  Quantum Optimal Control (QOC) supports the advance of quantum technologies by
tackling its problems at the pulse level: Numerical approaches iteratively work
towards a given target by parametrising the applied time-dependent fields with
a finite set of variables. The effectiveness of the resulting optimisation
depends on the complexity of the problem and the number of variables. We
consider different parametrisations in terms of basis functions, asking whether
the choice of the applied basis affects the quality of the optimisation.
Furthermore, we consider strategies to choose the most suitable basis. For the
comparison, we test three different randomisable 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 speed-up by a factor of up to 10 may be crucial for
the optimisation's feasibility. We conclude that a problem-dependent basis
choice is an influential factor for QOC efficiency and provide advice for its
approach.
