Neural Operator Quantum State: A Foundation Model for Quantum Dynamics

TL;DR

This paper introduces Neural Operator Quantum State (NOQS), a foundation model that learns the solution operator for quantum dynamics, enabling rapid predictions of time-evolved states under various protocols without re-training.

Contribution

The work presents NOQS as a novel foundation model that generalizes quantum dynamics across protocols, outperforming traditional methods that require re-computation for each new protocol.

Findings

NOQS accurately predicts quantum states for unseen protocols.

It generalizes to out-of-distribution driving functions.

The model can be transferred across different temporal resolutions.

Abstract

Capturing the dynamics of quantum many-body systems under time-dependent driving protocols is a central challenge for numerical simulations. Existing methods such as tensor networks and time-dependent neural quantum states, however, must be re-run for every protocol. In this work, we introduce the Neural Operator Quantum State (NOQS) as a foundation model for quantum dynamics. Rather than solving the Schr\"odinger equation for individual trajectories, our approach aims to \emph{learn the solution operator} that maps entire driving protocols to time-evolved quantum states. Once trained, the NOQS predicts time evolution under unseen protocols in a single forward pass, requiring no additional optimization. We validate NOQS on the two-dimensional Ising model with time-dependent longitudinal and transverse fields, demonstrating accurate prediction not only for unseen in-distribution protocols, but also for qualitatively different, out-of-distribution functional forms of driving. Further, a single NOQS model can be transferred between different temporal resolutions, and can be efficiently fine-tuned with sparse experimental measurements to improve predictions across all observables at negligible cost. Our work introduces a new paradigm for quantum dynamics simulation and provides a practical computational-experimental interface for driven quantum systems.