• quantum computing
• quantum clustering
• markov clustering algorithm

Quantum computing is an emerging technology that uses the principles of quantum mechanics to solve problems faster than classical computers. In recent years, a growing number of new quantum methods have been proposed.
In this thesis, we investigate the possibility of realising a quantum version of a well-known graph-based clustering algorithm, the Markov Clustering algorithm. We propose a quantum procedure to show how, by exploiting quantum computing, it is possible to achieve a speedup in terms of time complexity for this algorithm, moving from O(N^3) to O(N^2 log N) for graphs of N nodes.