We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92\%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50\% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (\url{https://github.com/divelab/AIRS}).

翻译：我们考虑哈密顿矩阵的预测问题，该问题在量子化学和凝聚态物理中具有重要应用。效率和等变性是两个重要但相互冲突的因素。在本工作中，我们提出名为QHNet的SE(3)-等变网络，实现了效率与等变性的统一。我们的关键突破在于QHNet架构的创新设计，该架构不仅遵循内在对称性，还能将张量积的数量减少92%。此外，QHNet避免了涉及更多原子类型时通道维度的指数级增长。我们在包含四个分子系统的MD17数据集上进行实验。实验结果表明，我们的QHNet能以显著更快的速度达到与现有最优方法相当的性能。此外，得益于其精简的架构，QHNet可节省50%的内存消耗。我们的代码已作为AIRS库的一部分公开（\url{https://github.com/divelab/AIRS}）。