Role of bases in quantum optimal control

Quantum optimal control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: numerical approaches iteratively work toward a given target by parametrizing the applied time-dependent fields with a finite set of variables. The effectiveness of the resulting optimization depends on the complexity of the problem and the number of variables. We consider different parametrizations in terms of basis functions, asking whether the choice of the applied basis affects the quality of the optimization. Furthermore, we consider strategies to choose the most suitable basis. For comparison, we test three different randomizable bases---introducing the sinc and sigmoid bases as alternatives to the Fourier basis---on QOC problems of varying complexity. For each problem, the basis-specific convergence rates result in a unique ranking. Especially for expensive evaluations, e.g., in closed loop, a potential speedup by a factor of up to 10 may be crucial for the optimization's feasibility. We conclude that a problem-dependent basis choice is an influential factor for QOC efficiency and provide advice for its approach.