生成Dicke态图

中文摘要 AI 辅助

图论是量子计算中的强大工具，其应用范围从量子电路综合与优化到纠缠映射。近期工作展示了如何利用边着色图来模拟生成GHZ态和W态的光子实验。然而，该工作也证明了验证一个图是否模拟Dicke态实验是coNP完全的。在本工作中，我们提供了生成$|D_{k}^a\rangle \bigotimes |0\rangle^{\bigotimes b}$的图族，其中$b = |a-2k|$是旁观者模式的数量。图结构由$a$个顶点上的双重完全子图以及一组辅助顶点组成。我们证明了每次符合事件恰好携带$k$个激发，长度为$a$的比特串上的每个权重为$k$的计算基态都被实现，并且每个这样的比特串恰好被实现$(n/2)!$次，其中$n = a+b$。由于验证Dicke FORALL条件在一般情况下是coNP完全的，构建可证明生成Dicke态的显式图族具有重要意义。

英文摘要

Graph theory is a powerful tool in quantum computing, with applications ranging from quantum circuit synthesis and optimization to entanglement mapping. Recent work has shown how one can use edge-colored graphs to model photonic experiments that generate GHZ and W states. However, the latter work also proved that verifying that a graph models a Dicke state experiment is coNP-complete. In this work, we provide families of graphs that generate $|D_{k}^a\rangle \otimes |0\rangle^{\otimes b }$, where $b = |a-2k|$ is the number of spectator modes. The graph setup consists of a doubled complete subgraph on $a$ vertices and a collection of auxiliary vertices. We prove that every coincidence carries exactly $k$ excitations, every weight-$k$ computational basis state on bitstrings of length $a$ is realized, and each of those bitstrings is realized exactly $(n/2)!$ times, where $n = a+b$. Since verifying the Dicke FORALL condition is coNP-complete in general, constructing explicit families that provably generate Dicke states is of interest.

发表机构

• University of Tennessee（田纳西大学）

机构由 AI 辅助整理，请以论文原文为准。