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Analog Computing for Science

Conventional digital computing faces fundamental physical limits: large scale computing systems already con sume tens of Megawatts of power, Dennard scaling has ended, and data movement costs dominate application performance. Next generation experimental facilities generate data at rates that overwhelm conventional pro cessing and demand real-time analysis at the source. Analog computing, which exploits the continuous dynamics of physical systems to perform computation, promises a transformative path toward orders-of-magnitude gains in energy efficiency and time-to-solution for scientific workloads.

97 MATHEMATICS AND COMPUTING↗

An Integrated High-performance Computing and Digital Real-time Simulation Testbed to Benchmark Closed-loop Load Shedding Algorithms in Power Systems

An integrated testbed using digital real-time simulator (DRTS) and a high-performance computing (HPC) cluster is presented here to compare speed and performance of computational schemes to mitigate time-critical issues in electric power systems. The first approach in this testbed validation is taken by running a set of closed-loop load shedding algorithms to compare and contrast two paradigms of arresting cascading failure propagation. Two algorithms involve solving DC and AC power flow model-based optimization problems to compute load shedding at different buses, while a model-based stochastic search using parallel computing provides a viable alternative. The algorithms are implemented in the DRTS-HPC testbed for the IEEE 14-bus benchmark transmission system. As a proof of the concept, simulation results are presented for implementation of closed-loop load-shedding algorithms for cascading failures in the DRTS-HPC testbed

24 POWER TRANSMISSION AND DISTRIBUTION↗

Controlled Formation of Conduction Channels in Memristive Devices Observed by X–ray Multimodal Imaging

Neuromorphic computing provides a means for achieving faster and more energy efficient computations than conventional digital computers for artificial intelligence (AI). However, its current accuracy is generally less than the dominant software-based AI. The key to improving accuracy is to reduce the intrinsic randomness of memristive devices, emulating synapses in the brain for neuromorphic computing. Here using a planar device as a model system, the controlled formation of conduction channels is achieved with high oxygen vacancy concentrations through the design of sharp protrusions in the electrode gap, as observed by X-ray multimodal imaging of both oxygen stoichiometry and crystallinity. Classical molecular dynamics simulations confirm that the controlled formation of conduction channels arises from confinement of the electric field, yielding a reproducible spatial distribution of oxygen vacancies across switching cycles. Furthermore, this work demonstrates an effective route to control the otherwise random electroforming process by electrode design, facilitating the development of more accurate memristive devices for neuromorphic computing.

36 MATERIALS SCIENCE↗

Oracles for Gauss's law on digital quantum computers

Formulating a lattice gauge theory using only physical degrees of freedom generically leads to nonlocal interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace of a much larger Hilbert space in which Gauss's law is not automatic. Digital quantum simulations of this local formulation will wander into unphysical sectors due to errors from Trotterization or from quantum noise. In this work, oracles are constructed that use local Gauss law constraints to projectively distinguish physical and unphysical wave functions in Abelian lattice gauge theories. Such oracles can be used to detect errors that break Gauss's law.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simulating fermions with a digital quantum computer

Quantum computers are expected to become a powerful tool for studying physical quantum systems. Consequently, a number of quantum algorithms to determine the physical properties of such systems have been developed. Although qubit-based quantum computers are naturally suited to the study of spin-1/2 systems, systems containing other degrees of freedom must first be encoded into qubits. Transformations to and from fermionic degrees of freedom have long been an important tool in physics and chemistry, which is now finding another application in the simulation of fermionic systems on quantum computers based on qubits. In this work, we discuss methods for encoding fermionic degrees of freedom into qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum simulations in effective model spaces: Hamiltonian-learning variational quantum eigensolver using digital quantum computers and application to the Lipkin-Meshkov-Glick model

