标题： 混合量子-经典旅行商问题优化 显示英文标题

标题： Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem

摘要： 旅行商问题（TSP）是一个基本的NP难优化挑战，在物流、运筹学和网络设计等领域有着广泛的应用。虽然经典算法能够有效地解决小型到中型实例，但由于指数级复杂性，它们在可扩展性方面存在困难。 在这项工作中，我们提出了一种混合量子-经典方法，利用IBM的Qiskit Runtime将量子优化技术与经典的机器学习方法相结合，特别是K-Means聚类和随机森林分类器。这些机器学习组件有助于问题分解和噪声缓解，从而提高量子解决方案的质量。 对于从4到8个城市实例的TSP实验结果显示，纯量子方法产生的解决方案比经典基线差21.7%，而混合方法将8个城市实例的成本增加减少到了11.3%。这表明混合方法相比纯量子方法能提高解的质量，但仍然不如经典求解器最优。 尽管目前硬件存在限制，这些结果展示了量子增强方法在组合优化中的潜力，并为未来可扩展量子计算框架的发展铺平了道路。 显示英文摘要

摘要： The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized instances, they struggle with scalability due to exponential complexity. In this work, we present a hybrid quantum-classical approach that leverages IBM's Qiskit Runtime to integrate quantum optimisation techniques with classical machine learning methods, specifically K-Means clustering and Random Forest classifiers. These machine learning components aid in problem decomposition and noise mitigation, improving the quality of quantum solutions. Experimental results for TSP instances ranging from 4 to 8 cities reveal that the quantum-only approach produces solutions up to 21.7% worse than the classical baseline, while the hybrid method reduces this cost increase to 11.3% for 8 cities. This demonstrates that hybrid approaches improve solution quality compared to purely quantum methods but remain suboptimal compared to classical solvers. Despite current hardware limitations, these results highlight the potential of quantum-enhanced methods for combinatorial optimisation, paving the way for future advancements in scalable quantum computing frameworks.