A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problem
Computing in Science and Engineering
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Graph embedding using quantum commute times
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Graph similarity using interfering quantum walks
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Discriminating graphs through spectral projections
Computer Networks: The International Journal of Computer and Telecommunications Networking
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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.