A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Graph matching using Random Walks
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Graph Edit Distance from Spectral Seriation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Matching using Interference of Coined Quantum Walks
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Graph embedding using quantum commute times
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Coined quantum walks lift the cospectrality of graphs and trees
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Graph Edit Distance without Correspondence from Continuous-Time Quantum Walks
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
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We consider how continuous-time quantum walks can be used for graph matching, both exact and inexact, and measuring graph similarity. Our approach is to simulate the quantum walk on the two graphs in parallel by using an auxiliary graph that incorporates both graphs. The auxiliary graph allows quantum interference to take place between the two walks. Modelling the resultant interference amplitudes, which result from the differences in the two walks, we calculate probabilities for matches between pairs of vertices from the graphs. Using the Hungarian algorithm on these probabilities we recover a mapping between the graphs. To calculate graph similarity, we combine these probabilities with edge consistency information to give a consistency measure. We analyse our approach experimentally using synthetic graphs.