Inefficient quantum walks on networks: the role of the density of states

Details Inefficient quantum walks on networks: the role of the density of states Inefficient quantum walks on networks: the role of the density of states

2007-10-18

arxiv.org/abs/0710.3453v1

Physics

Quantum Physics

6 pages, 4 figures

Scientific paper

We show by general arguments that networks whose density of states contains few highly degenerate eigenvalues result in inefficient performances of continuous-time quantum walks (CTQW) over these networks, while systems whose eigenvalues all have the same degeneracy lead to very efficient transport. We exemplify our results by considering CTQW and, for comparison, its classical counterpart, continuous-time random walks, over simple structures, whose eigenvalues and eigenstates can be calculated analytically. Extensions to more complicated, hyper-branched networks are discussed.

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