Quantum Walks on Finite Graphs

2013 ◽  
pp. 85-120
Author(s):  
Renato Portugal
Keyword(s):  
Quantum Walks ◽  
Finite Graphs

scholarly journals A remark on zeta functions of finite graphs via quantum walks

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Yusuke Higuchi ◽  
Norio Konno ◽  
Iwao Sato ◽  
Etsuo Segawa
Keyword(s):  
Zeta Functions ◽  
Quantum Walks ◽  
Finite Graphs

Photonic Quantum Walks on Finite Graphs and with Non-Localised Initial States

CLEO: 2015 ◽  
2015 ◽  
Author(s):  
Sonja Barkhofen ◽  
Fabian Elster ◽  
Thomas Nitsche ◽  
Jaroslav Novotný ◽  
Aurél Gábris ◽  
...  
Keyword(s):  
Quantum Walks ◽  
Finite Graphs ◽  
Initial States

Localization of quantum walks on finite graphs

2016 ◽  
Vol 25 (12) ◽  
pp. 120303
Author(s):  
Yang-Yi Hu ◽  
Ping-Xing Chen
Keyword(s):  
Quantum Walks ◽  
Finite Graphs

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

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1169
Author(s):  
Norio Konno ◽  
Etsuo Segawa ◽  
Martin Štefaňák
Keyword(s):  
Graph Theory ◽  
Random Walk ◽  
Survival Probability ◽  
Quantum Walks ◽  
Time Limit ◽  
Finite Graphs ◽  
Long Time

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.

scholarly journals Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Sho Kubota ◽  
Etsuo Segawa ◽  
Tetsuji Taniguchi
Keyword(s):  
Quantum Walks ◽  
Adjacency Matrices

scholarly journals Mass-conserving diffusion-based dynamics on graphs

2021 ◽  
pp. 1-49
Author(s):  
J.M BUDD ◽  
Y. VAN GENNIP
Keyword(s):  
Multiscale Modeling ◽  
Classification Problems ◽  
Theoretical Justification ◽  
Finite Graphs ◽  
Discrete Scheme ◽  
Cahn Equation ◽  
Separating Flows ◽  
Special Case ◽  
Appl Math ◽  
Convergence Of The Scheme

An emerging technique in image segmentation, semi-supervised learning and general classification problems concerns the use of phase-separating flows defined on finite graphs. This technique was pioneered in Bertozzi and Flenner (2012, Multiscale Modeling and Simulation10(3), 1090–1118), which used the Allen–Cahn flow on a graph, and was then extended in Merkurjev et al. (2013, SIAM J. Imaging Sci.6(4), 1903–1930) using instead the Merriman–Bence–Osher (MBO) scheme on a graph. In previous work by the authors, Budd and Van Gennip (2020, SIAM J. Math. Anal.52(5), 4101–4139), we gave a theoretical justification for this use of the MBO scheme in place of Allen–Cahn flow, showing that the MBO scheme is a special case of a ‘semi-discrete’ numerical scheme for Allen–Cahn flow. In this paper, we extend this earlier work, showing that this link via the semi-discrete scheme is robust to passing to the mass-conserving case. Inspired by Rubinstein and Sternberg (1992, IMA J. Appl. Math.48, 249–264), we define a mass-conserving Allen–Cahn equation on a graph. Then, with the help of the tools of convex optimisation, we show that our earlier machinery can be applied to derive the mass-conserving MBO scheme on a graph as a special case of a semi-discrete scheme for mass-conserving Allen–Cahn. We give a theoretical analysis of this flow and scheme, proving various desired properties like existence and uniqueness of the flow and convergence of the scheme, and also show that the semi-discrete scheme yields a choice function for solutions to the mass-conserving MBO scheme.

scholarly journals Quantum walks simulating non-commutative geometry in the Landau problem

2021 ◽  
Vol 62 (6) ◽  
pp. 062205
Author(s):  
F. Debbasch
Keyword(s):  
Quantum Walks

scholarly journals General condition of quantum teleportation by one-dimensional quantum walks

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Tomoki Yamagami ◽  
Etsuo Segawa ◽  
Norio Konno
Keyword(s):  
General Condition ◽  
Quantum Teleportation ◽  
Quantum Walks ◽  
One Dimensional
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