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

@article{Konno2021RelationBQ,
  title={Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs},
  author={Norio Konno and Etsuo Segawa and Martin {\vS}tefaň{\'a}k},
  journal={Symmetry},
  year={2021},
  volume={13},
  pages={1169}
}
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… 
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References

SHOWING 1-10 OF 28 REFERENCES
A dynamical system induced by quantum walk
We consider the Grover walk model on a connected finite graph with two infinite length tails and we set an $\ell^\infty$-infinite external source from one of the tails as the initial state. We show…
Percolated quantum walks with a general shift operator: From trapping to transport
We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry…
Quantum walks on graphs and quantum scattering theory
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply…
Spectral and asymptotic properties of Grover walks on crystal lattice
Modifying quantum walks: A scattering theory approach
We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to…
An Analysis of Absorbing Times of Quantum Walks
TLDR
The absorbing probability and time of quantum walks is introduced and both numerical simulation results and theoretical analyses on Hadamard walks on the line and symmetric walked on the hypercube from the viewpoint of absorbing probabilities and time are given.
Counterintuitive role of geometry in transport by quantum walks
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We…
Quantum walks with infinite hitting times
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite.…
One-dimensional quantum walks
TLDR
A quantum analog of the symmetric random walk, which the authors call the Hadamard walk, is analyzed, which has position that is nearly uniformly distributed in the range after steps, in sharp contrast to the classical random walk.
Electric Circuit Induced by Quantum Walk
We consider the Szegedy walk on graphs adding infinite length tails to a finite internal graph. We assume that on these tails, the dynamics is given by the free quantum walk. We set the $$\ell…
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