Abstract Simulating the dynamics of many-body quantum systems is a significant challenge, especiallyin higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer apromising tool for representing quantum wavefunctions, but their application to time evolutionfaces scaling challenges. We introduce the time-dependent neural quantum state (t-NQS), a novelapproach incorporating explicit time dependence into the neural network ansatz. This frameworkoptimizes a single, time-independent set of parameters to solve the time-dependent Schr¨odingerequation across an entire time interval. We detail an autoregressive, attention-based transformerarchitecture and techniques for extending the model’s applicability. To benchmark and demonstrateour method, we simulate quench dynamics in the 2D transverse field Ising model and the time-dependent preparation of the 2D antiferromagnetic state in a Heisenberg model, demonstrating stateof the art performance, scalability, and extrapolation to unseen intervals. These results establisht-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.
Walle et al. (2025) studied this question.