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
16 Citations
Localization of Discrete Time Quantum Walks on the Glued Trees
- Mathematics, Computer Science
- Entropy
- 2014
- 6
- PDF
Kinematics and dynamics of quantum walks in terms of systems of imprimitivity
- Physics, Mathematics
- 2019
- 5
- PDF
Minicourse IV: Asymptotic Spectral Analysis of Growing Graphs —— a quantum probability point of view
- 2019
- 4
- PDF
A QUANTUM WALK WITH A DELOCALIZED INITIAL STATE: CONTRIBUTION FROM A COIN-FLIP OPERATOR
- Physics, Mathematics
- 2013
- 5
- PDF
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
- 76
- PDF
Quantum speed-up of Markov chain based algorithms
- Mathematics, Computer Science
- 45th Annual IEEE Symposium on Foundations of Computer Science
- 2004
- 458
- PDF