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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N -qubit product state | 0 〉 ⊗ N and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

Dupont, Maxime↗
DOE OSTI2024

Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. Here, we establish communication lower bounds that determine how much data movement is required (under mild conditions) to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that, with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations when the input and output tensors vary greatly in size.

HBL-inequalities↗
DOE OSTI2022

A nonsmooth nonconvex optimization algorithm for two-stage optimization problems

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Bayesian optimization algorithms for accelerator physics

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques toward solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Algorithmic optimization of quantum optical storage in solids

Quantum memory devices with high storage efficiency and bandwidth are essential elements for future quantum networks. Solid-state quantum memories can provide broadband storage, but they primarily suffer from low storage efficiency. We use passive optimization and algorithmic optimization techniques to demonstrate nearly a sixfold enhancement in quantum memory efficiency. In this regime, we demonstrate coherent and single-photon-level storage with a high signal-to-noise ratio. The optimization technique presented here can be applied to most solid-state quantum memories to significantly improve the storage efficiency without compromising the memory bandwidth. Published by the American Physical Society 2024

Lei, Yisheng↗
NASA NTRS1980

Solar collector parameter identification from unsteady data by a discrete-gradient optimization algorithm

A discrete-gradient optimization algorithm is used to identify the parameters in a one-node and a two-node capacitance model of a flat-plate collector. Collector parameters are first obtained by a linear-least-squares fit to steady state data. These parameters, together with the collector heat capacitances, are then determined from unsteady data by use of the discrete-gradient optimization algorithm with less than 10 percent deviation from the steady state determination. All data were obtained in the indoor solar simulator at the NASA Lewis Research Center.

Hotchkiss, G. B.↗
DOE OSTI2025

Quantifying the impact of precision errors on quantum approximate optimization algorithms

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm that seeks to achieve approximate solutions to optimization problems by iteratively alternating between intervals of controlled quantum evolution. Here, we examine the effect of analog precision errors on QAOA performance from the perspective of both algorithmic training and performance guarantees. Leveraging cumulant expansions, we recast the faulty QAOA as a control problem in which precision errors are expressed as multiplicative control noise and derive bounds on the performance of QAOA. We show using both analytical techniques and numerical simulations that fixed precision implementations of QAOA circuits are subject to an exponential degradation in performance dependent upon the number of optimal QAOA layers and magnitude of the precision error. Despite this significant reduction, we show that it is possible to mitigate precision errors in QAOA via digitization of the variational parameters at the cost of increasing circuit depth.

quantum algorithms↗
DOE OSTI2022

Multi-angle quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Optimization Algorithms as Quantum Performance Benchmarks

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) have the potential to demonstrate significant run-time performance benefits over current state-of-the-art solutions. Using existing methods for characterizing classical optimization algorithms, we analyze solution quality obtained by solving Max-Cut problems using a quantum annealing device and gate-model quantum simulators and devices. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through effective visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. The framework is an enhancement to the existing open-source QED-C Application-Oriented Benchmark suite and can connect to the open-source analysis libraries. The suite can be executed on various quantum simulators and quantum hardware systems.

benchmarking↗
NASA NTRSDate not supplied

Investigation of a Smooth Local Correlation-based Transition Model in a Discrete-Adjoint Aerodynamic Shape Optimization Algorithm

A smooth local correlation-based transition model is fully coupled to a RANS-based Newton-Krylov flow solver and discrete-adjoint gradient-based optimization algorithm. The free-transition optimization framework is evaluated using lift-constrained drag minimizations of airfoils at design conditions ranging from light to single-aisle aircraft and an infinite swept wing at design conditions representative of a transonic strut-braced wing aircraft. The impact of the streamwise grid resolution on the ability of the optimization algorithm to delay boundary-layer transition is investigated, with the results demonstrating that streamwise grid resolution requirements increase as the transition length decreases with increasing Reynolds number. The optimization problem at the light aircraft design conditions is demonstrated to be multi-modal, with the optimization algorithm producing two distinct designs: one with a thin, reflexed trailing edge and steep pressure recovery regions, the other with increased aft loading, with the latter design outperforming the former. A drag minimization of an airfoil at transonic design conditions demonstrates that the optimization algorithm successfully trades a decrease in viscous drag by delaying boundary-layer transition with an increase in wave drag, while the drag minimization of an infinite swept wing demonstrates the capability of the optimizational gorithm to delay both Tollmien-Schlichting and stationary crossflow instabilities.

AATT↗
NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
NASA NTRS1998

Bell-Curve Based Evolutionary Optimization Algorithm

The paper presents an optimization algorithm that falls in the category of genetic, or evolutionary algorithms. While the bit exchange is the basis of most of the Genetic Algorithms (GA) in research and applications in America, some alternatives, also in the category of evolutionary algorithms, but use a direct, geometrical approach have gained popularity in Europe and Asia. The Bell-Curve Based Evolutionary Algorithm (BCB) is in this alternative category and is distinguished by the use of a combination of n-dimensional geometry and the normal distribution, the bell-curve, in the generation of the offspring. The tool for creating a child is a geometrical construct comprising a line connecting two parents and a weighted point on that line. The point that defines the child deviates from the weighted point in two directions: parallel and orthogonal to the connecting line, the deviation in each direction obeying a probabilistic distribution. Tests showed satisfactory performance of BCB. The principal advantage of BCB is its controllability via the normal distribution parameters and the geometrical construct variables.

Sobieszczanski-Sobieski, J.↗
NASA NTRS2021

Thermal Conductivity Estimation from Transient Test Data with Embedded Thermocouples using Genetic Algorithm Optimization

Inverse heat transfer methodology previously developed to estimate thermal properties of high temperature fibrous insulation from embedded thermocouples was applied to the thermoplastic polymer, polyether-ether-ketone (PEEK). A small experimental setup was utilized to test the PEEK sample between temperatures of 300 K and 525 K at atmospheric pressure. Cylindrical plugs of PEEK with three thermocouples embedded at various depths were incorporated in the test sample. The experimental PEEK thermocouple data were used as the boundary and initial conditions of a one-dimensional numerical thermal model to predict the internal temperatures of the material. The thermal conductivity of PEEK was estimated with the Continuous Genetic Algorithm optimization technique by searching for the coefficients of a functional form of thermal conductivity that minimized the difference between the experimentally measured and model predicted internal temperature values. The thermal testing, one-dimensional numerical thermal model, optimization algorithm, analysis, and results are presented.

Thermal Properties↗
DOE OSTI2025

Quantum Approximate Optimization Algorithm on Different Qubit Systems

Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗
DOE OSTI2023

Resilient Design of Continuous-time Distributed Optimization Algorithm in the Presence of Cyber-attacks

This paper presents a continuous-time resilient distributed optimization algorithm based on competitive interaction design method on connected graphs in the presence of adversaries. Here, the competitive interaction method allows us to design a network that protects the multi-agent systems from adversaries without requiring high network connectivity. In addition, the proposed algorithm does not require the global information about the number of adversaries. First, we show that the proposed distributed algorithm solves the resilient distributed optimization problem with no attack on the communication links. Second, we show that the proposed continuous-time distributed optimization algorithm on connected graphs converges to the small neighborhood of the optimal solution in the presence of cyber-attacks onto the communication channel. Simulations are presented to illustrate our theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Plunkett, C. L.↗