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arXiv 2406.07124cs.AIcs.LG
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CHARME:一种基于链式强化学习的 minor 嵌入问题求解方法

CHARME: A chain-based reinforcement learning approach for the minor embedding problem

Department of Computer and Information Science and Engineering, University of Florida(计算机与信息科学与工程系,佛罗里达大学);Theoritical Division, Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室理论部)

Hoang M. Ngo, Nguyen H K. Do, Minh N. Vu, Tre' R. Jeter, Tamer Kahveci, My T. Thai

AI总结:

针对量子退火中minor嵌入这一NP难问题的可扩展性瓶颈,提出含GNN策略、状态转移算法和顺序探索策略的强化学习框架CHARME,在量子比特使用率上优于多种现有嵌入方法并提升训练效率。

摘要:

量子退火(QA)在高效求解组合优化问题方面具备巨大潜力。然而,QA算法的有效性高度依赖于将以逻辑图表示的问题实例嵌入到量子处理单元(QPU)中——QPU的拓扑结构为有限连通图形式,这一问题被称为minor嵌入问题。由于minor嵌入问题是NP难问题,现有求解方法在面对更大规模问题时存在可扩展性不足的问题。本文提出了一种利用强化学习(RL)技术求解minor嵌入问题的新方法,命名为CHARME。CHARME包含三个核心组件:用于策略建模的图神经网络(GNN)架构、保证解有效性的状态转移算法,以及用于高效训练的顺序探索策略。通过在合成实例和真实世界实例上开展的综合实验,我们验证了所提出的顺序探索策略以及RL框架CHARME的效率。具体而言,与Minorminer、ATOM等快速嵌入方法相比,CHARME在量子比特使用量方面能生成更优的解。此外,我们的方法在若干案例中优于基于OCT的方法——该方法以运行速度慢但解质量高著称。另外,与贪心策略相比,我们提出的探索策略能提供更优的解,从而提升了CHARME框架的训练效率。

英文摘要:

Quantum annealing (QA) has great potential to solve combinatorial optimization problems efficiently. However, the effectiveness of QA algorithms is heavily based on the embedding of problem instances, represented as logical graphs, into the quantum processing unit (QPU) whose topology is in the form of a limited connectivity graph, known as the minor embedding problem. Because the minor embedding problem is an NP-hard problem~\mbox{\cite{Goodrich2018}}, existing methods for the minor embedding problem suffer from scalability issues when faced with larger problem sizes. In this paper, we propose a novel approach utilizing Reinforcement Learning (RL) techniques to address the minor embedding problem, named CHARME. CHARME includes three key components: a Graph Neural Network (GNN) architecture for policy modeling, a state transition algorithm that ensures solution validity, and an order exploration strategy for effective training. Through comprehensive experiments on synthetic and real-world instances, we demonstrate the efficiency of our proposed order exploration strategy as well as our proposed RL framework, CHARME. In particular, CHARME yields superior solutions in terms of qubit usage compared to fast embedding methods such as Minorminer and ATOM. Moreover, our method surpasses the OCT-based approach, known for its slower runtime but high-quality solutions, in several cases. In addition, our proposed exploration enhances the efficiency of the training of the CHARME framework by providing better solutions compared to the greedy strategy.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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