Localization of the Grover Walks on Spidernets and Free Meixner Laws
@article{Konno2013LocalizationOT,
title={Localization of the Grover Walks on Spidernets and Free Meixner Laws},
author={N. Konno and N. Obata and E. Segawa},
journal={Communications in Mathematical Physics},
year={2013},
volume={322},
pages={667-695}
}A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the n-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of… CONTINUE READING
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References
SHOWING 1-10 OF 37 REFERENCES
Localization of discrete-time quantum walks on a half line via the CGMV method
- Mathematics, Physics
- 2010
- 28
- PDF
Localization of quantum walks induced by recurrence properties of random walks
- Mathematics, Physics
- 2011
- 38
- PDF
Localization and fractality in inhomogeneous quantum walks with self-duality.
- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2010
- 75
- PDF
Quantum speed-up of Markov chain based algorithms
- Mathematics, Computer Science
- 45th Annual IEEE Symposium on Foundations of Computer Science
- 2004
- 455
- PDF