  We explore the applicability of quantum annealing to the approximation task
of curve fitting. To this end, we consider a function that shall approximate a
given set of data points and is written as a finite linear combination of
standardized functions, e.g., orthogonal polynomials. Consequently, the
decision variables subject to optimization are the coefficients of that
expansion. Although this task can be accomplished classically, it can also be
formulated as a quadratic unconstrained binary optimization problem, which is
suited to be solved with quantum annealing. Given the size of the problem stays
below a certain threshold, we find that quantum annealing yields comparable
results to the classical solution. Regarding a real-word use case, we discuss
the problem to find an optimized speed profile for a vessel using the framework
of dynamic programming and outline how the aforementioned approximation task
can be put into play.
