QUANTUM 3D GRAPH STRUCTURE LEARNING WITH APPLICATIONS TO MOLECULE COMPUTING

Abstract

Graph representation learning has been extensively studied over the last decade, and recent models start to pay attention to a relatively new area i.e. 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 information is still a bottleneck for existing models. On the other hand, quantum computing is known to be a promising direction for its theoretically verified supremacy for large-scale graph and combinatorial problem as well as the increasing evidence for the availability to physical quantum devices in the near term. In this paper, for the first time to our best knowledge, 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. Specifically, the 3D Cartesian coordinates of nodes are converted 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 the output of the PQC is adopted as the final 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 the computational power on the classic machine, we have shown the capability of our model with very few parameters and the potential to execute on a real quantum device.

1. INTRODUCTION

Graph representation, or specifically 3D graph representation as considered in this paper, has received extensive attention over the last decade. Beyond tasks like node classification or link prediction, it further facilitates various downstream applications such as molecular property prediction (Liu et al., 2021) and drug design (Gaudelet et al., 2021) . Recently, machine learning approaches have been well developed for learning latent node embedding on molecules (Schütt et al., 2017; Unke & Meuwly, 2019; Gasteiger et al., 2019; 2021) . However, the mainstream of such researches is still facing the challenges of better processing the 3D Cartesian coordinates and learning the latent representation of the 3D graph structure. On the other hand, there are also emerging lines of researches in the area of quantum computing. State-of-the-art quantum computing hardwares are now stepping into the Noisy Intermediate-Scale Quantum (NISQ) era, which leads to the possibility to implement applications in specific scientific domains in the near term (Preskill, 2018; Arute et al., 2019; Zhong et al., 2020; Huang et al., 2020) . The overlap between quantum computing and machine learning has emerged as one of the most encouraging areas for quantum computing, as termed by quantum machine learning (Biamonte et al., 2017) . Quantum paradigms or hybrid paradigms have been carefully designed to fulfill quantum supremacy in quantum chemistry problems (Aspuru-Guzik et al., 2005; O'Malley et al., 2016) . Existing approaches mainly focus on the quantum simulation of molecular energies, which enables effective prediction of chemical reaction rates. However, these quantum approaches (Romero et al., 2018; Peruzzo et al., 2014; O'Malley et al., 2016; Yung et al., 2014) are still simulating the energies of certain small molecules like H 2 , LiH, etc. In this paper, we aim to develop quantum machine learning approaches to learn the latent representation of the 3D graph structure of molecules instead of directly simulating the molecular energies with Hamiltonians. Graph learning may not be as precise as molecular simulation approaches for

