Many-body dynamics with explicitly time-dependent neural quantum states

TL;DR

The paper introduces a novel time-dependent neural quantum state (t-NQS) framework that efficiently simulates quantum dynamics in many-body systems, demonstrating state-of-the-art results in 2D models.

Contribution

It presents the t-NQS approach with explicit time dependence, enabling scalable and accurate simulation of quantum dynamics using a single neural network ansatz.

Findings

Achieved state-of-the-art simulation accuracy for 2D quantum models.

Demonstrated scalability and ability to extrapolate beyond trained intervals.

Validated the method on quench dynamics and state preparation in complex systems.

Abstract

Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions, but their application to time evolution faces scaling challenges. We introduce the time-dependent neural quantum state (t-NQS), a novel approach incorporating explicit time dependence into the neural network ansatz. This framework optimizes a single, time-independent set of parameters to solve the time-dependent Schr\"odinger equation across an entire time interval. We detail an autoregressive, attention-based transformer architecture and techniques for extending the model's applicability. To benchmark and demonstrate our 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 state of the art performance, scalability, and extrapolation to unseen intervals. These results establish t-NQS as a powerful framework for exploring quantum dynamics in strongly correlated systems.