  Routing problems are a common optimization problem in industrial
applications, which occur on a large scale in supply chain planning. Due to
classical limitations for solving NP-hard problems, quantum computing hopes to
improve upon speed or solution quality. Several suggestions have been made for
encodings of routing problems to solve them with variational quantum
algorithms. However, for an end user it is hard to decide a priori which
encoding will give the best solutions according to their needs. In this work,
we investigate different encodings for the Travelling Salesperson Problem. We
compare their scaling and performance when using the Quantum Approximate
Optimization Algorithm and the Variational Quantum Eigensolver and provide a
clear guide for users when to choose which encoding. For small instances, we
find evidence that the permutation encoding can yield good results since it
does not suffer from feasibility issues.