Quantum simulations offer the potential to predict the structure and dynamics of nuclear many-body systems that are beyond the capabilities of classical computing. Generally, preparing the ground state of strongly-interacting many-body systems relevant to nuclear physics is however inefficient, even using ideal quantum computers. In addition, currently available NISQ-era quantum devices possess modest numbers of qubits, limiting the size of quantum many-body systems that can be simulated. In this context, a reformulation of the quantum many-body problems using truncated model spaces and Hamiltonians is desirable to make them more amenable to near-term quantum computers. The importance of symmetries in low-energy theories, including effective field theories (EFTs), lattice quantum chromodynamics (QCD), and effective model spaces for nuclear systems, in particular their interplay with the reduction of active Hilbert spaces, is well known. Lesser known is the fact that the non-commutivity of some symmetries and truncations of the model space can be profitably combined with variational calculations to rearrange the entanglement into localized structures and enable more efficient simulations. Here, the goal of the present study is to explore and utilize the non-commutivity of symmetries and model-space truncations of quantum many-body systems important to nuclear physics, particularly in combination with variational algorithms for quantum simulations and effective Hamiltonian learning. We introduce an iterative hybrid classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wavefunction. Quantum simulations, using classical computers and IBM's superconducting-qubit quantum computers, are performed to demonstrate the HL-VQE algorithm, in the context of the Lipkin-Meshkov-Glick (LMG) model of interacting fermions, where the Hamiltonian transformation corresponds to an orbital rotation. We use a mapping where the number of qubits scales with the $\log$ of the size of the effective model space, rather than the particle number. HL-VQE is found to provide an exponential improvement in LMG-model calculations of the ground-state energy and wavefunction, compared to naive truncations without Hamiltonian learning, throughout a significant fraction of the Hilbert space. In the context of EFT, this corresponds to counterterms scaling exponentially with the cut-off as opposed to power law. Implementations on IBM's QExperience quantum computers and simulators for 1- and 2-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions. For a range of parameters defining the LMG model, the HL-VQE algorithm is found to have better scaling of quantum resources requirements than previously explored algorithms. In particular, the HL-VQE scales efficiently over a large fraction of the model space, in contrast to VQE alone. This work constitutes a step in the development of entanglement-driven quantum algorithms for descriptions of nuclear many-body systems. This, in part, leverages the potential of noisy intermediate-scale quantum (NISQ) devices. The exponential scaling of counterterms observed in this study suggests the possibility of more general applicability to other non-perturbative EFTs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Robust Measurements of n -Point Correlation Functions of Driven-Dissipative Quantum Systems on a Digital Quantum Computer

We propose and demonstrate a unified hierarchical method to measure n -point correlation functions that can be applied to driven, dissipative, or otherwise open or nonequilibrium quantum systems. In this method, the time evolution of the system is repeatedly interrupted by interacting an ancilla qubit with the system through a controlled operation, and measuring the ancilla immediately afterward. We discuss the robustness of this method as compared to other ancilla-based interferometric techniques (such as the Hadamard test), and highlight its advantages for near-term quantum simulations of open quantum systems. We implement the method on a quantum computer in order to measure single-particle Green’s functions of a driven-dissipative fermionic system. This Letter shows that dynamical correlation functions for driven-dissipative systems can be robustly measured with near-term quantum computers. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits

The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L = 14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L = 50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Brochure on the 2024 ASCR Workshop on Analog Computing for Science

Analog computing fundamentally differs from digital by representing data with fully continuous physical quantities, such as voltages, probabilities, chemical concentrations, or light intensities, rather than encoding values in discrete binary states. While digital computing has historically excelled in precision, scalability, and noise resistance, newer analog approaches are gaining interest for their potential to dramatically improve energy efficiency and processing speed. Analog systems can inherently solve mathematical problems through their physical behavior and offer distinct advantages in scenarios where continuous operations are more effective than Boolean logic.

97 MATHEMATICS AND COMPUTING↗

Quantum Foundations of Classical Reversible Computing

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer’s Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

97 MATHEMATICS AND COMPUTING↗

Quantum computing without quantum computers: Database search and data processing using classical wave superposition

Quantum computers are proven to be more efficient at solving a specific class of problems compared to traditional digital computers. Superposition of states and quantum entanglement are the two key ingredients that make quantum computing so powerful. However, not all quantum algorithms require quantum entanglement (e.g., search through an unsorted database). Is it possible to utilize classical wave superposition to speed up database searching as much as by using quantum computers? There were several attempts to mimic quantum computers using classical waves. It was concluded that the use of classical wave superposition comes with the cost of an exponential increase in resources. In this work, we consider the feasibility of building classical wave-based devices able to provide fundamental speedup over digital counterparts without the exponential overhead. We present experimental data on database searching through a magnetic database using spin wave superposition. The results demonstrate the same speedup as expected for quantum computers. Also, we present examples of numerical modeling demonstrating classical wave interference for period finding. This approach may not compete with quantum computers with efficiency but outperform classical digital computers. We argue that classical wave-based devices can perform some of the quantum algorithms with the same efficiency as quantum computers as long as quantum entanglement is not required.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Demonstration and Evaluation of the Human-Technology Integration Guidance for Plant Modernization

