach uniquely combines: (1) systematic refinement of eight mass models through their residuals, (2) physics-informed features, including magic numbers, nucleon parity numbers, neutron excess, and nuclear collectivity, and (3) theory-to-theory validation demonstrating robust extrapolation capability. We find that the Matérn kernel provides superior uncertainty quantification compared to the RBF kernel, with a length-scale analysis revealing enhanced inter-nuclei correlations. We provide complete mass predictions for all unknown nuclides in AME2020, offering valuable constraints for nuclear structure studies and astrophysical modeling when used with proper uncertainty propagation.

Gaussian processes↗

Uncovering heterogeneous intercommunity disease transmission from neutral allele frequency time series

The COVID-19 pandemic has underscored the need for accurate epidemic forecasting to predict pathogen spread, evolution, and evaluate intervention strategies. Forecast reliability hinges on detailed knowledge of disease transmission across population segments, which may be inferred from contact surveys or mobility data. However, these indirect approaches make it difficult to estimate rare transmissions between socially or geographically distant communities. We show that the steep ramp-up of genome sequencing surveillance during the pandemic can be leveraged to directly identify transmission patterns between geographically defined communities. Our approach uses a hidden Markov model to infer the fraction of infections a community imports from others based on how rapidly allele frequencies in the focal community converge to those in the donor communities. Applying this method to SARS-CoV-2 sequencing data from England and the United States, we uncover networks of intercommunity transmission that reflect geographical relationships while exposing significant long-range interactions. The scaling of importation rate with distance is consistent across both countries, yet weaker than expected based on mobility data, highlighting limitations of indirect inference. We show that transmission patterns can change between waves of variants of concern and analyze how the inferred heterogeneity in intercommunity transmission impacts evolutionary forecasts. While applied here to geographically defined communities, our approach could be applied to those defined by other traits (e.g., age, socioeconomic status), provided time-series data can be stratified accordingly. Overall, our study highlights population genomic time series data as a crucial record of epidemiological interactions, which can be deciphered using tree-free inference methods.

Okada, Takashi [Department of Physics; University ↗

SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking (FY2020 Progress Report)

The development of algorithms for machine learning and data analysis for the 3013 Surveillance Program is a collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). For corrosion detection, Laser Confocal Microscope (LCM) or Wide Area 3D Measurement System (WAMS) data is extracted from large binary files, with software written to convert the data to physical attributes (e.g. height, color and grayscale values; all as functions of a location in a plane projection). It is the objective of this project to produce a user-friendly interface that incorporated all operations needed to perform surface examination. For this reason, a Matlab-based Graphical User Interface (GUI) was created to integrate data input with software developed for processing and evaluation. In summary, the GUI permits selective downloading of binary data, interrogation of attributes, data labeling, flagging of significant features, execution of Machine Learning (ML) algorithms, output of parameters for trained ML algorithms, reports of ML model accuracy with respect to labeled data, and generation of graphical representations of various analyses.

