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At least 19 records

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers

Classical optimization with imaginary-time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. Here, we develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Zhong, Dawei [University of Southern California, L

A Multilevel Approach For SolvingLarge-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one ofthe promising candidates for useful quantum computation,particularly in the context of finding approximate solutionsto Quadratic Unconstrained Binary Optimization (QUBO)problems. However, the existing quantum processing units(QPUs) are of relatively small size, and canonical mappingsof QUBO via the Ising model require one qubit per vari-able, rendering direct large-scale optimization infeasible.In classical optimization, a general strategy for addressingmany large-scale problems is via multilevel/multigrid meth-ods, where the large target problem is iteratively coarsenedand the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentallytest how existing QPUs perform when used as a sub-solverwithin such a multilevel strategy. To this aim, we com-bine and extend (via additional classical processing steps)the recently proposed Noise-Directed Adaptive Remapping(NDAR) and Quantum Relax&Round (QRR) algorithms.We first demonstrate the effectiveness of our heuristicextensions on Rigetti’s superconducting transmon deviceAnkaa-2. We find approximate solutions to10instances offully connected82-qubit Sherrington-Kirkpatrick graphswith random integer-valued coefficients obtaining normal-ized approximation ratios (ARs) in the range∼0.98−1.0,and the same class with real-valued coefficients (ARs∼0.94−1.0). Then, we implement the extended NDAR andQRR algorithms as subsolvers in the multilevel algorithmfor6large-scale graphs with at most∼27,000variables.In practice, the QPU (with classical post-processing steps)is used to find approximate solutions to dozens of at most82-qubit problems, which are iteratively used to constructthe global solution. We observe that quantum optimizationresults are competitive in terms of the quality of solutionswhen compared to classical heuristics used as subsolverswithin the multilevel approach.Reproducibility: source code and data are available at[TBA upon acceptance]

quantum computing

Feedback-based quantum algorithms for ground state preparation

The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024

Larsen, James B. (ORCID:000000020777440X)

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

The suitability of selected multidisciplinary design and optimization techniques to conceptual aerospace vehicle design

Four methods for preliminary aerospace vehicle design are reviewed. The first three methods (classical optimization, system decomposition, and system sensitivity analysis (SSA)) employ numerical optimization techniques and numerical gradients to feed back changes in the design variables. The optimum solution is determined by stepping through a series of designs toward a final solution. Of these three, SSA is argued to be the most applicable to a large-scale highly coupled vehicle design where an accurate minimum of an objective function is required. With SSA, several tasks can be performed in parallel. The techniques of classical optimization and decomposition can be included in SSA, resulting in a very powerful design method. The Taguchi method is more of a 'smart' parametric design method that analyzes variable trends and interactions over designer specified ranges with a minimum of experimental analysis runs. Its advantages are its relative ease of use, ability to handle discrete variables, and ability to characterize the entire design space with a minimum of analysis runs.

Olds, John R.

Quantum annealing for combinatorial optimization: a benchmarking study

Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.

97 MATHEMATICS AND COMPUTING

Transonic Flutter Suppression Control Law Design Using Classical and Optimal Techniques with Wind-Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek

Transonic Flutter Suppression Control Law Design Using Classical and Optimal Techniques with Wind-Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf. The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed.

Mukhopadhyay, Vivek

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo

Surrogate Optimization for Quantum Circuits

Variational quantum Eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has yet to be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods to improve the convergence is essential to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to classical circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the presence of quantum circuit shot noise by a factor of 2-4

quantum computing

A Review of Quantum Computing Technologies in Power System Optimization

As modern power grids increasingly integrate variable renewable generation, distributed energy resources, and energy storage systems, classical optimization techniques are facing unprecedented challenges. This review examines the emerging application of quantum computing to overcome these challenges in power system optimization, including optimal power flow (OPF), unit commitment (UC), economic dispatch (ED), and intelligent switching and topology optimization (IS-TO). Recent research has introduced various quantum methodologies—such as gate-based, annealing-based, variational algorithms, and quantum-inspired algorithms—to address the combinatorial complexity inherent in grid reconfiguration and energy management. The review summaries the quantum algorithms, quantum devices and the power system test cases, highlighting hybrid quantum–classical strategies that leverage the complementary strengths of both paradigms. Some quantum advantages have been observed, including theoretical speedup, accurate simulation results, scalable qubit usage, efficient QUBO mapping. In particular, the review emphasizes the importance of integrating quantum optimization techniques with classical control frameworks, these hybrid approaches demonstrate the potential to improve real-time grid management and operational reliability. A significant portion of the analysis is devoted to the practical limitations of current quantum devices. Present-day quantum hardware, operating in the noisy intermediate-scale quantum (NISQ) era, remains highly sensitive to noise and limited in qubit connectivity, which constrains the scale and accuracy of implemented algorithms. The review delves into specific challenges such as the need for qubit-efficient encoding techniques and error mitigation strategies that are critical for handling real-world grid optimization problems. In addition, the work draws attention to the performance discrepancies between theoretical quantum speedups and experimental validations, underscoring the importance of rigorous benchmark studies using representative power grid test cases. In summary, this review highlights both the promise and limitations of quantum computing for power system optimization. It provides a comprehensive overview of the state-of-the-art technologies, categorizes recent advancements in algorithm design, and discusses practical considerations for implementation, and serves as an informative resource on current research. Future research directions include developing robust hybrid frameworks, advancing qubit-efficient formulations, and scaling up experimental demonstrations to confirm the theoretical advantages of quantum methods in large-scale power system operations.

