Machine Learning-aided Optimal Control of a Qubit subject to Environmental Noise

We apply a graybox machine-learning framework to model and control a qubit subject to environmental noise and undergoing Markovian and non-Markovian dynamics. The approach combines physics-informed equations with a RNN-based neural network trained on tomographically complete simulated data. It learns an effective operator that predicts observables accurately, even with strong memory effects. We study Random Telegraph and Ornstein–Uhlenbeck noise, both inducing pure dephasing, across a range of coupling strengths. At weak coupling, the model achieves prediction errors below 1% and maintains good accuracy in more challenging regimes. The trained emulator supports gradient-based quantum optimal control, achieving gate fidelities above 90%, and exceeding 99% in certain regimes. To further enhance the performance of the control protocol, we also implemented an attention-based neural architecture trained directly on gate fidelities. This model refines the emulator’s outputs to improve fidelity predictions and guides control optimization more effectively. As quantum technologies near practical deployment, data-efficient models grounded in physics are increasingly valuable for scalable, noise-aware control.