Equivariant quantum graph circuits: constructions for universal approximation over graphs

Abstract

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. This 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. We also provide experimental evidence, and observe that the performance of EQGCs scales well with the depth of the model.