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

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

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 eigens...

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Main Authors: Norio Konno, Etsuo Segawa, Martin Štefaňák
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Symmetry
Subjects:
quantum walk
survival probability
attractor eigenspace
dressed photon
Online Access:https://www.mdpi.com/2073-8994/13/7/1169
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spelling doaj-393a29994ff84bb0b780dd667921f1632021-07-23T14:09:08ZengMDPI AGSymmetry2073-89942021-06-01131169116910.3390/sym13071169Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite GraphsNorio Konno0Etsuo Segawa1Martin Štefaňák2Department of Applied Mathematics, Yokohama National University, Yokohama 240-8501, JapanGraduate School of Environment Information Sciences, Yokohama National University, Yokohama 240-8501, JapanDepartment of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech RepublicWe 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.https://www.mdpi.com/2073-8994/13/7/1169quantum walksurvival probabilityattractor eigenspacedressed photon
collection DOAJ
language English
format Article
sources DOAJ
author Norio Konno
Etsuo Segawa
Martin Štefaňák
spellingShingle Norio Konno
Etsuo Segawa
Martin Štefaňák
Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
Symmetry
quantum walk
survival probability
attractor eigenspace
dressed photon
author_facet Norio Konno
Etsuo Segawa
Martin Štefaňák
author_sort Norio Konno
title Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
title_short Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
title_full Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
title_fullStr Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
title_full_unstemmed Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs
title_sort relation between quantum walks with tails and quantum walks with sinks on finite graphs
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-06-01
description 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.
topic quantum walk
survival probability
attractor eigenspace
dressed photon
url https://www.mdpi.com/2073-8994/13/7/1169
work_keys_str_mv AT noriokonno relationbetweenquantumwalkswithtailsandquantumwalkswithsinksonfinitegraphs
AT etsuosegawa relationbetweenquantumwalkswithtailsandquantumwalkswithsinksonfinitegraphs
AT martinstefanak relationbetweenquantumwalkswithtailsandquantumwalkswithsinksonfinitegraphs
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