发表机构
University of Tennessee, Knoxville; Argonne National Laboratory（田纳西大学诺克斯维尔分校; 阿贡国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对连续时间量子游走模拟的哈密顿量分解，训练机器学习模型预测稀疏/稠密图对应的高效分解方式，在8顶点图数据集上调参后MCC达0.593，对更大图的迁移效果随顶点数增加提升至MCC=1。
AI 中文摘要
在量子计算的电路模型中，模拟图上的连续时间量子游走（CTQW）需要将其哈密顿量分解为可通过Trotter化转换为硬件原生门的项。我们考虑两种此类分解：标准泡利（Pauli）分解和近期提出的匹配分解。已有研究表明，匹配分解在稀疏图上使用更少的CX门，而泡利分解在更稠密的图上使用更少的CX门。由于CX门决定了当前硬件的误差和运行时间，我们训练机器学习模型，针对给定图预测两种分解中哪一种会产生更少的CX门数量。我们使用Brendan McKay数据库中全部11117个连通8顶点图的完整集合进行训练和评估，因此类别平衡和重叠可直接测量而非估算。我们使用12个特征：10个图的拓扑属性，以及泡利分解和匹配分解产生的项数（n_Pauli和n_match）这两个特征，二者均可在不 transpile 模拟电路的情况下计算。仅标准拓扑属性的预测能力很弱，主要信号来自n_Pauli，这是哈密顿量分解的属性而非图的固有属性；度方差是唯一带有信号的其他特征。在一系列模型中，马修斯相关系数（MCC）处于狭窄区间，未调参时为0.569，调参后为0.593，因此没有单一架构表现突出。我们采用单隐藏层神经网络，MCC为0.593。将该模型冻结后应用于由结构化图和Erdos-Renyi家族组成的更大图（最多256个顶点）的预留类别平衡测试集，模型可迁移，MCC从N=8时的0.785上升至N≥64时的1。
英文摘要
Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms that can be Trotterized into hardware-native gates. We consider two such decompositions: the standard Pauli decomposition and the recently introduced matching decomposition. Prior work suggests that the matching decomposition uses fewer CX gates on sparse graphs, while the Pauli decomposition uses fewer on denser graphs. Since CX gates dominate error and runtime on current hardware, we train machine learning models to predict, for a given graph, which of the two decompositions produces the smaller CX gate count. We train and evaluate on the complete population of all 11,117 connected eight-vertex graphs from Brendan McKay's database, so the class balance and overlap are measured directly rather than estimated. We use twelve features: ten topological properties of the graph and two that count the terms the Pauli and matching decompositions produce (n_Pauli and n_match), both computable without transpiling the simulation circuit. Standard topological properties alone provide little predictive power. Instead, the dominant signal comes from n_Pauli, a property of the Hamiltonian decomposition rather than an intrinsic property of the graph; degree variance is the only other feature that carries signal. Across a range of models the Matthews correlation coefficient (MCC) falls in a narrow band, from 0.569 untuned to 0.593 after tuning, so no single architecture stands out. We adopt a single-hidden-layer neural network at MCC 0.593. Applied frozen to a held-out, class-balanced test set of larger graphs (up to 256 vertices) from structured and Erdos-Renyi families, the model transfers, with MCC rising from 0.785 at N=8 to 1 at N>=64.
Comments12 pages, 6 figures
