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. 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. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0578 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0578 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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. 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. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0578 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0578 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Y. Ha and S. Shashaani also gratefully acknowledge the U.S. National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation Grant CMMI-2226347 and the U.S. Office of Naval Research [Grant N000142412398]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0575 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0575 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
In the field of robotics, optimization problems with high computational costs, such as motion planning, multi-robot cooperation, and manipulation, are constrained by the exponential growth of the complexity of classical algorithms. This paper discusses practical methods for robot optimization, specifically using noise-aware variational quantum algorithms (VQAs) on current noisy intermediate-scale quantum hardware. To address the inherent errors of quantum devices, a specific framework has been proposed. The framework clearly defines noise modeling, adjusts error mitigation methods, and creates quantum-classical workflows. Using actual quantum computers and high-fidelity simulations, this paper will systematically evaluate four benchmark robotic domains. The statistical data from numerous experiments (up to 100 trials per scenario) indicate that, in the presence of significant hardware noise, noise-aware VQAs can improve the target value by up to 14% compared to standard quantum methods and reduce the number of convergence iterations by 45%. Cross-platform tests indicate that all six robotic tasks run stably, with an accuracy rate exceeding 90% for all devices. In real-world environments, this trajectory generation method performs excellently under noisy conditions when using physical robots. In order to ensure the accuracy of quantum accelerated optimization in robotics, it is necessary to reduce noise. According to the aforementioned research, reducing noise can be practically applied outside of laboratory conditions.
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on noise characterization, mitigation, and suppression. Crucially, these methods must also be efficient in terms of their classical and quantum overhead. Here, we efficiently characterize and mitigate crosstalk noise, which is a severe error source in, for example, cross-resonance based superconducting quantum processors. For crosstalk characterization, we develop a simplified measurement experiment. Furthermore, we analyze the problem of optimal experiment scheduling and solve it for common hardware architectures. After characterization, we mitigate noise in quantum circuits by a noise-aware qubit routing algorithm. Our integer programming algorithm extends previous work on optimized qubit routing by swap insertion. We incorporate the measured crosstalk errors in addition to other, more easily accessible noise data in the objective function. Furthermore, we strengthen the underlying integer linear model by proving a convex hull result about an associated class of polytopes, which has applications beyond this work. We evaluate the proposed method by characterizing crosstalk noise for two chips with up to 127 qubits and leverage the resulting data to improve the approximation ratio of the Quantum Approximate Optimization Algorithm by up to 10% compared with other established noise-aware routing methods. Our work clearly demonstrates the gains of including noise data when mapping abstract quantum circuits to hardware native ones. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue on Quantum Computing. Funding: This work was supported by Bavarian state government; Bayerische Staatsministerium für Wirtschaft, Landesentwicklung und Energie. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0551 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0551 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.
The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.
In this thesis, we develop, analyze, and implement effective and efficient methods for constrained stochastic and derivative-free optimization. For each method, we prove the convergence result under general assumptions. We also conduct numerical experiments to demonstrate the efficiency and efficacy of our proposed methods. In Chapter 2, we develop a model-based derivative-free optimization method. A key component of variational quantum algorithms (VQAs) is the choice of a classical optimizer to update the ansatz parameterization. Quantum algorithms, however, are destined to run on noisy hardware with limited fidelity, leading to objective function evaluations–such as those in the quantum approximate optimization algorithm (QAOA) or the variational quantum eigensolver (VQE)–that are compromised by both stochastic errors and hardware-induced noise. To address these challenges, 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. 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. Moreover, we propose a series of sequential quadratic programming (SQP) methods tailored for stochastic equality constrained optimization. In Chapter 3, we develop a stochastic method for solving equality constrained problems that utilizes predictive variance reduction within the SQP paradigm, and prove that a measure of first-order stationarity converges to zero in expectation under reasonable assumptions, with practical performance demonstrated on constrained binary classification problems. In Chapter 4, we propose a line search SQP method for general nonlinear equality constrained optimization that employs a modified line search strategy using second-order information to mitigate the Maratos effect, thereby achieving global convergence and local superlinear convergence. We further extend this approach to settings where the objective function is stochastic or represented as a finite sum, and design a practical inexact matrix-free variant and demonstrate the numerical performance empirically. Finally, in Chapter 5, we propose, analyze, and implement an SQP algorithm for minimizing a nonlinear smooth function subject to smooth equality constraints with noisy function and derivative estimates, addressing the challenges posed by bounded noise in the objective and constraint functions as well as potential rank-deficiency in the constraint Jacobians. This algorithm employs a decomposition approach to compute inexact search directions and utilizes adaptive step size selection schemes, which guarantee global convergence of infeasible stationarity error to a neighborhood of zero that is proportional to the noise level.