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**Hilton Memorial Lecture**

seminars:comb:abstract.200905tam

Given a simple, undirected, regular graph G = (V, E) with adjacency matrix A, a continuous-time quantum walk on G is given by v_{t} = exp(−iAt) v_{0} , where v_{0} is a unit |V|-dimensional vector. The probability distribution induced by such a walk at time t on vertex u is p_{u}(t) = |v_{t}[u]|^{2}. A quantum walk on G is called “uniform mixing” if there is a time t* such that p_{u}(t*) = 1/|V| for all u in V.

Classical random walks on well-behaved graphs are known to mix to the uniform distribution. But this is a property not shared by most quantum walks. This talk describes counter-intuitive differences in mixing phenomena between classical and quantum walks on graphs.

seminars/comb/abstract.200905tam.txt · Last modified: 2020/01/29 14:03 (external edit)

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