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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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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↗
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↗
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↗
DOE OSTI2023

Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm

We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depth p required for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOA p ≤ 11 does not scale with N. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

A large-scale benchmarking of deterministic and stochastic derivative-free optimization algorithms

This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.

36 MATERIALS SCIENCE↗
DOE OSTI2025

End-to-end protocol for high-quality quantum approximate optimization algorithm parameters with few shots

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance, QAOA performance depends crucially on the choice of the parameters. While average-case optimal parameters are available in many cases, meaningful performance gains can be obtained by fine-tuning these parameters for a given instance. This task is especially challenging, however, when the number of circuit executions (shots) is limited. In this work, we develop an end-to-end protocol that combines multiple parameter settings and fine-tuning techniques. We use large-scale numerical experiments to optimize the protocol for the shot-limited setting and observe that optimizers with the simplest internal model (linear) perform best. We implement the optimized pipeline on a trapped-ion processor using up to 32 qubits and 5 QAOA layers, and we demonstrate that the pipeline is robust to small amounts of hardware noise. To the best of our knowledge, these are the largest demonstrations of QAOA parameter fine-tuning on a trapped-ion processor in terms of two-qubit gate count.

quantum algorithms & computation↗
DOE OSTI2025

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Chapter 6: Surrogate Model Guided Optimization Algorithms and Their Potential Use in Autonomous Experimentation

This chapter reviews the basics of derivative-free optimization methods based on surrogate models and outlines how these methods can straightforwardly be applied to autonomously steering experimentation. It summarizes general solution approaches that use surrogate models and active learning. Surrogate modeling is often combined with active learning strategies, where in each iteration of the optimization algorithm, the surrogate model is used to identify which new inputs should be evaluated next and given the new input-output pair, the surrogate model is updated. Regardless of feasibility, the surrogate models for the constraints are updated in each iteration of the optimization algorithm, while the surrogate model for the objective function is only updated when a feasible point has been found. Similarly to the case of computationally cheap constraints, the surrogate models of the constraints should be incorporated into the definition of the auxiliary optimization problem that is solved to select new sample points.

active learning↗
DOE OSTI2026

Distributed quantum approximate optimization algorithm on a quantum-centric supercomputing architecture

Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for high-dimensional problems due to the large number of qubits required and the complexity of deep circuits, limiting its scalability for real-world applications. In this study, we present a distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than are necessary to solve the original problem. These sub-problems are processed using a combination of high-performance and quantum computing resources. The global solution is iteratively updated by aggregating sub-solutions, allowing convergence toward the optimal solution. We demonstrate that DQAOA can handle considerably large-scale optimization problems (e.g., 1000-bit problem), achieving a high solution quality and short time-to-solution, outperforming existing strategies. Furthermore, we realize DQAOA on a quantum-centric supercomputing architecture, paving the way for practical applications of gate-based quantum computers in real-world optimization tasks. To extend DQAOA’s applicability to materials science, we further develop an active learning algorithm integrated with our DQAOA (AL-DQAOA), which involves machine learning, DQAOA, and active data production in an iterative loop. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible. We expect the proposed DQAOA to be applicable to a wide range of optimization problems and AL-DQAOA to find broader applications in material design.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗
DOE OSTI2025

Simulations of Quantum Approximate Optimization Algorithm on HPC-QC Integrated Systems

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