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DOE OSTI2023

A Systematic, Polynomial-Cost Approach to Exact Correlation Energies (Final Technical Report)

The full configuration interaction (FCI) wave function provides the exact solution to the Schrödinger equation in a given basis set. While FCI is intractable due to exponential computational costs, the many-body expansion (or the method of increments) can reduce scaling to a low-order polynomial with system size. This project entailed advances in the incremental FCI (iFCI) approach, designed to allow iFCI to reach larger system sizes and maintain its intrinsic high accuracy. This document describes advances in solvers for iFCI, strategies to treat multiple charge and spin states, and virtual state management methods to reduce memory requirements. Overall, this project allows iFCI to correlate (for the first time) 142 valence electrons in 444 orbitals in a realistic model of a transition metal complex.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Effect of Grain Boundary Misorientation on Spall Strength in Ta via Shock-Free Simulations with Relatively Few Atoms

A suite of 37 molecular dynamics simulations is conducted at two system sizes to systematically characterize the role of grain boundary (GB) misorientation on spall strength in pure BCC tantalum (Ta). The systems studied consist of bicrystals with a single [110] symmetric tilt grain boundary. Two loading conditions are compared: (i) homogeneous extension under uniaxial strain simulated in this study and (ii) piston/flyer impact of sample, which induces heterogeneous deformation via shockwave propagation along the length of the sample. The piston/flyer impact is taken from the literature and run on the same set of GB misorientation angles using LAMMPS. The major finding here is that both methods result in similar spall strength predictions, but the homogeneous extension method generally requires two to three orders of magnitude fewer atoms and similar reductions in computational costs. Spall strength results systematically overpredict using this method, by about 10% for the dataset three orders of magnitude smaller than piston/flyer simulations, and 5% for the dataset two orders of magnitude smaller. Lastly, the effect of system size and pre-compression magnitude on spall strength is systematically characterized.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗

DOE OSTI2025

Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States

Abstract Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we prove that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.

Barthel, Thomas↗

DOE OSTI2022

Optimizing DER Deployment for Climate, Health, Resilience, and Energy Bill Benefits Using the REopt Model

Climate change, public health, and resilience to power outages are of critical concern to local governments, federal agencies, and the private sector, and are increasingly motivating investments in distributed energy resources (DERs). However, designing a solar-plus-storage system to co-optimize for climate, health, resilience, and energy bill benefits requires complex trade-offs. To address this need, the National Renewable Energy Laboratory has integrated climate and health impacts of grid-purchased electricity and on-site fuel consumption into the publicly-available REopt web tool and API - a techno-economic model that determines the cost-optimal DER system sizes and dispatch strategy. This presentation will provide an overview of the tool's methodology, datasets, and capabilities, including costing emissions into system sizing and dispatch and setting emissions reductions targets. Results of previous work will demonstrate the use of new emissions accounting capabilities by quantifying the impact of including climate and health costs on the optimal resilient microgrid configurations for a hospital, school, and warehouse across 14 U.S. cities.

climate↗

DOE OSTI2024

Robustness and Eventual Slow Decay of Bound States of Interacting Microwave Photons in the Google Quantum AI Experiment

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated 𝑋⁢𝑋⁢𝑍 spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan et al., Nature 612, 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes.

Exact diagonalization↗

DOE OSTI2023

Quantifying agricultural productive use of energy load in Sub-Saharan Africa and its impact on microgrid configurations and costs

The use of advanced energy technologies for agricultural purposes—such as irrigation, refrigeration, crop processing, and egg incubation—has the potential to increase crop yield, reduce vulnerability to changing precipitation patterns, increase shelf life, strengthen income and employment opportunities in rural areas, and reduce emissions by displacing fossil fuel-based technologies. These productive uses of energy (PUE) in remote areas could potentially be powered by microgrids that additionally serve otherwise unelectrified communities, most of which are located in rural Sub-Saharan Africa. Here, in this paper, we use high-resolution geospatial data to estimate the end-use electricity demand for a range of agricultural PUE across Sub-Saharan Africa, and we share these data in an open-access mapping tool. Next, we use REopt®, a techno-economic optimization model of energy systems, to determine the cost and system sizing implications of incorporating agricultural PUE into microgrid designs in Kenya and Zambia. We estimate the upper bound of agricultural PUE demand for irrigation, milling, shelling, refrigeration, and egg incubation across Sub-Saharan to be 16.8 TWh/yr. We find that incorporating local agricultural PUE into microgrid system designs increases the required system sizing while having minimal impact on the levelized cost of energy of these systems. Our analysis is the first to demonstrate the PUE potential in the agricultural sector at a 10x10-kilometer resolution across Sub-Saharan Africa and to show, at scale, how site-specific PUE can impact the cost and sizing of microgrids that are otherwise deployed to serve local household and community load.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Heuristic Dispatch Based on Price Signals for Behind-the-Meter PV-Battery Systems in the System Advisor Model

The economic potential of a behind-the-meter (BTM) PV-battery system depends greatly on how the battery is dispatched. Different utility rates, system sizes, generation and load profiles can all require different dispatch strategies. This paper presents price signals dispatch, a new algorithm for automated economic dispatch of BTM PV-battery systems, which utilizes 24-hour PV and load forecasts, degradation data, and utility rates. The algorithm is integrated with the System Advisor Model (SAM) tool and is tested with a nonlinear generic electrochemical battery model. Price signals dispatch outperforms SAM's existing algorithms in cases requiring a balance between demand charge management and energy arbitrage, and in cases where battery degradation imposes a significant cost.

batteries↗

DOE OSTI2023

Hugoniot properties of porous stainless steel: Insights from molecular dynamics simulations

