Inverse Design of Quantum Control Sequences with Fourier Neural Operators

Quantum optimal control is essential for manipulating molecular ions, but the computational cost of simulating these systems scales exponentially with the dimension of the Hilbert space. This paper addresses the challenge of designing precise control sequences for high-dimensional molecular systems—specifically the hydronium ion (H3O+)—where traditional numerical methods become prohibitively slow.

The researchers developed a framework based on Fourier Neural Operators (FNOs) to act as a fast, differentiable surrogate for quantum dynamics. Unlike standard neural networks that map fixed-size vectors, FNOs learn mappings between functions, allowing them to predict population dynamics across different control parameters (laser frequency, pulse duration, and polarization) in a single forward pass. This surrogate is integrated into a stochastic pulse-measurement planner (FNO-SPMP), which iteratively selects and refines control pulses to steer an initially mixed thermal Boltzmann distribution toward a target pure state.

The FNO surrogate achieved a speedup of up to 1.84 × 10^7 compared to GPU-accelerated numerical propagation. When applied to an 888-dimensional subspace of the hydronium molecule, the FNO-SPMP protocol successfully achieved a target-state population of 0.98 with an 86.2% success rate. Compared to reinforcement learning baselines, the FNO-SPMP approach required roughly half the number of control pulses and reduced the total time for generating pulse sequences from approximately 10 hours to 10–20 minutes.

This work demonstrates that operator-learning surrogates can effectively bypass the computational bottlenecks of traditional quantum control. By enabling rapid inverse design in high-dimensional Hilbert spaces, this methodology facilitates the use of complex polyatomic molecules for quantum information processing and precision spectroscopy, such as probing fundamental constant variations related to dark energy.