scholarly journals Effects of Disorder on Non-unitary PT Symmetric Quantum Walks

2017 ◽  
Vol 23 (1) ◽  
pp. 95-103 ◽  
Author(s):  
Ken MOCHIZUKI ◽  
Hideaki OBUSE
Keyword(s):  
Quantum Walks ◽  
Effects Of Disorder ◽  
Symmetric Quantum

scholarly journals Asymmetries in symmetric quantum walks on two-dimensional networks

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
Oliver Mülken ◽  
Antonio Volta ◽  
Alexander Blumen
Keyword(s):  
Quantum Walks ◽  
Two Dimensional ◽  
Symmetric Quantum

scholarly journals Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs

2020 ◽  
Vol 125 (24) ◽  
Author(s):  
Tong Wu ◽  
J. A. Izaac ◽  
Zi-Xi Li ◽  
Kai Wang ◽  
Zhao-Zhong Chen ◽  
...  
Keyword(s):  
Directed Graphs ◽  
Quantum Walks ◽  
Symmetric Quantum

scholarly journals Quantum centrality testing on directed graphs via PT -symmetric quantum walks

2017 ◽  
Vol 96 (3) ◽  
Author(s):  
J. A. Izaac ◽  
J. B. Wang ◽  
P. C. Abbott ◽  
X. S. Ma
Keyword(s):  
Directed Graphs ◽  
Quantum Walks ◽  
Symmetric Quantum

scholarly journals Complete homotopy invariants for translation invariant symmetric quantum walks on a chain

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 95 ◽  
Author(s):  
C. Cedzich ◽  
T. Geib ◽  
C. Stahl ◽  
L. Velázquez ◽  
A. H. Werner ◽  
...  
Keyword(s):  
Practical Method ◽  
Quantum Walks ◽  
Translation Invariance ◽  
Translation Invariant ◽  
Symmetric Quantum ◽  
Space Projection ◽  
Exponential Behaviour ◽  
A Chain ◽  
The One ◽  
Locality Conditions

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv:1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrödinger equation. We show exponential behaviour, and give a practical method for computing the decay constants.

scholarly journals The Topological Classification of One-Dimensional Symmetric Quantum Walks

2017 ◽  
Vol 19 (2) ◽  
pp. 325-383 ◽  
Author(s):  
C. Cedzich ◽  
T. Geib ◽  
F. A. Grünbaum ◽  
C. Stahl ◽  
L. Velázquez ◽  
...  
Keyword(s):  
Quantum Walks ◽  
Topological Classification ◽  
One Dimensional ◽  
Symmetric Quantum
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