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Register a new userRelation between quantum walks with tails and quantum walks with sinks on finite graphs
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We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in the graph theory.
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We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new class of coined quantum walk by a special choice of quantum coins determined by corresponding quantum graph, called quantum graph walk. We show that a stationary state of quantum graph walk describes the eigenfunction of the quantum graph.
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Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized at their initial position. Eigenvectors of time evolution operators are deeply related to the amount of trapping. In this paper, we introduce the analytical method for the eigenvalue problem using a transfer matrix to quantitatively evaluate localization by deriving the time-averaged limit distribution and reveal the condition of strong trapping.
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