Title: Decomposing discrete quantum walks into continuous quantum walks
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The Grover walk is a discrete quantum walk inspired by Grover's search algorithm. It takes place on the arcs of a graph, and alternates between "coin flips" and "arc reversal". In this talk, I show that for a distance regular graph X with diameter d and intertible A(X), the Grover walk on X can be "decomposed" into at most d "commuting" continuous quantum walks. Moreover, each of them is a continuous quantum walk on some distance digraph of the line digraph of X.