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Keywords = attractor eigenspace

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21 pages, 810 KB  
Article
Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
by Norio Konno, Etsuo Segawa and Martin Štefaňák
Symmetry 2021, 13(7), 1169; https://doi.org/10.3390/sym13071169 - 29 Jun 2021
Cited by 6 | Viewed by 2119
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 [...] Read more.
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 graph theory. Full article
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
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