发表机构
Graduate School of Engineering Science, The University of Osaka; Center for Quantum Information and Quantum Biology, The University of Osaka; RIKEN Center for Quantum Computing (RQC); Graduate School of Informatics, Kyoto University（大阪大学工学研究科; 大阪大学量子信息与量子生物学中心; 理化学研究所量子计算中心; 京都大学情报学府）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过系统表达性分析揭示泡利关联编码（PCE）性能饱和的主因是可训练性而非表达性，并提出多阶段连续框架，在800顶点G-set实例上优于传统PCE，媲美图神经网络方法。
AI 中文摘要
近年来，针对组合优化问题的量子方法引起了广泛关注。在这些方法中，泡利关联编码（PCE）因其将优化变量嵌入泡利字符串的期望值中，已成为量子比特资源有限的量子设备的一个有前景的框架。然而，其性能背后的机制及其饱和的原因仍不清楚。在本工作中，我们通过系统性的表达性和可训练性分析来研究这些问题。首先，我们将PCE与基于张量网络的经典代理模型进行比较，这些模型的结构逐渐接近PCE电路的拓扑结构。结果表明，PCE以显著更少的可训练参数达到了相当的解决方案质量，显示出强大的参数效率。其次，为了确定传统PCE的性能饱和是由表达性不足还是优化困难引起的，我们进行了一项诊断性表达性测试，在该测试中，电路针对Max-Cut的参考配置进行训练。结果表明，即使是浅层PCE电路也能表示强解，这表明主要瓶颈不是拟设的表示能力，而是在松弛目标函数下的可训练性。受此发现启发，我们提出了一个多阶段连续框架，该框架逐渐将平滑的松弛目标转变为更接近目标离散问题的更尖锐目标。在包含800个顶点的G-set实例上的数值实验表明，所提出的方法始终优于传统PCE，并与具有代表性的图神经网络（GNN）方法具有竞争力。这些结果阐明了PCE性能背后的主要因素，并为在量子比特资源有限的量子设备上改进PCE提供了一种实用策略。
英文摘要
Quantum approaches for combinatorial optimization problems have attracted considerable attention in recent years. Among these approaches, Pauli Correlation Encoding (PCE) has emerged as a promising framework for quantum devices with limited qubit resources because it embeds optimization variables in expectation values of Pauli strings. However, the mechanisms underlying its performance and the reasons for its saturation remain unclear. In this work, we investigate these questions through a systematic analysis of expressivity and trainability. First, we compare PCE with classical surrogate models based on tensor networks whose structures progressively approach the topology of the PCE circuit. The results show that PCE attains comparable solution quality with substantially fewer trainable parameters, indicating strong parameter efficiency. Second, to determine whether the performance saturation of conventional PCE is caused by insufficient expressivity or by optimization difficulty, we perform a diagnostic expressivity test in which the circuit is trained toward reference configurations for Max-Cut. The results show that even shallow PCE circuits can represent strong solutions, indicating that the main bottleneck is not the representational power of the ansatz, but the trainability under the relaxed objective function. Motivated by this finding, we propose a multistage continuation framework that gradually transforms a smooth relaxed objective into a sharper objective that more closely approximates the target discrete problem. Numerical experiments on G-set instances with 800 vertices show that the proposed method consistently outperforms conventional PCE and is competitive with representative graph neural network (GNN) methods. These results clarify the main factors behind PCE performance and provide a practical strategy for improving PCE on quantum devices with limited qubit resources.
Comments10 pages, 7 figures, 1 table
