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Article

Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs

1
Department of Applied Mathematics, Yokohama National University, Yokohama 240-8501, Japan
2
Graduate School of Environment Information Sciences, Yokohama National University, Yokohama 240-8501, Japan
3
Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic
*
Author to whom correspondence should be addressed.
Academic Editor: Motoichi Ohtsu
Symmetry 2021, 13(7), 1169; https://doi.org/10.3390/sym13071169
Received: 7 May 2021 / Revised: 23 June 2021 / Accepted: 24 June 2021 / Published: 29 June 2021
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
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. View Full-Text
Keywords: quantum walk; survival probability; attractor eigenspace; dressed photon quantum walk; survival probability; attractor eigenspace; dressed photon
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MDPI and ACS Style

Konno, N.; Segawa, E.; Štefaňák, M. Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs. Symmetry 2021, 13, 1169. https://doi.org/10.3390/sym13071169

AMA Style

Konno N, Segawa E, Štefaňák M. Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs. Symmetry. 2021; 13(7):1169. https://doi.org/10.3390/sym13071169

Chicago/Turabian Style

Konno, Norio, Etsuo Segawa, and Martin Štefaňák. 2021. "Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs" Symmetry 13, no. 7: 1169. https://doi.org/10.3390/sym13071169

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