Computing Graph Edit Distance with Algorithms on Quantum Devices
Abstract
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 graphshaped 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 NPhard 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 gatebased quantum computer, respectively. Considering the current state of noisy intermediatescale quantum computers, we base our study on proofofprinciple tests of their performance.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.10183
 Bibcode:
 2021arXiv211110183I
 Keywords:

 Quantum Physics;
 Computer Science  Machine Learning
 EPrint:
 12 pages, 9 figures. Comments are welcome