Hybrid quantum-classical algorithms for quantum optimal control
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Magann, Alicia Bette [Sandia National Laboratories↗
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A Constrained Data Assimilation Algorithm Based on GSI Hybrid 3D-EnVar and Its Application
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54 ENVIRONMENTAL SCIENCES↗
Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
Models of interacting many-body quantum systems that may realize new exotic phases of matter, notably quantum spin liquids, are challenging to study using even state-of-the-art classical methods such as tensor network simulations. Quantum computing provides a promising route for overcoming these difficulties to find ground states, dynamics, and more. In this paper, we argue that recently developed hybrid quantum-classical algorithms based on real-time evolution are promising methods for solving a particularly important model in the search for spin liquids, the antiferromagnetic Heisenberg model on the two-dimensional kagome lattice. We show how to construct efficient quantum circuits to implement time evolution for the model and to evaluate key observables on the quantum computer, and we argue that the method has favorable scaling with increasing system size. We then restrict to a 12-spin star plaquette from the kagome lattice and a related 8-spin system, and we give an empirical demonstration on these small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve. For these demonstrations, we use four levels of approximation: exact state vectors, exact state vectors with statistical noise from sampling, noisy classical emulators, and (for the 8-spin system only) real quantum hardware, specifically the Quantinuum H1-1 processor; for the noisy simulations and hardware demonstration, we also employ error mitigation strategies based on the symmetries of the Hamiltonian. Our results strongly suggest that these hybrid algorithms present a promising direction for studying quantum spin liquids and more generally for resolving important unsolved problems in condensed matter theory and beyond.
97 MATHEMATICS AND COMPUTING↗
Quantum Local Search with the Quantum Alternating Operator Ansatz
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erdős-Rényi graphs with up to 100 nodes.
Tomesh, Teague↗
Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition
High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. Here this algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.
97 MATHEMATICS AND COMPUTING↗
FORCE Development Status Update: Vertical Integration and Benchmarking of System Dynamics
Recent efforts to establish effective models for grid energy analysis, especially given the increase in variable renewable energy (VRE) sources and the economic challenges faced by traditional nuclear energy, have generated new technological considerations. One effort to improve the economic viability of nuclear power involves investigating integrated energy systems (IES) which include secondary energy systems that introduce flexibility and secondary market possibilities to existing and perceived future nuclear energy generation technologies. To analyze the technical and economic potential of IES, the Framework for Optimization of Resources and Economics (FORCE) tool suite was developed through a collaboration among national laboratories. Within the FORCE tool suite, the Holistic Energy Resource Optimization Network (HERON) provides algorithms for analyzing the long-term viability of potential IES technologies, while HYBRID provides algorithms and models to achieve high-resolution analysis of coupling physics over a short time period. Continued maturing of the FORCE tool suite requires further interconnections between the various tools in the suite in order to ensure consistent analysis. Analyses performed by applying HYBRID to transient process modeling should be easily harvestable as inputs to HERON analyses. The first item in this status update is a demonstration of an automated data pipeline for loading data from HYBRID into HERON analyses. Application of HYBRID results to HERON, as part of using the FORCE tool suite, relies on robust modeling assumptions for the various models included in HYBRID. The second result of this status update is the benchmarking and validation of cost and operational data, with a particular focus on natural gas energy generators. These generators are benchmarked with a focus on contrasting them with proposed thermal energy storage (TES) technologies.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost .
Tomesh, Teague↗
Digital Twin Based Condition Monitoring of LCC-LCC Inductive Power Transfer Systems
Inductive power transfer (IPT) systems provide a flexible, hands-free charging opportunity to electric vehicles (EV). The resonant network components and the transmitter and receiver coils are often subjected to high voltages or currents. Component aging in the compensation network and coils of resonant IPT systems is detrimental to the reliability and power transfer efficiency of the IPT system. Monitoring the component health of such multi-element complex systems requires robust optimization algorithms. This paper discusses condition monitoring of a resonant IPT system for an EV charger using a digital twin model. A hybrid estimation algorithm based on genetic algorithms and adaptive particle swarm optimization is developed to estimate the parameters of the digital twin model. Simulation results are used to verify the monitoring capabilities of the developed algorithm under various operating conditions of the IPT system.
