Relation between quantum walks with tails and quantum walks with sinks on finite graphs
Mathematical Physics
2021-05-10 v1 math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2105.03111,
title = {Relation between quantum walks with tails and quantum walks with sinks on finite graphs},
author = {Norio Konno and Etsuo Segawa and Martin Štefaňák},
journal= {arXiv preprint arXiv:2105.03111},
year = {2021}
}
Comments
26 pages; 4 figures