Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance

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 comparative study of two quantum approaches to computing GED: quantum annealing and variational quantum algorithms, which refer to the two types of quantum hardware currently available, namely 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 the performance of these quantum algorithms.