QFORMER: An Efficient Foundational PDE Model for the Time-Dependent Schr ̈odinger Equation

The QFORMER project aims to develop a novel Transformer-based deep learning model for solving the time-dependent Schrödinger equation with high accuracy and efficiency. Building on advances in multiscale operator transformers (MOTs) and physics-informed neural networks (PINNs), QFORMER integrates elements from POSEIDON and PINNsFormer to capture both temporal dependencies and multiscale quantum phenomena. Unlike previous Transformer-based approaches, which focus on steady-state solutions, QFORMER is designed to generalize across arbitrary electron configurations and initial states, significantly enhancing its applicability in quantum chemistry, condensed matter physics, and materials science. The model is pretrained on analytically solvable quantum systems, including the harmonic oscillator with time-dependent frequency, the Rabi model, and the Landau-Zener problem, ensuring robust performance across diverse Hamiltonians. By leveraging the semi-group property of the Schrödinger equation, QFORMER aims to reduce computational costs and improve scalability, offering a potential breakthrough in quantum mechanical simulations. If successful, this model could revolutionize computational quantum mechanics by providing an efficient, scalable, and generalizable deep learning framework for solving complex quantum systems.