Here, we present a systematic study of Hugoniot properties of porous 316L stainless steel using both a simple interpolation scheme and direct shock simulations in order to probe pore collapse kinetics as well as final thermodynamic states. Both methods indicate that equilibrated Hugoniot properties depend on pore density only and not on the pore distribution or size. We then create a simple porous equation of state model that is shown to be accurate for a range of validation data. This allows us to extend our simulations to make direct comparison to experimental data that have generally significantly larger system sizes and durations. In addition, our direct shock simulations indicate that the relaxation time after hotspot formation is system size dependent and can reach nanosecond timescales for the largest pores investigated in our study, thereby possibly having a measurable effect on fast dynamic loading experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A Randomization-Based, Zero-Trust Cyberattack Detection Method for Hierarchical Systems

This paper demonstrates a novel randomization-based approach for verifying power system control signals with application to detecting cyberattacks. We consider fully connected hierarchical systems containing multiple local agents and a global "trust" agent. The global agent uses a time-varying randomized assignment scheme to identify corrupt network links based on principles of zero trust and majority rule. To evaluate the performance of this detection approach, we implement our algorithm in MATLAB and run it against nearly 43 million unique attack scenarios spanning a range of system sizes. For each scenario, the algorithm determines whether the identified corruptions satisfy a set of validity constraints reflecting network topology and uses that result to say whether the recovered state value for one or more local agents is malicious. We compare the algorithm's determination to the true state of the system to assess performance and find that classification accuracy converges to 100% as system size increases, suggesting that the validity constraints become more difficult to satisfy for larger systems. We further explore the scenarios that evade detection to understand practical implications for employing this detection approach.

cybersecurity↗

DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗

DOE OSTI2024

Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States, 2024 Edition [Slides]

Berkeley Lab’s annual Tracking the Sun report describes trends among grid-connected, distributed solar photovoltaic (PV) and paired PV+storage systems in the United States. For the purpose of this report, distributed solar includes residential systems, roof-mounted non-residential systems, and ground-mounted systems up to 5 MW-AC. Ground-mounted systems larger than 5 MW-AC are covered in Berkeley Lab’s companion annual report, Utility-Scale Solar. The latest edition of the report is based on 3.7 million systems installed through year-end 2023, representing close to 80% of systems installed to date. The report describes and discusses key trends related to: -Project characteristics, including system size, module efficiencies, roof-coverage ratios, prevalence of paired PV with storage, use of module-level power electronics, third-party ownership, mounting configurations, panel orientation, and customer segmentation -Median installed-price trends, both nationally and by state -Variability in pricing according to system size, state, installer, equipment type, and other factors, relying on both descriptive analysis and a multi-variate regression to estimate the effects of key pricing drivers for residential systems installed in 2023.

14 SOLAR ENERGY↗

DOE OSTI2023

Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States (2023 Edition) [Slides]

Berkeley Lab’s annual Tracking the Sun report describes trends among grid-connected, distributed solar photovoltaic (PV) and paired PV+storage systems in the United States. For the purpose of this report, distributed solar includes residential systems, roof-mounted non-residential systems, and ground-mounted systems up to 5 MW-AC. Ground-mounted systems larger than 5 MW-AC are covered in Berkeley Lab’s companion annual report, Utility-Scale Solar. The latest edition of the report is based on 3.2 million systems installed through year-end 2022, representing more than 80% of systems installed to date. The report describes and discusses key trends related to: -Project characteristics, including system size, module efficiencies, prevalence of paired PV with storage, use of module-level power electronics, third-party ownership, mounting configurations, panel orientation, and non-residential customer segmentation ownership -Median installed-price trends, both nationally and by state -Variability in pricing according to system size, state, installer, equipment type, and other factors, relying on both descriptive and econometric analysis The report also includes a multi-variate regression analysis to estimate the effects of key pricing drivers for residential systems installed in 2022.

14 SOLAR ENERGY↗

DOE OSTI2021

Vapor–liquid equilibrium of water with the MB-pol many-body potential

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water's solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor-liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor-liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor-liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. Furthermore, these results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol's application across a large swath of water's phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Many-Body Majorana Braiding without an Exponential Hilbert Space

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. Here, we show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.

Majorana bound states↗

DOE OSTI2024

Quantum Monte Carlo Calculations of Chemical Binding and Reactions

The auxiliary field quantum Monte Carlo method developed by the PIs has been shown to provide the most accurate description of strongly correlated electronic systems, from molecules to solids. Unlike other explicitly many‐body approaches, the quantum Monte Carlo method scales as a low order polynomial of systems size, similar to mean‐field methods such as density functional theory. However, the auxiliary field quantum Monte Carlo algorithm is significantly more expensive than traditional density functional calculations. This creates a bottleneck for applications to extended systems, such as large molecules and solids. One principal objective of this proposal was to develop new auxiliary field quantum Monte Carlo computational strategies to achieve improved scaling with system size, using downfolding and localization schemes, without sacrificing the predictive power of the calculations. A second goal is to extend the reach of auxiliary field quantum Monte Carlo to calculate excited states. This final report summarizes what has been achieved during the course the project toward these goals.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Time Evolution of Correlation Functions in Quantum Many-Body Systems

We give rigorous analytical results on the temporal behavior of two-point correlation functions—also known as dynamical response functions or Green’s functions—in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times $\langle$A ( t ) B$\rangle$ β → $\langle$ A$\rangle$ β $\langle$ B$\rangle$ β , thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For autocorrelation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values and does not increase with system size. We give numerical examples that show that this bound is a good estimate in nonintegrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Diabatic quantum annealing for the frustrated ring model

Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