发表机构
Instituto de Pesquisas Eldorado; Universidade Federal de Santa Catarina; Universidade Federal do Rio Grande do Sul（埃尔多拉多研究所; 圣卡塔琳娜联邦大学; 南里奥格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于稀疏Walsh/Pauli相关性编码的量子启发MaxCut求解器，通过经典计算相关性实现紧凑可微松弛，在Gset实例上优于随机搜索和禁忌搜索，且运行时间最短。
AI 中文摘要
我们提出了一种基于稀疏Pauli-相关性编码的量子启发Walsh/PCE求解器，用于解决MaxCut问题。该方法不是直接将每个图顶点分配一个量子比特或一个变量，而是通过对角Pauli/Walsh可观测量的期望值来表示松弛的二元变量。这些相关性通过稀疏Walsh自相关从经典计算中得出，从而产生MaxCut目标的紧凑可微松弛。我们在选定的Gset实例G1、G6、G12和G18上评估了该方法，并与随机搜索和禁忌搜索在10个独立种子上进行了比较。所提出的模型使用801个活动参数，仅占18个量子比特上完整Walsh空间的0.306%。经过最终的比特翻转局部搜索后，Walsh/PCE在G1上达到0.99033 ± 0.00226的近似比，在G6上达到0.95647 ± 0.01604，在G12上达到0.96007 ± 0.00951，在G18上达到0.92964 ± 0.02202，在所有测试实例上均优于两个基线。该方法在所有情况下也实现了最低的平均运行时间。这些结果表明，稀疏Walsh/PCE表示为MaxCut提供了一条高效的量子启发途径，并可进一步扩展到基于硬件的Pauli/Walsh相关性估计。
英文摘要
We present a quantum-inspired Walsh/PCE solver for MaxCut based on sparse Pauli-correlation encodings. Instead of assigning one qubit or one variable to each graph vertex directly, the method represents relaxed binary variables through expectation values of diagonal Pauli/Walsh observables. These correlators are computed classically from sparse Walsh autocorrelations, producing a compact differentiable relaxation of the MaxCut objective. We evaluate the method on selected Gset instances, G1, G6, G12, and G18, and compare it with random search and tabu search over 10 independent seeds. The proposed model uses $801$ active parameters, corresponding to only $0.306\%$ of the full Walsh space over $18$ qubits. After a final bitflip local search, Walsh/PCE achieves approximation ratios of $0.99033 \pm 0.00226$ on G1, $0.95647 \pm 0.01604$ on G6, $0.96007 \pm 0.00951$ on G12, and $0.92964 \pm 0.02202$ on G18, outperforming both baselines on all tested instances. The method also yields the lowest average runtime in all cases. These results suggest that sparse Walsh/PCE representations provide an efficient quantum-inspired route for MaxCut and may be further extended to hardware-based estimation of Pauli/Walsh correlators.
