Computing Graph Edit Distance with Algorithms on Quantum Devices
This work addresses the computational challenge of graph similarity for pattern recognition and machine learning applications, but it is incremental as it adapts existing quantum methods to a new formulation.
The authors tackled the NP-hard problem of computing Graph Edit Distance (GED) by formulating it as a QUBO problem, enabling implementation on quantum devices such as quantum annealers and gate-based computers, with proof-of-principle tests conducted to assess performance.
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.