Computing Graph Edit Distance with Algorithms on Quantum Devices

TL;DR

This paper introduces a quantum computing approach to approximate the Graph Edit Distance, leveraging current quantum hardware to explore potential advantages in solving NP-hard graph similarity problems.

Contribution

It presents a QUBO formulation of GED enabling implementation on both quantum annealers and gate-based quantum computers, with proof-of-principle tests on existing hardware.

Findings

QUBO formulation suitable for quantum algorithms

Demonstrated proof-of-principle on current quantum hardware

Explored potential of quantum methods for graph similarity measures

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 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.