Physics-informed Neural Networks (PINNs) show that embedding physical laws directly into the learning objective can significantly enhance the efficiency and physical consistency of neural network solutions. Similar to optimizing loss functions in machine learning, evolutionary algorithms iteratively optimize objective functions by simulating natural selection processes. Inspired by this principle, we ask a natural question: can physical information be similarly embedded into the fitness function of evolutionary algorithms? In this work, we propose Physics-informed Evolution (PIE), a novel framework that incorporates physical information derived from governing physical laws into the evolutionary fitness landscape, thereby extending Physics-informed artificial intelligence methods from machine learning to the broader domain of evolutionary computation. As a concrete instantiation, we apply PIE to quantum control problems governed by the Schrödinger equation, where the goal is to find optimal control fields that drive quantum systems from initial states to desired target states. We validate PIE on three representative quantum control benchmarks: state preparation in V-type three-level systems, entangled state generation in superconducting quantum circuits, and two-atom cavity QED systems. Within the PIE framework, we systematically compare the performance of ten single-objective and five multi-objective evolutionary algorithms. Experimental results demonstrate that by embedding physical information into the fitness function, PIE effectively guides evolutionary search, yielding control fields with high fidelity, low state deviation, and robust performance across different scenarios. Our findings further suggest that the Physics-informed principle extends naturally beyond neural network training to the broader domain of evolutionary computation.
Physics-informed Neural Networks (PINNs) show that embedding physical laws directly into the learning objective can significantly enhance the efficiency and physical consistency of neural network solutions. Similar to optimizing loss functions in machine learning, evolutionary algorithms iteratively optimize objective functions by simulating natural selection processes. Inspired by this principle, we ask a natural question: can physical information be similarly embedded into the fitness function of evolutionary algorithms? In this work, we propose Physics-informed Evolution (PIE), a novel framework that incorporates physical information derived from governing physical laws into the evolutionary fitness landscape, thereby extending Physics-informed artificial intelligence methods from machine learning to the broader domain of evolutionary computation. As a concrete instantiation, we apply PIE to quantum control problems governed by the Schrödinger equation, where the goal is to find optimal control fields that drive quantum systems from initial states to desired target states. We validate PIE on three representative quantum control benchmarks: state preparation in V-type three-level systems, entangled state generation in superconducting quantum circuits, and two-atom cavity QED systems. Within the PIE framework, we systematically compare the performance of ten single-objective and five multi-objective evolutionary algorithms. Experimental results demonstrate that by embedding physical information into the fitness function, PIE effectively guides evolutionary search, yielding control fields with high fidelity, low state deviation, and robust performance across different scenarios. Our findings further suggest that the Physics-informed principle extends naturally beyond neural network training to the broader domain of evolutionary computation.
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.
Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.
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.
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.
Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion (RD) systems. We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings, enabling a controlled comparison between feedforward neural network-based feature maps and parameterized quantum circuit embeddings. The first architecture is the classical embedding feed-forward neural network-based TE-QPINN (FNN-TE-QPINN), while the latter variant is a purely quantum one, referred to as quantum embedding neural network-based TE-QPINN (QNN-TE-QPINN). The proposed framework employs hardware-efficient variational quantum circuits and species-specific readout operators to approximate coupled multi-field dynamics while enforcing governing equations, boundary conditions, and initial conditions through a physics-informed loss function. By isolating the embedding mechanism while keeping the variational ansatz, loss formulation, and optimization procedure fixed, we analyze the impact of embedding design on gradient structure, parameter scaling, and quantum resource requirements. Numerical experiments on one- and two-dimensional RD equations demonstrate that quantum embeddings can replace classical embeddings without degradation in solution accuracy and, in certain regimes, exhibit improved optimization behavior compared to classical PINNs and hybrid quantum models with fixed embeddings. These results provide architectural insight into hybrid quantum PDE solvers and inform the design of resource-efficient quantum physics-informed learning methods.
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.