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arXiv:2508.11546 · Physical Review C

Highly efficient nuclear population transfer through physics-informed neural networks

Jing Liu, Fu-Quan Dou

Published Feb 10, 2026• 1 citation
arXivHTMLPDF

Abstract

Nuclear coherent population transfer (NCPT) offers numerous potential applications, particularly in next-generation nuclear clocks and nuclear batteries. However, the realization of high fidelity, fast operation, and low energy consumption in NCPT remains so far challenging. Here, we employ physics-informed neural networks (PINNs) to the population transfer in an open three-level nuclear system with spontaneous emission. The method embeds the system's control equations and boundary conditions into the loss function, thereby enabling the automatic learning of optimal laser pulse sequences that drive highly efficient population transfer. We take a short-lived excited state of $^{172}\mathrm{Yb}$ and a long-lived state of $^{229}\mathrm{Th}$ as representative examples, and systematically compare the performance of the PINNs approach with three conventional control strategies. We show that PINNs can achieve higher transfer efficiency with smaller pulse areas and shorter durations across different lifetime regimes. Our results provide a new perspective to overcome the lifetime limitation and enhance the efficiency of nuclear state transfer.

DOI
10.1103/gdpq-k6lj

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Nuclear coherent population transfer (NCPT) offers numerous potential applications, particularly in next-generation nuclear clocks and nuclear batteries. However, the realization of high fidelity, fast operation, and low energy consumption in NCPT remains so far challenging. Here, we employ physics-informed neural networks (PINNs) to the population transfer in an open three-level nuclear system with spontaneous emission. The method embeds the system's control equations and boundary conditions into the loss function, thereby enabling the automatic learning of optimal laser pulse sequences that drive highly efficient population transfer. We take a short-lived excited state of 172Yb^{172}\mathrm{Yb}172Yb and a long-lived state of 229Th^{229}\mathrm{Th}229Th as representative examples, and systematically compare the performance of the PINNs approach with three conventional control strategies. We show that PINNs can achieve higher transfer efficiency with smaller pulse areas and shorter durations across different lifetime regimes. Our results provide a new perspective to overcome the lifetime limitation and enhance the efficiency of nuclear state transfer.
Nuclear coherent population transfer (NCPT) plays an important role in the exploration and application of atomic nuclei. How to achieve high-fidelity NCPT remains so far challenging. Here, we investigate the complete population transfer of nuclear states. We first consider a cyclic three-level system, based on the mixed-state inverse engineering scheme by adding additional laser fields in an open three-level nuclear system with spontaneous emission. We find the amplitude of the additional field is related to the ratio of the pump and Stokes field amplitudes. As long as an appropriate additional field is selected, complete transfer can be achieved even when the intensities of the pump and Stokes fields are exceedingly low. The transfer efficiency exhibits excellent robustness with respect to laser peak intensity and pulse delay. We demonstrate the effectiveness through examples such as 229Th,223Ra,113Cd^{229}\mathrm{Th}, ^{223}\mathrm{Ra}, ^{113}\mathrm{Cd}229Th,223Ra,113Cd, and 97Tc^{97}\mathrm{Tc}97Tc, which have a long lifetime excited state, as well as 187Re,172Yb,168Er^{187}\mathrm{Re}, ^{172}\mathrm{Yb}, ^{168}\mathrm{Er}187Re,172Yb,168Er, and 154Gd^{154}\mathrm{Gd}154Gd with a short lifetime excited state. Focusing on the case without additional coupling, we further reduce the three-level system to an effective two-level problem. We modify the pump and Stokes pulses by using counterdiabatic driving to implement high-fidelity population transfer. The schemes open up new possibilities for controlling nuclear states.
Physics-informed neural networks (PINNs) represent a methodology that integrates physical equations into neural networks. By incorporating the residuals of physical equations as part of the loss function, PINNs enable the network to learn data features while simultaneously satisfying the constraints imposed by physical laws. The underlying principle of PINNs involves using optimization algorithms to iteratively update the network parameters until the value of a specified physics-informed loss function decreases to an acceptable level, thereby driving the network towards the solution of the differential equations. This approach is not merely a tool but serves as a bridge integrating scientific computing with artificial intelligence, offering novel paradigms for modeling and predicting complex systems. In this paper, we propose a non-Hermitian shortcut to adiabaticity (STA) scheme based on physics-informed neural networks. We utilize the physics-informed neural networks to solve parameterized differential equations, employing the neural networks as an approximating function for the quantum adiabatic evolution process. This provides an interpretable and end-to-end framework (termed STAPINNs) for control-field optimization, distinct from traditional gradient-based approaches like gradient ascent pulse engineering (GRAPE), which require pre-defined pulse parameterization. The parameterized differential equations, along with various physical constraints, are incorporated into the network's loss function. Training the networks allows them to fit the quantum system's evolution process and obtain the driving control function for population inversion. Compared to conventional STA techniques, our approach introduces machine learning into non-Hermitian quantum systems, enabling highly robust and high-fidelity population transfer. Numerical simulations demonstrate that the proposed method significantly outperforms traditional STA protocols under dissipative conditions, achieving fidelities above 0.99 even in the presence of substantial decoherence. Moreover, the framework demonstrates strong generalization across wide parameter ranges and is inherently scalable to multi-level and many-body systems due to the mesh-free, high-dimensional handling capability of PINNs. Neural networks possess strong computational capabilities suitable for generating driving control functions in complex systems, and are equally applicable to non-Hermitian STA techniques. The STAPINNs framework not only enhances control flexibility but also provides a powerful tool for optimizing quantum operations in open and noisy systems.
Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems, delivering powerful applications for various atomic, optical, mechanical, and solid-state systems. In recent years, traditional control techniques based on optimization processes have been translated into efficient artificial intelligence algorithms. Here, we introduce a computational method for optimal quantum control problems via physics-informed neural networks (PINNs). We apply our methodology to open quantum systems by efficiently solving the state-to-state transfer problem with high probabilities, short-time evolution, and using low-energy consumption controls. Furthermore, we illustrate the flexibility of PINNs to solve the same problem under changes in physical parameters and initial conditions, showing advantages in comparison with standard control techniques.
We propose a physics-informed neural network (PINN) scheme for designing shortcuts to adiabaticity in a three-level non-Hermitian quantum system. The PINN is used to solve an inverse control problem in which the state amplitudes and the auxiliary driving field are learned simultaneously from the Schrödinger residual, the initial and target population constraints and a probability conservation constraint on the control pulse. The learned compensation field counteracts the loss of the intermediate state and enables high-fidelity population inversion in an open-system setting. Importantly, the imposed probability conservation is treated as an auxiliary constraint along the learned trajectory rather than as an intrinsic property of the non-Hermitian Hamiltonian. Under this constrained evolution, the Hamiltonian expectation value evaluated on the obtained state remains real within numerical accuracy. Numerical simulations and independent propagation with the fitted control field verify the population inversion and exhibit strong generalization capability over a range of coupling strengths and dissipation rates, as verified by retraining the network independently for each parameter set. The results demonstrate that PINNs provide a flexible inverse design tool for non-Hermitian shortcut to adiabaticity protocols when the governing dynamics and physical constraints are explicitly incorporated into the loss function.
Achieving scalable quantum computing demands high-fidelity operations capable of mitigating population leakage into non-computational states. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful paradigm to unify quantum hardware characterization (inverse problems) and pulse engineering (direct problems), laying the foundational architecture for autonomous quantum processors. However, standard PINN frameworks face severe numerical bottlenecks, such as spectral bias, when attempting to simultaneously solve highly oscillatory multi-level dynamics and optimize continuous control fields under strict global phase constraints. In this work, we propose an enhanced PINN scheme for quantum optimal control (PINNQOC) that circumvents these limitations by incorporating Fourier feature embeddings, dynamic epoch normalization, and an informed pre-training routine. To rigorously evaluate its performance, we systematically benchmark our framework against two premier continuous control solvers: the first-order Krotov method and the second-order Projection Operator Newton Method for Trajectory Optimization (PRONTO). These techniques are applied to implement multiple quantum gates on a truncated three-level fluxonium qubit and a four-level Nitrogen-Vacancy center coupled to a Carbon-13 nuclear spin. Our advanced PINNQOC approach successfully suppresses population leakage while achieving gate fidelities exceeding 99.9%\%%, matching the efficacy of traditional solvers. Finally, we provide a comprehensive analysis of computational times, iteration efficiency, and mean leakage, highlighting the distinct trade-offs and avenues for embedding physics-guided machine learning into automated quantum hardware pipelines.
In this paper, authors present a physics-informed neural networks (PINN) approach for solving the optimal control problem (OCP) of the stochastic Schrödinger equation (SSE), with an emphasis on applications in quantum optics. The SSE models quantum systems under uncertainty, a scenario often encountered in open quantum systems where environmental interactions introduce randomness into the system dynamics. These stochastic dynamics are particularly relevant in quantum optics, where precise control over quantum states is crucial for applications such as quantum computing, secure communication, and measurement protocols. Traditional numerical methods for solving such problems face limitations due to high computational costs and the complexity associated with stochastic partial differential equations. The proposed approach utilises PINN, a type of deep learning model that integrates physical laws directly into the learning process by incorporating loss functions based on governing equations, initial and boundary conditions. The fidelity-based objective function is constructed to achieve the desired quantum state so as to develop an OCP solving algorithm. The proposed work is distinguished between deterministic drift-based training and post-training stochastic validation. Extensive numerical experiments are demonstrated near-unity deterministic fidelity. Further, a systematic architecture study validated that a moderately deep network yielded optimal performance with reduced computational cost. Fidelity dissipation analysis confirmed that the method maintained accuracy even under strong damping. These findings established the PINN as an efficient and physically consistent framework for quantum optimal control in open systems.