Graph Matching using Interference of Coined Quantum Walks

In this paper we consider how coined quantum walks can be applied to exact graph matching. The matching problem is abstracted using an auxiliary structure that connects pairs of vertices from the graphs to be matched by way of auxiliary vertices. We locate matches using coined quantum walks on this structure. We have tested the algorithm on graphs derived from the NCI molecule database and found it to significantly reduce the space of possible matchings thereby allowing the graphs to be matched directly. We also perform a sensitivity analysis on the algorithm in order to examine its behaviour in the presence of noise