The significance of nuclear power in its role producing carbon-free electricity to the U.S. cannot be overstated. However, with changes in the energy market coupled with changes in incentives given to certain resources like solar and wind, the operating and maintenance costs for these sources have seen a significant reduction, which has consequently negatively impacted the economic viability of the existing U.S. nuclear power plant fleet. Digital instrumentation and control (I&C) and control room modernization is a major critical work domain to reduce operating and maintenance costs. Existing nuclear power plants are commonly configured with mostly legacy analog I&C as well as isolated pockets of digital I&C (a plant process computer, digital recorders, etc.). One challenge with this analog I&C is that replacement parts are becoming prohibitively more expensive and difficult to obtain. Moreover, a significant challenge with the existing analog I&C is that the way in which plants are currently operated and maintained is no longer competitive with other electricity generating sources, like natural gas, where advanced digital I&C technologies are commonplace. This gap between the waynuclear power plants are operated compared to other electricity generating sources significantly challenges the economic viability of the nuclear industry. Indeed, digital I&C systems can fundamentally change the way the plant is operated (i.e., the concept of operation). The introduction of digital I&C technologies offers a wealth of benefits to the nuclear industry. However, it is important to emphasize that, to realize these benefits, a careful understanding of how to integrate technology in a collaborative way that leverages the capabilities of people and technologies is necessary. Human-technology integration applies human factors engineering methods and tools to ensure the safe and reliable use of these technologies while ensuring that the inherent features of the technologies that provide economic value are not missed. The scope of this work documents the demonstration of the recently developed human and technology integration methodology, as applied to developing a new vision and concept of operations for a major U.S. nuclear power plant fleet. This report focuses on the methodological aspects of developing a vision and concept of operations. This report shares the tools, activities, and lessons learned during a modernization currently underway for industry as a whole to consider when planning any significant digital modification and developing a new vision and concept of operations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Integrating Sudo-Kaminaga Correlation to the Safety Analysis Code PARET-ANL

The accuracy and reliability of the reactor safety analysis code are critical because the specifications of the safety systems will depend on the analytical results for initiating events that could occur to the reactor. In safety analyses for power reactors, there exist many proficient and applicable computer codes such as RELAP5, CATHARE, RETRAN, or CATHENA. For non-power research reactors, an issue arises, however, due to lacking of such specialized codes. As a result, computer codes developed for the transient analysis of power reactors need to be applied carefully after proving their applicability to a specified research reactor. The safety analysis discussed in this paper concerns the prevention of fuel damage in hypothetical accidental scenarios for the new research reactor design at National Institute of Standards and Technology (NIST). One fuel integrity criterion is analyzed by investigating the Minimum Critical Heat Flux Ratio (MCHFR) in the core during the accidental transients. Some previous studies develop a relationship that correlates the nominal value of the minimum CHFR with the probability of CHF occurring and causing fuel damage. Using a statistical approach, the nominal value of the MCHFR for the low-enriched uranium (LEU) reactor needs to remain above the recommended limiting value to better ensure the safety of the research reactor. The probability of no fuel failure increases as the MCHFR increases. More importantly, as long as the MCHFR remains above the recommended limiting value of 1.301, the reactor will have a 90% probability that CHF is not reached. The safety analysis program PARET, developed by Argonne National Laboratory (ANL), is employed to obtain the CHFR information in this study. PARET/ANL is a digital computer programming code intended primarily for the analysis of test and research reactors that use plate-type (flat) fuel elements. This program has its own set of correlations that are used to calculate the CHFR. One of them is the Mirshak correlation, which was believed to provide the best estimation of the critical heat flux under the operating conditions of the new reactor at the time. Following the critical heat flux (CHF) experiments for vertical rectangular channels in the JRR-3 (Japan Research Reactor unit 3), the CHF calculations now use the Sudo- Kaminaga correlation. This correlation is of our interest because this method has an enhanced geometric similarity and an increased range of applicability that are more representative of the actual operating conditions of our current design, and has a more mechanistic approach [9]. Since the source code of PARET/ANL is inaccessible, a MATLAB-based utility has been written to integrate the Sudo-Kaminaga correlation as a substitute for the Mirshak correlation in the code. As a result, both the Mirshak and the Sudo-Kaminaga correlations are used to analyze the standard output from the PARET program to calculate the CHFR.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