A unifying primary framework for quantum graph neural networks from quantum graph states

TL;DR

This paper shows that a quantum graph neural network model can be understood and realized based on graph states, and shows that the graph states can be used either as a parametrized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.

Abstract

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural network model can be understood and realized based on graph states. We show that they can be used either as a parameterized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.

Figures (2)

• Figure 1: An example graph neural network: Each node accumulates information through the nodes in the subsequent layers where only nodes in the neighborhood of the node in the original graph are considered. As an example, the vertex A is connected to E, D, and B in the original graph. Therefore, it is updated using these vertices in the previous layer.
• Figure 2: The circuit for construction of the polynomial of the Laplacian operator. $U_L(i)$ represents the $i^\text{th}$ power of the matrix given in Eq.\ref{['eq:UL']}