Weldehawaryat, Lidya Mussie [graduate research ass↗
Dynamic Asset Allocation with Expected Shortfall via Quantum Annealing
Recent advances in quantum hardware offer new approaches to solve various optimization problems that can be computationally expensive when classical algorithms are employed. We propose a hybrid quantum-classical algorithm to solve a dynamic asset allocation problem where a target return and a target risk metric (expected shortfall) are specified. We propose an iterative algorithm that treats the target return as a constraint in a Markowitz portfolio optimization model, and dynamically adjusts the target return to satisfy the targeted expected shortfall. The Markowitz optimization is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The use of the expected shortfall risk metric enables the modeling of extreme market events. We compare the results from D-Wave’s 2000Q and Advantage quantum annealers using real-world financial data. Both quantum annealers are able to generate portfolios with more than 80% of the return of the classical optimal solutions, while satisfying the expected shortfall. We observe that experiments on assets with higher correlations tend to perform better, which may help to design practical quantum applications in the near term.
97 MATHEMATICS AND COMPUTING↗
Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.
97 MATHEMATICS AND COMPUTING↗
Optimizing the physical design and layout of a resilient wind, solar, and storage hybrid power plant
We report as wind and solar technologies improve and their costs decrease, the share of power produced by these sources will increase. As the market penetration increases, these power sources will need to provide grid services, such as dispatchability, in addition to providing energy. One way to reduce variability, provide higher quality power to the grid, and address local grid stability issues is through colocating wind and solar power plants. In addition to operating reliably during normal operating conditions, in scenarios with high penetrations of renewable generation, it is important that these hybrid plants can withstand production disruptions and continue to supply power despite prolonged resource reduction, extreme weather events, or other disruptions. In this paper, we present a methodology to optimize a wind-solar-battery hybrid power plant down to the component level that is resilient against production disruptions and that can continually produce some minimum required power. We introduce the models and assumptions we used to simulate a hybrid power plant as well as the design variable parameterization and specific methods we used to optimize the plant. We demonstrate the performance of our method by comparing a plant optimized for different objectives, generation outage durations, minimum power requirements, and power purchase agreements. Although the plant design is sensitive to model parameters and various other assumptions, our results demonstrate some of the optimal designs that occur in different scenarios and what one should expect when designing a hybrid wind-solar-storage power plant.
14 SOLAR ENERGY↗
Simulating strongly correlated molecules with a superconducting quantum processor
Many of the biggest challenges in expanding the nation’s access to clean and low-cost energy resources are fundamentally chemistry or materials challenges. An important case is the development of new catalysts for the up-conversion of cheap and readily available materials such as methane or water into materials suitable for use as a fuel such as methanol or oxygen. To understand and exploit such processes, computer simulations of chemical reactions provide a natural complement to experimental studies. Unfortunately, most catalytic reactions involve so-called “strongly correlated” molecules which are notoriously difficult to study with simulation algorithms that can be executed on existing (classical) computers. The recent growth in quantum information science offers an alternative potential route for simulating these difficult systems. As a result, an increasing number of computational chemists are becoming interested in quantum computing. At the same time, quantum information scientists have identified chemistry simulation as a possible first demonstration of a quantum computer providing an improvement over a classical computer. The objective of this project is to accurately simulate strongly correlated molecules on a quantum processor. To meet the high challenges of this objective, new hybrid quantum/classical algorithms will be co-designed with advanced quantum gate developments and computed on customized quantum hardware. Some of the developed techniques will be transferable to study other molecular systems, while the project as a whole will help define better strategies for advancing the quantum simulation of matter more generally.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations
We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-X operations and all-to-all Ising Hamiltonian HIsing evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all HIsing pulses, we show that for a (1−ϵ) factor loss in the Max-Cut approximation (ϵ>0), our compilations improve the (worst-case) number of HIsing pulses from O(n2) to O(nlog(n/ϵ)) and the (worst-case) number of Pauli-X bit flips from O(n2) to O(nlog(n/ϵ)ϵ2) for n-node graphs. This is an asymptotic improvement for any constant ϵ>0. We demonstrate that significant improvements to the approximation ratio are obtained using decomposition in simulated trapped-ion experiments with dephasing noise. We further present a generic argument showing that sparsification results in an exponentially improved circuit fidelity lower bound in digital computing schemes based on one- and two-qubit gates, which are relevant to a wide variety of hardwares such as superconducting qubits and certain neutral atom or trapped ion setups, and more sophisticated noise models. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.
