Finite elements and moving asymptotes accelerate quantum optimal control - FEMMA

Quantum optimal control is central to designing spin manipulation pulses. While GRAPE efficiently computes gradients, realistic ensemble models make optimization time-consuming. In this work, we accelerated single-spin optimal control by combining the finite element method with the method of moving asymptotes. By treating discretized time as spatial coordinates, the Liouville-von Neumann equation was reformulated as a linear system, yielding gradients solving over an order of magnitude faster than GRAPE with less than one percent relative-accuracy loss. The moving asymptotes further improves convergence, outperforming L-BFGS and approaching Newton-level efficiency.