3013 corrosion↗

FY21 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

The development of algorithms for machine learning and data analysis for the 3013 Surveillance Program is a collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). For corrosion detection, Laser Confocal Microscope (LCM) or Wide Area 3D Measurement System (WAMS) data is extracted from large binary files, with software written to convert the data to physical attributes (e.g., height, color and grayscale values; all as functions of a location in a plane projection). A user-friendly Matlab Graphical User Interface (GUI) that reads data from either LCM or WAMS files was developed to integrate input data with software developed for processing and evaluation. The GUI can selectively download binary data, interrogate data attributes, label data, flag significant features, execute Machine Learning (ML) algorithms, output parameters for trained ML algorithms, report ML model accuracy with respect to labeled data, and generate graphical representations for various analyses. Features can be called out by user-specified thresholds, manual labeling or machine learning algorithms when they have been completed. The ability to rapidly label data is important because of the volume of data required for training machine learning algorithms. The GUI has the flexibility to allow addition of improved ML algorithms, methods for data visualization, and statistical computations. Statistical analyses via the GUI include areas of pits within a defined range of pit depths, correlations between Red-Green-Blue (RGB) or grayscale intensity and relative surface height, covariances between values associated with features, and feature histograms. The development of supervised machine learning algorithms, however, has been hindered by a lack of training data. The machine learning algorithms for crack identification are being refined but require improvements to the true positive rate for crack detection. This shortcoming is an artifact of the limited training data currently available, perhaps more so than the structure of the neural networks. At present, the best results are had from a consensus over an ensemble of randomly generated Deep Neural Network (DNN) or Convolutional Neural Network (CNN) algorithms. Although the consensus accuracy method has yielded optimum true positive and true negative rates in excess of 80%, additional validation testing is necessary. In addition to the suite of LCM data that was initially used, and which represents the majority of the work presented in this report, WAMS image data was also reviewed at a preliminary level. The review included a comparison between image resolution and dynamic range for each method. WAMS (ZON file) image data was found to have a pixel pitch of 3.69μm compared to 1 μm for the LCM (vk4 file) data, which implies a lower resolution for the WAMS images. Conversely, the ratio of dynamic range of the WAMS data to the LCM data was approximately 41:20 for height data, suggesting that information from WAMS should more accurately determine the depth of pits. At present, the significance of the greater dynamic range of the WAMS data relative to the LCM data has not yet been evaluated.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NREL Programs Channel Students Toward the Future Water Power Workforce

Water power is a flourishing segment of the renewable energy industry, and resilient, reliable technologies like marine energy and hydropower are poised to play a significant role in our energy demands in the years to come. Continuing this trajectory of growth, however, requires new talent and innovation. As part of the effort to thoughtfully attract the best and most qualified workers, the National Renewable Energy Laboratory's (NREL's) Science, Technology, Engineering, and Mathematics (STEM) and workforce development programs raised student awareness of and made connections to water power career opportunities throughout fiscal year 2021.

HYDRO ENERGY,TIDAL AND WAVE POWER↗

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.

97 MATHEMATICS AND COMPUTING↗

Modeling and Detection of Future Cyber-Enabled DSM Data Attacks

Demand-Side Management (DSM) is an essential tool to ensure power system reliability and stability. In future smart grids, certain portions of a customer’s load usage could be under the automatic control of a cyber-enabled DSM program, which selectively schedules loads as a function of electricity prices to improve power balance and grid stability. In this scenario, the security of DSM cyberinfrastructure will be critical as advanced metering infrastructure and communication systems are susceptible to cyber-attacks. Such attacks, in the form of false data injections, can manipulate customer load profiles and cause metering chaos and energy losses in the grid. The feedback mechanism between load management on the consumer side and dynamic price schemes employed by independent system operators can further exacerbate attacks. To study how this feedback mechanism may worsen attacks in future cyber-enabled DSM programs, we propose a novel mathematical framework for (i) modeling the nonlinear relationship between load management and real-time pricing, (ii) simulating residential load data and prices, (iii) creating cyber-attacks, and (iv) detecting said attacks. In this framework, we first develop time-series forecasts to model load demand and use them as inputs to an elasticity model for the price-demand relationship in the DSM loop. This work then investigates the behavior of such a feedback loop under intentional cyber-attacks. We simulate and examine load-price data under different DSM-participation levels with three types of random additive attacks: ramp, sudden, and point attacks. We conduct two investigations for the detection of DSM attacks. The first studies a supervised learning approach, with various classification models, and the second studies the performance of parametric and nonparametric change point detectors. Results conclude that higher amounts of DSM participation can exacerbate ramp and sudden attacks leading to better detection of such attacks, especially with supervised learning classifiers. We also find that nonparametric detection outperforms parametric for smaller user pools, and random point attacks are the hardest to detect with any method.

97 MATHEMATICS AND COMPUTING↗