Finite elements and moving asymptotes accelerate quantum optimal control -- FEMMA

Quantum optimal control is central to designing spin manipulation pulses. Gradient-based pulse optimization can be facilitated by either accelerating gradient evaluation or enhancing the convergence rate. 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, efficiently yielding a joint solution of the spin trajectory and control gradient. The method of moving asymptotes, relying on the ensemble fidelities and gradients, achieves rapid convergence for a target fidelity of 0.995.