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.
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.
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.
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.
Pulse-level compilation can reduce the depth and calibration overhead associated with decomposing continuously parameterized quantum operations into fixed gate libraries, but conventional optimal control requires a new optimization for each target and can be sensitive to hardware uncertainty. We introduce a physics-informed neural compilation framework that learns a reusable map from continuously parameterized single-qubit gate targets directly to experimentally admissible control waveforms. The compiler is trained end-to-end through differentiable quantum dynamics without precomputed optimal-pulse labels, and its robustness is improved by first diagnosing physically relevant failure modes and then applying tail-risk-aware fine-tuning. On a three-qubit liquid-state nuclear magnetic resonance (NMR) model, the learned compiler generalizes across Haar-distributed single-qubit targets with mean nominal fidelity above 0.99 and generates new pulses in submillisecond inference time. Matched benchmarks reveal complementary advantages: robust gradient ascent pulse engineering (GRAPE) achieves the highest per-target fidelity, whereas the trained neural compiler amortizes the optimization cost across the target family, enabling substantially faster online pulse generation. Risk-aware training substantially broadens tolerance to radio-frequency (RF)-amplitude errors, including perturbations beyond the training range. Experiments on a three-spin NMR processor reproduce the predicted broadening of the RF-tolerance response, although the absolute experimental correlations are lower than the simulated values. These results establish a general workflow combining amortized machine learning, physical sensitivity diagnosis, risk-aware control, optimal-control benchmarking, and hardware testing, providing a route toward fast and robust pulse-level compilation for repeatedly varying quantum operations.
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.
Real-time adaptive control of quantum systems requires rapid generation of robust, high-fidelity pulses across a continuous range of operating conditions. Standard optimization algorithms such as gradient-ascent pulse engineering (GRAPE) solve each instance independently, discarding information between runs and requiring costly reinitialization when parameters change. We present an approach to robust optimal quantum control based on model-based reinforcement learning, in which a single neural network -- embedding the Hamiltonian directly into the training pipeline -- generates robust gates across an entire family of gate configurations, without pre-computed training data. Demonstrated on a single-spin (two-level) system, the trained networks produce pulses for arbitrary rotation angles over a range of pulse durations, detunings, and field inhomogeneities in milliseconds, at fidelities comparable to multi-seed GRAPE. The framework is inherently adaptable: any parameter entering the Hamiltonian can serve as a network input, extending the approach to different systems and control settings. Beyond speed, the network reveals structure in the control landscape: it discovers the same structured phase profiles that appear in GRAPE solutions -- made identifiable through fidelity-invariant symmetry transformations -- but more consistently than independent optimization. This consistency enables smooth interpolation across the entire trained parameter space.
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.