发表机构
Ivan Franko National University of Lviv（利沃夫伊万·弗兰科大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将3一致边序加权超图编码为多量子比特态，推导纠缠的解析表达式，揭示其与超图局部结构及顶点度的关联，并用量子计算量化多种超图态的纠缠。
AI 中文摘要
提出了将3一致边序加权超图编码为多量子比特量子态的方法。我们推导了超图量子态几何纠缠测度的解析表达式，并建立了其与超图性质的关系。结果表明，超图的局部结构、超边权重与相应量子态的纠缠之间存在直接联系。对于等权重超图，证明了纠缠显式依赖于顶点度。利用解析方法和量子计算研究了纠缠对超图参数的依赖关系。研究了与链、星形、规则格和二叉树超图相关的超图态，并使用量子计算对其纠缠进行了量化。这些结果开辟了利用量子编程研究超图性质的可能性。
英文摘要
The encoding of 3-uniform edge-ordered weighted hypergraphs into multiqubit quantum states is proposed. We derive an analytical expression for the geometric measure of entanglement of hypergraph quantum states and establish its relation to hypergraph properties. The results establish a direct connection between the local structure of hypergraphs, hyperedge weights, and the entanglement of the corresponding quantum states. For equally weighted hypergraphs, it is shown that the entanglement depends explicitly on the vertex degree. The dependence of entanglement on hypergraph parameters is studied analytically and using quantum computing. Hypergraph states associated with chain, star, regular lattice, and binary-tree hypergraphs are examined, and their entanglement is quantified using quantum computing. These results open up the possibility of studying hypergraph properties with quantum programming.
Comments13 pages, 13 figures
