Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
On the Digraph of a Unitary Matrix
SIAM Journal on Matrix Analysis and Applications
Edit Distance From Graph Spectra
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Graph matching using Random Walks
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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In this paper we explore how a spectral technique suggested by quantum walks can be used to distinguish non-isomorphic cospectral graphs. Reviewing ideas from the field of quantum computing we recall the definition of the unitary matrices inducing quantum walks. We show how the spectra of these matrices are related to the spectra of the transition matrices of classical walks. Despite this relationship the behaviour of quantum walks is vastly different from classical walks. We show how this leads us to define a new matrix whose spectrum can be used to distinguish between graphs that are otherwise indistinguishable by standard spectral methods.