Graph Edit Distance without Correspondence from Continuous-Time Quantum Walks

We consider how continuous-time quantum walks can be used for graph matching. We focus in detail on both exact and inexact graph matching, and consider in depth the problem of measuring graph similarity. We commence by constructing an auxiliary graph, in which the two graph to be matched are co-joined by a layer of indicator nodes (one for each potential correspondence between a pair of nodes). We simulate a continuous time quantum walk in parallel on the two graphs. The layer of connecting indicator nodes in the auxiliary graph allow quantum interference to take place between the two walks. The interference amplitudes on the indicator nodes are determined by differences in the two walks. We show how these interference amplitudes can be used to compute graph edit distances without explicitly determining node correspondences.