24 POWER TRANSMISSION AND DISTRIBUTION

Q-OPT:Quantum Optimization Toolkit

SF-2025-003 Quantum computing has the potential to solve classical optimization problems. To bring these algorithms into practical use, a comprehensive, high-performance and user-friendly toolkit is essential. The Q-OPT: Quantum Optimization Toolkit is a collection of software tools designed to support complete end-to-end framework for quantum optimization.

Hovland, Paul [Argonne National Laboratory (ANL),

Surrogate optimization of variational quantum circuits

Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has not yet been realized, with few claims of quantum advantage and high resource estimates, especially due to the need for optimization in the presence of noise. Finding algorithms and methods to improve convergence is important to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal, we look to use modern approaches developed in circuit simulations and stochastic classical optimization, which can be combined to form a surrogate optimization approach to quantum circuits. Using an approximate (classical CPU/GPU) state vector simulator as a surrogate model, we efficiently calculate an approximate Hessian, passed as an input for a quantum processing unit or exact circuit simulator. This method will lend itself well to parallelization across quantum processing units. We demonstrate the capabilities of such an approach with and without sampling noise and a proof-of-principle demonstration on a quantum processing unit utilizing 40 qubits.

Gustafson, Erik J. [RIACS, Mtn. View] (ORCID:00000

Quantum Computing in Next-Generation Transportation Optimization

We explore how quantum computing (QC) can advance transportation optimization, with a focus on two high-impact areas: traffic signal control and vehicle electrification with grid integration. As transportation systems grow in complexity, classical optimization methods increasingly struggle to deliver scalable and efficient solutions, particularly for real-time, data-rich environments. This work identifies key challenges within these two domains where QC may offer advantages, particularly in handling combinatorial decision spaces and dynamic constraints. We begin by outlining the limitations of classical approaches for traffic signal control optimization and electric vehicle charging coordination, highlighting where computational limitations arise. Previous quantum formulations are presented and new formulations are proposed to demonstrate how emerging quantum algorithms, including quantum annealing and the Quantum Approximation Optimization Algorithm, could be leveraged to reformulate and address these problems. We also evaluate the suitability of current quantum hardware and discuss recent trends that indicate when QC may become a viable tool for transportation applications. While acknowledging the present limitations of QC technologies, this poster emphasizes the importance of preparing quantum-compatible models today. By reviewing and establishing formulations that align with the strengths of quantum algorithms, researchers and practitioners can better position themselves to take advantage of QC advancements as they occur. This work aims to provide a practical, forward-looking perspective on the near-term potential of quantum computing in transportation optimization.

33 ADVANCED PROPULSION SYSTEMS

Enhanced Power Grid Maintenance Planning and Quantum-Inspired Combinatorial Prospects

Efficient and reliable scheduling of maintenance for power generation and transmission infrastructure is essential for minimizing operational costs and ensuring grid stability. This paper introduces an integrated optimization framework for coordinated maintenance scheduling of generators and transmission lines under resource and reliability constraints. The model minimizes a composite cost function including maintenance and generation costs, as well as penalties for delayed maintenance, while satisfying N−1 security constraints, operational limits, and crew availability. Case studies on the IEEE 300-bus test system demonstrate the effectiveness of the proposed approach in producing feasible and cost-effective maintenance schedules. To address scalability and combinatorial complexity, the model is mapped into a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling exploration of solution approaches based on Quantum Imaginary Time Evolution (QITE). While the QUBO reformulation provides a foundation for future quantum-inspired optimization, this study focuses primarily on the development and demonstration of the classical optimization framework and illustrates the potential applicability of QITE in large-scale maintenance scheduling.

Chen, Yang [ORNL] (ORCID:0000000271693874)

Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

Aldrich, Jack B.