Quantum annealing (QA) is a practical model of adiabatic quantum computation, already realized on hardware and considered promising for combinatorial optimization. However, its performance is critically dependent on the annealing schedule due to hardware decoherence and noise. Designing schedules that account for such limitations remains a significant challenge. We propose a trust region Bayesian optimization (TuRBO) framework that jointly tunes annealing time and Fourier-parameterized schedules. Given a fixed embedding on a quantum processing unit (QPU), the framework employs Gaussian process surrogates with expected improvement to balance exploration and exploitation, while trust region updates refine the search around promising candidates. The framework further incorporates mechanisms to manage QPU runtime and enforce feasibility under hardware constraints efficiently. Simulation studies demonstrate that TuRBO consistently identifies schedules that outperform random and greedy search in terms of energy, feasible solution probability, and chain break fraction. These results highlight TuRBO as a resource-efficient and scalable strategy for annealing schedule design, offering improved QA performance in noisy intermediate-scale quantum regimes and extensibility to industrial optimization tasks.
Quantum annealing (QA) is a practical model of adiabatic quantum computation, already realized on hardware and considered promising for combinatorial optimization. However, its performance is critically dependent on the annealing schedule due to hardware decoherence and noise. Designing schedules that account for such limitations remains a significant challenge. We propose a trust region Bayesian optimization (TuRBO) framework that jointly tunes annealing time and Fourier-parameterized schedules. Given a fixed embedding on a quantum processing unit (QPU), the framework employs Gaussian process surrogates with expected improvement to balance exploration and exploitation, while trust region updates refine the search around promising candidates. The framework further incorporates mechanisms to manage QPU runtime and enforce feasibility under hardware constraints efficiently. Simulation studies demonstrate that TuRBO consistently identifies schedules that outperform random and greedy search in terms of energy, feasible solution probability, and chain break fraction. These results highlight TuRBO as a resource-efficient and scalable strategy for annealing schedule design, offering improved QA performance in noisy intermediate-scale quantum regimes and extensibility to industrial optimization tasks.
Quantum-enhanced constraint satisfaction problems (CSPs) offer the potential for significant speedups compared to classical approaches, particularly for large and complex CSPs. This paper investigates a novel quantum-enhanced strategy for solving CSPs, utilizing a quantum annealer to efficiently explore the solution space and identify optimal configurations. We introduce a Bayesian optimization framework tailored for this application, integrating quantum annealing to accelerate the search process and improve solution quality. The core mechanism centers on leveraging quantum annealing to identify promising regions of the search space, guided by Bayesian optimization, resulting in significantly reduced computational cost and enhanced solution accuracy. The paper details the implementation of the quantum annealer, Bayesian optimization algorithm, and the resulting performance evaluation on a benchmark CSP. The results demonstrate a substantial improvement in solution finding time and solution quality compared to classical approaches, highlighting the potential of this quantum-enhanced strategy.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Bayesian optimization has emerged as a powerful technique for tackling high-dimensional black-box optimization problems. However, its performance often degrades significantly when the dimensionality of the search space increases, a phenomenon known as the "curse of dimensionality." This paper proposes a novel approach – Quantum-Inspired Bayesian Optimization – that addresses this limitation by incorporating principles inspired by quantum computing, specifically quantum annealing. The core idea is to utilize a modified version of quantum annealing to guide the acquisition of function evaluations, exploiting superposition and interference to enhance exploration in high-dimensional spaces. We formulate the optimization problem as a quantum-inspired search, where candidate solutions exist in a superposition of states and are refined through interference effects. The algorithm iteratively updates the probability distribution over the search space, favoring regions with high potential based on the quantum-inspired exploration strategy. We demonstrate the effectiveness of this approach through theoretical analysis and illustrate its potential through conceptual examples, highlighting its ability to mitigate the curse of dimensionality and improve optimization performance compared to traditional Bayesian optimization methods. The key contributions of this work include the formalization of the quantum-inspired Bayesian optimization framework, the design of the modified quantum annealing algorithm for Bayesian optimization, and the theoretical justification for its improved exploration capabilities.
This paper presents an adaptive quantum annealing algorithm designed to improve the performance of quantum annealing in solving combinatorial optimization problems. Traditional quantum annealing relies on a fixed annealing schedule, which may not be optimal for all problems. This work introduces a novel approach that utilizes reinforcement learning to dynamically adjust the annealing parameters during the annealing process, based on the observed progress towards a solution. The algorithm learns an optimal annealing schedule by interacting with the quantum annealing system, maximizing the probability of finding a good solution within a given time limit. We demonstrate the theoretical framework and outline the core components of the adaptive algorithm, highlighting its potential advantages over conventional fixed-schedule quantum annealing. The key performance metric is the solution quality (e.g., objective function value) achieved after annealing. The algorithm's effectiveness is evaluated through conceptual analysis and design considerations. This approach aims to bridge the gap between the theoretical potential of quantum annealing and its practical application in solving real-world combinatorial optimization challenges.
This study presents a comprehensive analysis of optimization methodologies in quantum annealing (QA), investigating both theoretical frameworks and practical implementations. We examine various techniques for enhancing quantum annealing performance, including embedding strategies, parameter optimization, and hybrid quantum-classical approaches. Our research identifies critical challenges: qubit connectivity constraints, noise susceptibility, and problem representation difficulties. Through quantitative comparisons of optimization strategies across various problem classes, we establish a systematic framework for evaluating quantum annealing solutions. Results indicate that while significant challenges persist, strategic optimization approaches can substantially improve quantum annealing performance for specific problem domains, suggesting potential quantum advantage for certain complex optimization tasks.
Quantum annealing is a practical approach to execute the native instruction set of the adiabatic quantum computation model. The key of running adiabatic algorithms is to maintain a high success probability of evolving the system into the ground state of a problem-encoded Hamiltonian at the end of an annealing schedule. This is typically done by executing the adiabatic algorithm slowly to enforce adiabacity. However, properly optimized annealing schedule can accelerate the computational process. Inspired by the recent success of DeepMind's AlphaZero algorithm that can efficiently explore and find a good winning strategy from a large combinatorial search with a neural-network-assisted Monte Carlo Tree Search (MCTS), we adopt MCTS and propose a neural-network-enabled version, termed QuantumZero (QZero), to automate the design of an optimal annealing schedule in a hybrid quantum-classical framework. The flexibility of having neural networks allows us to apply transfer-learning technique to boost QZero's performance. We find both MCTS and QZero to perform very well in finding excellent annealing schedules even when the annealing time is short in the 3-SAT examples we consider in this study. We also find MCTS and QZero to be more efficient than many other leading reinforcement leanring algorithms for the task of desining annealing schedules. In particular, if there is a need to solve a large set of similar problems using a quantum annealer, QZero is the method of choice when the neural networks are first pre-trained with examples solved in the past.