Inverse Design with Fourier Neural Operators for Quantum System Control

Real-time quantum control is essential for building scalable quantum devices. For example, molecules have a rich internal structure and can serve as exquisite sensors of fundamental symmetry violations, tests of local position invariance, and dark matter searches. Leveraging this complexity for Beyond Standard Model tests requires fast and precise control of their dynamics. However, existing optimization methods become inefficient in high-dimensional systems due to the high computational cost of conventional solvers. Here, we present a data-driven framework, based on the Fourier Neural Operator (FNO), that learns to simulate both unitary and dissipative population dynamics of hyperfine states in H3O+. The model incorporates a physics-informed embedding that encodes the external driving frequency and black-body radiation temperature, enabling prediction of the state dynamics in a single forward pass. We observe speedups exceeding six orders of magnitude compared to traditional numerical solvers, demonstrating the capability to tune external parameters in real-time. Leveraging the FNO’s speed and differentiability, we demonstrate two inverse-design strategies to control the external frequency drive and reach a target state in minimal time: (i) dense parameter-grid sampling for accurate solutions, and (ii) gradient-based optimization, which requires tuning but scales efficiently. Finally, we use this approach to explore pure-state preparation of H3O+.  These results demonstrate the potential of FNOs in providing both accurate forward simulation and scalable inverse design, opening new avenues for quantum control in high-dimensional, complex systems.