等价的量子图电路

我们研究了用于图表示学习的量子电路，并提出了等价量子图电路（EQGCs），作为一类参数化的量子电路，具有很强的关系归纳偏向，用于图结构数据的学习。从概念上讲，EQGCs是一个统一的量子图表示学习的框架，使我们能够定义几个有趣的子类，将现有的建议归入其中。在表示能力方面，我们证明感兴趣的子类是有界图域上函数的普遍近似物，并提供了实验证据。我们对量子图机器学习方法的理论观点为进一步的工作开辟了许多方向，并可能导致具有超越经典方法的能力的模型。

原文题目：Equivariant Quantum Graph Circuits

原文：We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured data. Conceptually, EQGCs serve as a unifying framework for quantum graph representation learning, allowing us to define several interesting subclasses subsuming existing proposals. In terms of the representation power, we prove that the subclasses of interest are universal approximators for functions over the bounded graph domain, and provide experimental evidence. Our theoretical perspective on quantum graph machine learning methods opens many directions for further work, and could lead to models with capabilities beyond those of classical approaches.