Practical Nitrogen-vacancy (NV)-center magnetometry requires both accurate modeling of open quantum dynamics and robust control under environmental drift. However, commonly used perturbative descriptions inadequately capture dissipative processes, while existing control strategies remain individually limited: open-loop protocols cannot adapt to unknown frequency variations, Lyapunov feedback typically converges only to a neighborhood of the optimal sensing state, and reinforcement learning alone lacks stability guarantees and requires extensive training. Here, we develop a Lindblad-based framework for one effective NV center that explicitly incorporates relaxation and dephasing; the analytical model does not describe a collective many-NV ensemble. We introduce a dissipation-triggered feedback mechanism that restores high-sensitivity states following spontaneous emission events. Building on this model, we propose a hybrid control architecture that combines Lyapunov stabilization with reinforcement-learning-based adaptive correction to compensate unknown Hamiltonian drift. Robustness tests over detuning and microwave-amplitude variations show that hybrid attains the highest quantum Fisher information (QFI), substantially lower cross-realization dispersion than pure reinforcement learning (RL) and robust gradient-ascent pulse engineering (GRAPE), faster fixed-budget learning than pure RL, and substantially lower offline dynamical-propagation cost with smoother control modulation than robust GRAPE. This physics-informed and data-driven strategy provides a robust and resource-efficient approach for maintaining high QFI in realistic NV sensing environments.
Practical Nitrogen-vacancy (NV)-center magnetometry requires both accurate modeling of open quantum dynamics and robust control under environmental drift. However, commonly used perturbative descriptions inadequately capture dissipative processes, while existing control strategies remain individually limited: open-loop protocols cannot adapt to unknown frequency variations, Lyapunov feedback typically converges only to a neighborhood of the optimal sensing state, and reinforcement learning alone lacks stability guarantees and requires extensive training. Here, we develop a Lindblad-based framework for one effective NV center that explicitly incorporates relaxation and dephasing; the analytical model does not describe a collective many-NV ensemble. We introduce a dissipation-triggered feedback mechanism that restores high-sensitivity states following spontaneous emission events. Building on this model, we propose a hybrid control architecture that combines Lyapunov stabilization with reinforcement-learning-based adaptive correction to compensate unknown Hamiltonian drift. Robustness tests over detuning and microwave-amplitude variations show that hybrid attains the highest quantum Fisher information (QFI), substantially lower cross-realization dispersion than pure reinforcement learning (RL) and robust gradient-ascent pulse engineering (GRAPE), faster fixed-budget learning than pure RL, and substantially lower offline dynamical-propagation cost with smoother control modulation than robust GRAPE. This physics-informed and data-driven strategy provides a robust and resource-efficient approach for maintaining high QFI in realistic NV sensing environments.
Superconducting-qubit control is fundamentally constrained by decoherence, finite bandwidth, and hardware-limited drive amplitudes, making high-fidelity state preparation sensitive to optimizer initialization under non-convex open-system dynamics. We propose a hybrid reinforcement learning (RL)–quantum optimal control (QOC) pipeline in which a lightweight, tabular, model-free RL agent is trained offline in simulation to generate feasible, bounded seed pulses, which are subsequently refined via GRAPE under Lindblad dynamics. Hard amplitude constraints are enforced consistently across both stages, ensuring strict feasibility throughout optimization. Performance is evaluated using a budget-matched protocol based on fidelity evaluations (F-evals), enabling controlled comparison with random-start multi-start GRAPE. On a transmon-like qubit benchmark with relaxation and dephasing, RL warm-starting reduces the median online refinement effort in the adopted finite-difference GRAPE implementation from 7568 to 3543 F-evals (2.14× reduction) while achieving terminal state fidelity ≥0.995 under identical constraints and evaluation budgets. We provide a theoretical interpretation of the improvement in terms of basin-of-attraction probability shaping in constrained control landscapes and an amortized cost analysis showing that the offline RL cost is recovered after a small number of reuse cycles. The results support the view that learning-based initialization can improve warm-start quality relative to uninformed feasible multi-start in constrained open-system quantum-control benchmarks, while broader practical comparison against stronger physics-guided seeds remains for future work.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation.Open-loop control tasks have been successfully solved using optimization techniques, including methods such as gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics.For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes.In this work, we introduce feedback GRAPE, which borrows some concepts from model-free reinforcement learning to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics.We illustrate its power considering various scenarios based on cavity-QED setups.Our method yields interpretable feedback strategies for state preparation and stabilization in the presence of noise.Our approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multiqubit devices to linear-optics quantum computation strategies, quantum enhanced sensing with adaptive measurements, and quantum error correction.
We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with reduced sample complexity over model-free RL. Sample complexity is defined as the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an autodifferentiable ODE, parametrized by a learnable Hamiltonian ansatz, to represent the model approximating the environment, whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic computational experiments incorporating single-shot measurements, arbitrary Hilbert space truncations, and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE (gradient ascent pulse engineering) for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm, which we apply to nitrogen vacancy (NV) centers and transmons, is well suited for controlling partially characterized one- and two-qubit systems.
Quantum sensors offer control flexibility during estimation by allowing manipulation by the experimenter across various parameters. For each sensing platform, pinpointing the optimal controls to enhance the sensor's precision remains a challenging task. While an analytical solution might be out of reach, machine learning offers a promising avenue for many systems of interest, especially given the capabilities of contemporary hardware. We have introduced a versatile procedure capable of optimizing a wide range of problems in quantum metrology, estimation, and hypothesis testing by combining model-aware reinforcement learning (RL) with Bayesian estimation based on particle filtering. To achieve this, we had to address the challenge of incorporating the many non-differentiable steps of the estimation in the training process, such as measurements and the resampling of the particle filter. Model-aware RL is a gradient-based method, where the derivatives of the sensor's precision are obtained through automatic differentiation (AD) in the simulation of the experiment. Our approach is suitable for optimizing both non-adaptive and adaptive strategies, using neural networks or other agents. We provide an implementation of this technique in the form of a Python library called qsensoropt, alongside several pre-made applications for relevant physical platforms, namely NV centers, photonic circuits, and optical cavities. This library will be released soon on PyPI. Leveraging our method, we've achieved results for many examples that surpass the current state-of-the-art in experimental design. In addition to Bayesian estimation, leveraging model-aware RL, it is also possible to find optimal controls for the minimization of the Cramér-Rao bound, based on Fisher information.
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.