  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.
