6,782 research outputs found
Discrete time quantum walks on percolation graphs
Randomly breaking connections in a graph alters its transport properties, a
model used to describe percolation. In the case of quantum walks, dynamic
percolation graphs represent a special type of imperfections, where the
connections appear and disappear randomly in each step during the time
evolution. The resulting open system dynamics is hard to treat numerically in
general. We shortly review the literature on this problem. We then present our
method to solve the evolution on finite percolation graphs in the long time
limit, applying the asymptotic methods concerning random unitary maps. We work
out the case of one dimensional chains in detail and provide a concrete, step
by step numerical example in order to give more insight into the possible
asymptotic behavior. The results about the case of the two-dimensional integer
lattice are summarized, focusing on the Grover type coin operator.Comment: 22 pages, 3 figure
Quantum walk-based search and centrality
We study the discrete-time quantum walk-based search for a marked vertex on a
graph. By considering various structures in which not all vertices are
equivalent, we investigate the relationship between the successful search
probability and the position of the marked vertex, in particular its
centrality. We find that the maximum value of the search probability does not
necessarily increase as the marked vertex becomes more central and we
investigate an interesting relationship between the frequency of the successful
search probability and the centrality of the marked vertex.Comment: 29 pages, 17 figure
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