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arXiv · 2105.03111

Relation between quantum walks with tails and quantum walks with sinks on finite graphs

Norio Konno·Etsuo Segawa·Martin Štefaňák
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Abstract

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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Norio Konno, Etsuo Segawa, Martin Štefaňák. 2021-05-07. Relation between quantum walks with tails and quantum walks with sinks on finite graphs. https://arxiv.org/abs/2105.03111

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