发表机构
University of Exeter; University of Sheffield（埃克塞特大学; 谢菲尔德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出一种量子谱特征提取方法，通过伊辛态密度矩学习带符号图的结构平衡，以挫折指数为基准，在14万图上以0.4误差恢复，并展示了量子优势。
AI 中文摘要
我们开发了一种从问题相关哈密顿量的态密度（DOS）中提取谱特征的量子方法，并将其应用于带符号图的机器学习。我们提出将带符号图嵌入为具有正负相互作用的伊辛模型实例，并使用伊辛态密度的标准化矩作为学习特征。我们证明这些矩计数带符号闭游走，具有切换不变性，并且构造上无尺寸依赖。作为基准，我们以学习挫折指数为目标，这是一种NP难的度量结构平衡的指标，在中等规模下可以精确标注。在零场情况下，模型可以经典采样，使得量子提取过程能够对照精确真值进行验证。我们提出DOS-QPE，一种对纯化最大混合探针的相位估计方法，它以比基于Hadamard测试的迹采样少几个数量级的射击次数采样谱密度，并将所得特征直接输入经典训练的模型。在$1.4\ imes10^5$个带标签图上，精确态密度确定挫折指数，五个矩以0.4的平均误差恢复它，远低于一次符号翻转。在零场之外，底层迹估计问题是DQC1完全的，提供了对没有已知高效经典采样方法的谱特征的访问。我们的工作为社交网络平衡分析、自旋玻璃研究、相关聚类和蛋白质相互作用网络中的量子应用开辟了途径。
英文摘要
We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.
Comments12 pages, 6 figures
