Quantum graph neural network for 3D point cloud inference

Quantum machine learning based on parameterized quantum circuits is one of the most promising approaches for harnessing practical benefits of near-term intermediate scale quantum computers. Ongoing experimental and theoretical studies have underscored that the effectiveness of quantum machine learning applications is strongly dependent on the ability to incorporate the intrinsic structure of the problem into the quantum model.. Graph-structured problems are pervasive, spanning domains from traffic prediction to molecular medicine. However, traditional classical graph neural networks (GNNs) encounter challenges in adequately capturing the overarching structural dependencies within these graphs, thus illuminating the potential practical benefits of quantum machine learning.

This study introduces a quantum machine learning framework based on equivariant quantum graph circuits, which efficiently captures the intrinsic symmetry of graph-related problems. We illustrate its utility through the processing of 3D point cloud data. Notably, our architecture has better expressiveness compared to the widely adopted classical alternative, the message-passing graph neural networks. We demonstrate our framework in simulation and experiments on trapped-ion quantum computers,  where our architecture attains performance on par with complex classical graph neural networks.  Furthermore, we highlight the potential for quantum advantage in our model, including signs of better generalizability and a potential solutions to the intricate challenge of scaling the training and inference of quantum machine learning models