Predicting and controlling driven quantum systems requires access to dynamics across physical parameters, initial states, and evolution times. A reusable neural model must capture this dependence while preserving unitary structure and maintaining accuracy over long-time coherent evolution. Here we introduce Quantum Evolution Networks (QENs), which map physical parameters and time to complete propagators for periodically driven three-spin registers. Shared networks learn unitary one-period propagators and compatible within-period paths, enabling predictions through known periodic composition without query-specific numerical integration. For transverse driving, the fifth-percentile fidelity, minimized over input states and sampled times, is 0.9947 over 24 periods on 256 held-out configurations. A leading-order analysis of spectrally resolved endpoint residuals predicts multicycle process error more accurately than quadratic or spectrum-averaged estimates. Interventions at matched single-period infidelity produce orders-of-magnitude differences in multicycle infidelity, demonstrating the importance of residual orientation. Compatible component replacements identify how endpoint and within-period approximations limit reconstruction accuracy. These results establish a reusable neural representation of the studied propagator families and connect its learned residual structure to its observed long-time reliability.
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Predicting and controlling driven quantum systems requires access to dynamics across physical parameters, initial states, and evolution times. A reusable neural model must capture this dependence while preserving unitary structure and maintaining accuracy over long-time coherent evolution. Here we introduce Quantum Evolution Networks (QENs), which map physical parameters and time to complete propagators for periodically driven three-spin registers. Shared networks learn unitary one-period propagators and compatible within-period paths, enabling predictions through known periodic composition without query-specific numerical integration. For transverse driving, the fifth-percentile fidelity, minimized over input states and sampled times, is 0.9947 over 24 periods on 256 held-out configurations. A leading-order analysis of spectrally resolved endpoint residuals predicts multicycle process error more accurately than quadratic or spectrum-averaged estimates. Interventions at matched single-period infidelity produce orders-of-magnitude differences in multicycle infidelity, demonstrating the importance of residual orientation. Compatible component replacements identify how endpoint and within-period approximations limit reconstruction accuracy. These results establish a reusable neural representation of the studied propagator families and connect its learned residual structure to its observed long-time reliability.
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a physics-informed deep learning approach based on Physics-Informed Neural Networks to estimate these operators over the full time domain. By incorporating physical constraints such as unitarity and leveraging the second-order Magnus expansion on the evolution operator, the proposed framework enables the estimation of unitary matrices at different time intervals. The model is trained using simulated unitary operators and evaluated on quantum systems ranging from 2 to 6 qubits. For larger many-body systems, specifically those with 7 and 8 qubits, the same methodology is employed to reconstruct an effective time-dependent Hamiltonian, from which the corresponding time-evolution operator is computed over the entire temporal domain. The proposed framework achieves fidelities exceeding 0.92 using a limited number of unitary samples, indicating a potential reduction in measurement and data acquisition costs. These results highlight the effectiveness of the approach for data-driven simulation and identification of quantum dynamical systems, with direct relevance to quantum computing and quantum simulation applications.
Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.
We explore the capability of linear fully connected neural networks (FCNs) to learn and predict quantum dynamics governed by various equations of motion, including the time-dependent Schrödinger equation, quantum Liouville equation, and thermofield dynamics (TFD). Given the inherent linearity of these equations, linear FCNs naturally align with the fundamental structure of quantum propagators, making them a promising machine-learning approach for simulating quantum systems. Through numerical experiments on different model systems, including single-state and two-state anharmonic potentials, we demonstrate that linear FCNs without hidden layers achieve high accuracy while preserving population conservation. For finite-temperature dynamics, we find that learning TFD is more efficient than learning density matrix evolution due to the suppressed noise from the partial trace over the fictitious Hilbert space. However, as system dimensionality increases, the computational cost of linear FCNs becomes substantial due to scaling and sampling challenges, suggesting the necessity of more efficient network structures. Our results highlight the potential of physics-informed neural networks for quantum dynamics and point toward future developments in neural network architectures inspired by physical principles.
Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with a physics-driven neural network to reconstruct long-time operator dynamics from short-time quantum data. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from the measurement data. Applied to the Ising spin chain with mixed fields, the operator learning method accurately extrapolates its long-time correlation function and resolves its excitation spectrum. We validate the framework by collecting short-time data from IBM's superconducting quantum processor and successfully reconstruct the Fourier spectrum of an N=8 Ising spin chain with 5 times enhanced precision. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.
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.
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.