Classical and quantum machine learning are being increasingly applied to various tasks in quantum information technologies. Here, we present an experimental demonstration of quantum control using a physics-informed neural network (PINN). PINN's salient feature is how it encodes the entire control sequence in terms of its network parameters. This feature enables the control sequence to be later adopted to any hardware with optimal time discretization, which contrasts with conventional methods involving a priori time discretization. Here, we discuss two important quantum information tasks: gate synthesis and state preparation. First, we demonstrate quantum gate synthesis by designing a two-qubit CNOT gate and experimentally implementing it on a heteronuclear two-spin nuclear magnetic resonance (NMR) register. Second, we demonstrate quantum state preparation by designing a control sequence to efficiently transfer the thermal state into the long-lived singlet state and experimentally implement it on a homonuclear two-spin NMR register. We present a detailed numerical analysis of the PINN control sequences regarding bandwidth, discretization levels, control field errors, and external noise.
Classical and quantum machine learning are being increasingly applied to various tasks in quantum information technologies. Here, we present an experimental demonstration of quantum control using a physics-informed neural network (PINN). PINN's salient feature is how it encodes the entire control sequence in terms of its network parameters. This feature enables the control sequence to be later adopted to any hardware with optimal time discretization, which contrasts with conventional methods involving a priori time discretization. Here, we discuss two important quantum information tasks: gate synthesis and state preparation. First, we demonstrate quantum gate synthesis by designing a two-qubit CNOT gate and experimentally implementing it on a heteronuclear two-spin nuclear magnetic resonance (NMR) register. Second, we demonstrate quantum state preparation by designing a control sequence to efficiently transfer the thermal state into the long-lived singlet state and experimentally implement it on a homonuclear two-spin NMR register. We present a detailed numerical analysis of the PINN control sequences regarding bandwidth, discretization levels, control field errors, and external noise.
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.
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.
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.
A quantum shortcut to adiabaticity scheme based on physics-informed neural networks is proposed in this work. Compared with traditional shortcut to adiabaticity technology, our method innovatively integrates machine learning methods by employing parameterized physics-informed neural networks to solve parameterized differential equations. The neural networks serve as an approximating function for quantum adiabatic evolution processes, while incorporating parameter-dependent differential equations and various physical constraints as components of the loss function. Through networks training, we effectively simulate quantum system dynamics and derive the driving control field for population inversion. Numerical simulations show that the quantum system can achieve rapid population inversion within significantly reduced time while maintaining high fidelity and exceptional robustness against parameter fluctuations. The neural networks exhibit remarkable computational capabilities, particularly suitable for generating control functions in complex quantum systems. Compared with conventional counter-diabatic driving and transitionless quantum driving methods, this PINN-based framework not only achieves better control performance but also provides the improved practicality for experimental implementations. The success of this method demonstrates its promising applications in quantum control tasks, including but not limited to quantum state preparation, quantum gate optimization, and adiabatic quantum computing acceleration.
Quantum gate design is often represented as pulse optimization, although the physical object that implements a gate is the full controlled evolution generated by the pulse. Here we use physics-informed neural networks to represent single-qubit gate design at this evolution level: the control fields, the Bloch-state trajectories, and the total duration are learned together under the Bloch equation. This changes the optimized object from pulse amplitudes to a differentiable physical process whose structure can be inspected and refined. For rotation gates, the optimized evolutions recover the physical organization expected for bounded single-qubit control, with no prescribed pulse ansatz or duration scan. For a geometric gate, the representation identifies localized bottlenecks in maintaining the geometric condition and turns this diagnosis into feedback, reducing the residual path error while preserving high fidelity. Thus physics-informed learning is used not only to synthesize gates, but also to make optimized quantum controls physically readable, diagnosable, and locally refinable. This process-level view may be especially useful for adapting gates to hardware-specific, task-specific, and locally varying experimental constraints.
Physics-informed neural networks (PINNs) provide a pathway to reunify the simulation and control of quantum systems, in which these two tasks are typically decoupled in traditional strategies. However, most work remains confined to Markovian environments. When applied to non-Markovian systems, standard PINN architectures fail to converge reliably due to multi-objective optimization conflicts arising from the coupled differential equations. To address this fundamental limitation, we extend our previously proposed forked PINN (FPINN) by incorporating a dedicated control branch. By decoupling the optimization objectives at the gradient level via selective gradient flow, our method turns a previously intractable multi-task optimization into a well-conditioned one, allowing simulation and control to be optimized jointly without compromise. Numerical simulations on a two-qubit Heisenberg XXX model confirm that our framework faithfully reproduces the features of non-Markovian dynamics, including decoherence and information backflow. Taking a state-preparation task on the same model as an example, our FPINN achieves higher fidelity than gradient ascent pulse engineering, chopped random basis, and standard PINNs, with the advantage becoming more pronounced as the environment becomes more dissipative and more Markovian. The generated pulses are also noticeably smoother, which is advantageous for experimental implementation. Our framework thus provides a unified, end-to-end differentiable paradigm for simulation and control of open quantum systems, with potential implications for quantum computing, simulation, and control.