A fast quantum mechanical algorithm for database search
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Graph matching using Random Walks
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Coined quantum walks lift the cospectrality of graphs and trees
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In this paper we consider how coined quantum walks can be applied to graph matching problems. The matching problem is abstracted using an auxiliary graph that connects pairs of vertices from the graphs to be matched by way of auxiliary vertices. A coined quantum walk is simulated on this auxiliary graph and the quantum interference on the auxiliary vertices indicates possible matches. When dealing with graphs for which there is no exact match, the interference amplitudes together with edge consistencies are used to define a consistency measure. 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. An analysis of the quantum walk in the presence of structural errors between graphs is used as the basis of the consistency measure. We test the performance of this measure on graphs derived from images in the COIL-100 database.