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Quantum Annealing Algorithm Optimization and Application

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as $H(t)$, where $t$ represents time. The objective function to be minimized is typically represented as $E[s]$, where $s$ is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as $\sigma(t)$, which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: $\min_{s} E[s] \quad \text{subject to} \quad \frac{dS}{dt} = - \beta(t) E[s] - \gamma(t) H(t)s$ where $\beta(t)$ is the annealing rate and $\gamma(t)$ is the magnetic field strength. The adaptive strategy involves updating $\beta(t)$ and $\gamma(t)$ based on the error in the current solution, aiming to reduce the variance $\sigma(t)$ and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.

DOI
10.5281/zenodo.22272188

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This paper presents an Adaptive Quantum Annealing Optimization Algorithm (AQAO) designed to address the limitations of traditional quantum annealing approaches in tackling complex, non-convex optimization problems. The core of the AQAO lies in its dynamic analysis of the objective function's energy landscape and the subsequent adaptive adjustment of annealing parameters. Unlike conventional quantum annealing, which often employs fixed parameters, the AQAO continuously monitors the quantum annealing process and adjusts parameters such as the annealing rate and jump probability based on real-time changes in the energy landscape. This adaptive mechanism aims to accelerate convergence towards optimal solutions by effectively responding to the evolving complexities of the optimization problem. The algorithm leverages the inherent search capabilities of quantum annealing while mitigating the issues of slow convergence or failure to find global optima frequently encountered with static parameter settings. The theoretical framework and algorithmic design are presented, emphasizing the key improvements and potential advantages of the AQAO compared to existing methods. The focus is on the adaptive control strategy, providing a robust approach to complex optimization challenges.
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Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.