Predicting quantum operator matrices such as Hamiltonian, overlap, and density matrices in the density functional theory (DFT) framework is crucial for understanding material properties. Current methods often focus on individual operators and struggle with efficiency and scalability for large systems. Here we introduce a novel deep learning model, SLEM (strictly localized equivariant message-passing) for predicting multiple quantum operators, that achieves state-of-the-art accuracy while dramatically improving computational efficiency. SLEM's key innovation is its strict locality-based design, constructing local, equivariant representations for quantum tensors while preserving physical symmetries. This enables complex many-body dependence without expanding the effective receptive field, leading to superior data efficiency and transferability. Using an innovative SO(2) convolution technique, SLEM reduces the computational complexity of high-order tensor products and is therefore capable of handling systems requiring the $f$ and $g$ orbitals in their basis sets. We demonstrate SLEM's capabilities across diverse 2D and 3D materials, achieving high accuracy even with limited training data. SLEM's design facilitates efficient parallelization, potentially extending DFT simulations to systems with device-level sizes, opening new possibilities for large-scale quantum simulations and high-throughput materials discovery.

翻译：在密度泛函理论框架中预测哈密顿量、重叠矩阵及密度矩阵等量子算符矩阵对于理解材料性质至关重要。现有方法通常针对单个算符进行建模，且在处理大体系时面临效率与可扩展性不足的问题。本文提出一种新型深度学习模型SLEM（严格局域化等变消息传递），用于同时预测多种量子算符，在显著提升计算效率的同时达到了最先进的预测精度。SLEM的核心创新在于其基于严格局域性的设计，能够在保持物理对称性的前提下为量子张量构建局部等变表示。该设计使得模型无需扩展有效感受野即可刻画复杂的多体依赖关系，从而实现了卓越的数据效率与迁移能力。通过采用创新的SO(2)卷积技术，SLEM降低了高阶张量积的计算复杂度，因此能够处理基组包含$f$轨道与$g$轨道的体系。我们在多种二维与三维材料体系上验证了SLEM的性能，即使在有限训练数据下仍能保持高精度预测。SLEM的设计支持高效并行化，有望将密度泛函理论模拟拓展至器件级尺寸的体系，为大规模量子模拟与高通量材料发现开辟了新途径。