发表机构
University of Sheffield; Imperial College London（谢菲尔德大学; 帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出自适应关系学习框架，利用SWAP/CYCLE测试与局部变换处理多实例量子数据，在光子系统中高效检测关系，优于非自适应方法，实现高精度低开销。
AI 中文摘要
将多个量子态并行加载到量子机器学习（QML）模型中，可以解锁关键信息存在于状态之间关系而非单个状态中的学习任务。我们针对此类多实例量子数据引入了一种自适应关系学习框架，该框架能够访问成对及更高阶的关系。我们的模型通过SWAP或CYCLE测试进行全局测量，以评估n态Bargmann不变量，并结合对每个输入状态局部应用的浅层可训练变换。我们展示了该方法在连续变量（CV）光子系统中的适用性，该系统天然提供对量子数据和必要计算操作的访问。我们解决了涉及隐藏关系检测、几何相位分类以及在存在未知共享干扰相互作用下的传感任务。我们将自适应模型与基于连续变量经典阴影的非自适应“先测量”方法进行基准比较，并表明阴影估计的成本随n快速增长，而我们的模型避免了这种依赖性。即使在n=2时，我们以500次推理射击实现了完美的测试准确率A=1.0，将平均测试准确率比基于阴影的方法提高了ΔA=0.15，同时每个数据点使用的射击次数减少了100倍。我们的工作为传感和量子数据应用开辟了途径，在这些应用中，自适应光子QML能够访问非自适应、先测量模型难以恢复的关系特征。
英文摘要
Loading multiple quantum states in parallel into a quantum machine learning (QML) model can unlock learning tasks where key information resides in the \emph{relations} between states rather than in individual states. We introduce an adaptive relational learning framework for such multi-instance quantum data that accesses pairwise and higher-order relations. Our model combines global measurements via SWAP or CYCLE tests for evaluating an $n$-state Bargmann invariant with shallow trainable transformations applied locally to each input state. We demonstrate the approach for continuous-variable (CV) photonic systems, which naturally provide access to quantum data and necessary computing operations. We solve tasks involving hidden relationship detection, geometric phase classification, and sensing in the presence of an unknown shared nuisance interaction. We benchmark the adaptive model against a non-adaptive ``measure-first'' approach based on continuous-variable classical shadows, and show that the cost of shadow estimation grows rapidly with $n$, while our model avoids this dependence. Already for $n=2$, we achieve perfect test accuracy $A=1.0$ with $500$ inference shots, improving average test accuracy over the shadow-based method by $ΔA=0.15$ while using $100$ times fewer shots per data point. Our work opens routes to sensing and quantum-data applications where adaptive photonic QML can access relational features that are costly to recover with non-adaptive, measure-first models.
Comments13 pages, 9 figures
