标题： 为旅行商问题的PCE进行热启动 显示英文标题

标题： Warm-Starting PCE for Traveling Salesman Problem

摘要： 变分量子算法在组合优化方面具有前景，但其可扩展性通常受到对量子比特需求较高的编码方案的限制。 为了克服这一瓶颈，保罗相关编码（PCE）已成为该场景中最具前景的算法之一。 该方法不仅在量子比特数量上实现了多项式级的减少，并抑制了平坦峡谷现象，而且在Maxcut问题上表现出与最先进方法相当的性能。 在本工作中，我们提出了一种热启动PCE，这是一种扩展方法，将来自Goemans-Williamson（GW）随机舍入算法的经典偏差引入损失函数，以引导优化过程以提高近似比。 我们使用QUBO到MaxCut的转换方法，在最多$5$层的情况下对旅行商问题（TSP）进行了评估。 我们的结果表明，热启动-PCE始终优于标准PCE，在$28\text{--}64\%$个实例中达到了最优解，而PCE则为$4\text{--}26\%$个实例，并且获得了更高的平均近似比，随着电路深度的增加而提升。 这些发现突显了这种热启动策略在增强近期硬件上的PCE基础求解器方面的实际价值。 显示英文摘要

摘要： Variational quantum algorithms are promising for combinatorial optimization, but their scalability is often limited by qubit-intensive encoding schemes. To overcome this bottleneck, Pauli Correlation Encoding (PCE) has emerged as one of the most promising algorithms in this scenario. The method offers not only a polynomial reduction in qubit count and a suppression of barren plateaus but also demonstrates competitive performance with state-of-the-art methods on Maxcut. In this work, we propose a warm-start PCE, an extension that incorporates a classical bias from the Goemans-Williamson (GW) randomized rounding algorithm into the loss function to guide the optimization toward improved approximation ratios. We evaluated this method on the Traveling Salesman Problem (TSP) using a QUBO-to-MaxCut transformation for up to $5$ layers. Our results show that Warm-PCE consistently outperforms standard PCE, achieving the optimum solution in $28\text{--}64\%$ of instances, versus $4\text{--}26\%$ for PCE, and attaining higher mean approximation ratios that improve with circuit depth. These findings highlight the practical value of this warm-start strategy for enhancing PCE-based solvers on near-term hardware.