Quantum 3D graph structure learning with applications to molecule computing

Graph representation learning has been extensively studied over the last decades, and recent models start to focus on an under-explored area of 3D graph learning with 3D spatial position as well as node attributes. Despite the progress, the ability to understand the physical meaning of the 3D topology data is still a bottleneck for existing models. On the other hand, quantum computing is known to be a promising direction for theoretically verified supremacy as well as increasing evidence for access to a physical quantum device in the near term. For the first time, we propose a quantum 3D embedding ansatz that learns the latent representation of 3D structures from the Hilbert space composed of the Bloch sphere of each qubit. We convert the 3D Cartesian coordinates of nodes into rotation and torsion angles and then encode them into the form of qubits. Moreover, Parameterized Quantum Circuit (PQC) is applied to serve as the trainable layers and we take the output of the PQC as the node embedding. Experimental results on two downstream tasks, molecular property prediction and 3D molecular geometries generation, demonstrate the effectiveness of our model. Though the results are still restricted by computational power, we have shown the capability of our model with very few parameters and the potential to execute on a real quantum device.