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Quantum Speed-Up of Markov Chain Based Algorithms
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Graph Edit Distance from Spectral Seriation
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ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
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In this paper, we explore analytically and experimentally a quasi-quantum analogue ofthe hitting time of the continuous-time quantum walk on a graph. For the classicalrandom walk, the hitting time has been shown to be robust to errors in edge weightstructure and to lead to spectral clustering algorithms with improved performance. Ouranalysis shows that the quasi-quantum analogue of the hitting time of the continuous-time quantum walk can be determined via integrals of the Laplacian spectrum, calculatedusing Gauss-Laguerre quadrature. We analyse the quantum hitting times with referenceto their classical counterpart. Specifically, we explore the graph embeddings that preservehitting time. Experimentally, we show that the quantum hitting times can be used toemphasise cluster-structure.