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arXiv:2603.25066

Neural Operator Quantum State: A Foundation Model for Quantum Dynamics

Zihao Qi, Christopher Earls, Yang Peng

quant-phcond-mat.quant-gascond-mat.stat-mechcond-mat.str-elSubmitted Mar 26, 2026• Announced Mar 27, 2026• 0 citations
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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 Schrödinger 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.

Comments
14 pages, 6 figures

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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 Schrödinger 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.
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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 Schrödinger 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.
Describing the dynamics of strong-laser driven open quantum systems is a very challenging task that requires the solution of highly involved equations of motion. While machine learning techniques are being applied with some success to simulate the time evolution of individual quantum states, their use to approximate time-dependent operators (that can evolve various states) remains largely unexplored. In this work, we develop driven (NQP), a universal neural network framework that solves driven-dissipative quantum dynamics by approximating propagators rather than wave functions or density matrices. NQP can handle arbitrary initial quantum states, adapt to various external fields, and simulate long-time dynamics, even when trained on far shorter time windows. Furthermore, by appropriately configuring the external fields, our trained NQP can be transferred to systems governed by different Hamiltonians. We demonstrate the effectiveness of our approach by studying the spin-boson and the three-state transition Gamma models.
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Abstract Fourier Neural Operators (FNOs) excel on functional data tasks, such as those originating from partial differential equations. This renders them effective at simulating the time evolution of quantum wavefunctions, a computationally challenging, yet coveted task. In this manuscript, we use FNOs to model the evolution of random quantum spin systems, chosen due to their representative dynamics. We find that traditional neural networks, such as U-Net, exhibit limited extrapolation beyond the training time interval, whereas FNOs capture the underlying time-evolution operator, generalizing to unseen times. Additionally, we apply FNOs to a compact set of Hamiltonian observables (~ poly( n )) instead of 2 n -component wavefunctions, greatly reducing the size of our inputs, outputs, and FNO models. This Hamiltonian observable-based method demonstrates that FNOs can distill information from high to low-dimensional spaces. We perform numerical experiments on a 20-qubit system, extrapolating Hamiltonian observables to twice the training time with a relative error of 5.8%. Notably, relative to numerical time-evolution methods, FNO achieves an inference speedup of approximately 10 4 × for 20-qubit systems, underscoring its computational efficiency. This extrapolation of observables past training times stands to fundamentally increase the simulatability of quantum systems beyond the limitations of quantum device coherence and tensor network circuit-depth.
The problem of reconstructing an unknown time-dependent Hamiltonian of a two-level quantum system from its observed dynamics is considered. A method based on a neural network in the Neural ODE framework is proposed, where the continuous evolution of the quantum state is modeled by integrating the Schrodinger equation with a parametric Hamiltonian model implemented by the network. The input data consist of measured time series of the expectation values of Pauli operators for a qubit. The network is trained by minimizing the difference between the experimentally observed and simulated trajectories of quantum observables. Using the example of spin dynamics in a time-varying magnetic field, it is shown that the proposed approach allows accurate reconstruction of the parameters of the time-dependent Hamiltonian without interrupting the quantum evolution. The results demonstrate that the Neural ODE model provides continuous handling of the time parameter and robust reconstruction of system dynamics under conditions of limited data and noise.