Curve fitting on a quantum annealer for an advanced navigation method

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-world 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. Similar to the curve fitting task, our findings indicate that quantum annealing is currently only feasible if the routing problem is modeled sufficiently small and sparse.