  Distance measures provide the foundation for many popular algorithms in
Machine Learning and Pattern Recognition. Different notions of distance can be
used depending on the types of the data the algorithm is working on. For
graph-shaped data, an important notion is the Graph Edit Distance (GED) that
measures the degree of (dis)similarity between two graphs in terms of the
operations needed to make them identical. As the complexity of computing GED is
the same as NP-hard problems, it is reasonable to consider approximate
solutions. In this paper we present a QUBO formulation of the GED problem. This
allows us to implement two different approaches, namely quantum annealing and
variational quantum algorithms that run on the two types of quantum hardware
currently available: quantum annealer and gate-based quantum computer,
respectively. Considering the current state of noisy intermediate-scale quantum
computers, we base our study on proof-of-principle tests of their performance.