Moondra, Jai [Georgia Institute of Technology]↗
Arbitrage and Capacity Firming in Coordination with Day-Ahead Bidding of a Hybrid PV Plant: Preprint
A hybrid PV plant (HPP) combines a photovoltaic (PV) plant with a battery energy storage system (BESS), which is considered a promising step towards the future of renewable power plants by the U.S. Department of Energy. When the renewable penetration reaches a significant level, a hybrid PV plant can bid in as a controllable thermal plant in the future electricity market. In this study, a bidding and BESS scheduling model is proposed for the HPP. The robust optimization (RO) technique has been utilized to identify the worst-case scenario of uncertainties during the bidding process. To address the overly conservative issue of the single-stage RO, we have decoupled the BESS schedule for arbitrage and PV capacity firming by a two-stage RO formulation. By comparing the output of single-stage RO and two-stage RO, the two-stage RO bids and schedules in a more aggressive manner, which increases the income of HPP. Also, the penalty of under-generation is considered in our model so that the day-ahead bidding decision and arbitrage schedules can be adjusted based on the potential UNDER-GENERATION penalty. Because the proposed model is non-convex and contains multi-stages, the Column-and-Constraint Generation (C&CG) algorithm is applied to the model as the solution. The proposed model has shown better economic performance compared to a state-of-art single-stage bidding method in case studies.
BESS scheduling↗
A Cartesian-diffusion Langevin method for hybrid kinetic-fluid Coulomb scattering in particle-in-cell plasma simulations
A novel, drag-diffusion Langevin method of hybrid, kinetic-fluid Coulomb scattering in plasmas is presented. Unlike previous methods, the frictional drag is always applied in the simulation frame of reference. The velocity-space diffusion is performed in the stationary-fluid frame of reference when anisotropic, and in the laboratory frame when isotropic. While the general method is mass-ratio independent, we focus on interactions of kinetic-ions and fluid-electrons to show first-order modifications to the electron velocity distribution function that are an important correction for the accurate calculation of electric resistivity. Inclusion of sub-cycling and a limit to the maximum collision frequency is shown to allow for arbitrarily large timesteps without numerical failure. Here the Langevin method is compared with a grid-based binary method and found to require a much less restrictive timestep in cases of ion–electron slowing and temperature equilibration; this finding differs from previous work and is dependent on the mass ratio.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Hybrid simulation of energetic particles interacting with magnetohydrodynamics using a slow manifold algorithm and GPU acceleration
The hybrid method combining particle-in-cell and magnetohydrodynamics can be used to study the interaction between energetic particles and global plasma modes. In this paper we introduce the M3D-C1-K code, which is developed based on the M3D-C1 finite element code solving the magnetohydrodynamics equations, with a newly developed kinetic module simulating energetic particles. The particle pushing is done using a new algorithm by applying the Boris pusher to the classical Pauli particles to simulate the slow-manifold of particle orbits, with long-term accuracy and fidelity. The particle pushing can be accelerated using GPUs with a significant speedup. The moments of the particles are calculated using the δƒ method, and are coupled into the magnetohydrodynamics simulation through pressure or current coupling schemes. Several linear simulations of magnetohydrodynamics modes driven by energetic particles have been conducted using M3D-C1-K with the δƒ method, including fishbone, toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes. Good agreement with previous results from other eigenvalue, kinetic and hybrid codes have been achieved.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.
Deflation↗