发表机构
ICQTs（量子科学与技术研究所）
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UCQM框架，整合六个互补指标定量评估连续变量团簇态质量，应用于四模拓扑，发现方形结构最优，适用于基于测量的量子计算。
AI 中文摘要
连续变量（CV）团簇态是基于测量的量子计算（MBQC）的核心资源之一。尽管在其理论发展和实验实现方面取得了显著进展，但比较不同团簇态拓扑结构的质量仍然具有挑战性，因为现有方法通常依赖于对协方差矩阵的定性检查，或依赖于仅表征底层关联结构单一方面的个别指标。在本工作中，我们提出了一个定量评估框架，整合了CV团簇态的六个互补描述符：总关联强度（SSC）、关联均匀性（CAV）、错误鲁棒性（EVC）、通信开销（COM）、路径冗余（RED）和瓶颈脆弱性（BOT）。这些量被组合成一个统一的团簇质量指标（UCQM），为评估和比较不同团簇态架构提供了一致的基础。所提出的框架被应用于压缩范围$r \in [0.2,1.8]$内的四模路径、方形和星形团簇拓扑。在所研究的参数范围内，方形拓扑始终获得最高的UCQM分数，表明在所考虑的拓扑中具有最均衡的结构特征，并支持其适用于基于测量的量子计算。由于所有六个指标直接来源于协方差矩阵元素以及图连通性，该框架自然扩展到任意$N$模团簇态、更高维的晶格几何以及实验重建的协方差矩阵。除了提供单一数值分数外，UCQM还为分析CV团簇态的结构质量提供了统一视角，并为其系统比较、优化和未来设计建立了实用框架。
英文摘要
Continuous-variable (CV) cluster states constitute one of the central resources for measurement-based quantum computation (MBQC). Despite substantial progress in their theoretical development and experimental realization, comparing the quality of different cluster-state topologies remains challenging, as existing approaches typically rely either on qualitative inspection of covariance matrices or on individual metrics that characterize only a single aspect of the underlying correlation structure. In this work, we propose a quantitative evaluation framework that integrates six complementary descriptors of CV cluster states: total correlation strength (SSC), correlation uniformity (CAV), error resilience (EVC), communication overhead (COM), path redundancy (RED), and bottleneck vulnerability (BOT). These quantities are combined into a single \textbf{Unified Cluster Quality Metric (UCQM)}, providing a consistent basis for evaluating and comparing different cluster-state architectures. The proposed framework is applied to four-mode path, square, and star cluster topologies over the squeezing range $r \in [0.2,1.8]$. Across the investigated parameter regime, the square topology consistently achieves the highest UCQM score, indicating the most balanced structural characteristics among the topologies considered and supporting its suitability for measurement-based quantum computation. Because all six metrics are derived directly from covariance-matrix elements together with graph connectivity, the framework naturally extends to arbitrary $N$-mode cluster states, higher-dimensional lattice geometries, and experimentally reconstructed covariance matrices. Beyond providing a single numerical score, UCQM offers a unified perspective for analyzing the structural quality of CV cluster states and establishes a practical framework for their systematic comparison, optimization, and future design.
