scholarly journals Continuous-time quantum walks: Models for coherent transport on complex networks

2011 ◽  
Vol 502 (2-3) ◽  
pp. 37-87 ◽  
Author(s):  
Oliver Mülken ◽  
Alexander Blumen
Keyword(s):  
Complex Networks ◽  
Continuous Time ◽  
Quantum Walks ◽  
Coherent Transport ◽  
Time Quantum

scholarly journals Marking Vertices to Find Graph Isomorphism Mapping Based on Continuous-Time Quantum Walk

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 586 ◽  
Author(s):  
Xin Wang ◽  
Yi Zhang ◽  
Kai Lu ◽  
Xiaoping Wang ◽  
Kai Liu
Keyword(s):  
Polynomial Time ◽  
Continuous Time ◽  
Graph Isomorphism ◽  
Quantum Walk ◽  
Isomorphism Problem ◽  
Quantum Walks ◽  
Regular Graphs ◽  
Structure Preserving ◽  
Topological Structures ◽  
Time Quantum

The isomorphism problem involves judging whether two graphs are topologically the same and producing structure-preserving isomorphism mapping. It is widely used in various areas. Diverse algorithms have been proposed to solve this problem in polynomial time, with the help of quantum walks. Some of these algorithms, however, fail to find the isomorphism mapping. Moreover, most algorithms have very limited performance on regular graphs which are generally difficult to deal with due to their symmetry. We propose IsoMarking to discover an isomorphism mapping effectively, based on the quantum walk which is sensitive to topological structures. Firstly, IsoMarking marks vertices so that it can reduce the harmful influence of symmetry. Secondly, IsoMarking can ascertain whether the current candidate bijection is consistent with existing bijections and eventually obtains qualified mapping. Thirdly, our experiments on 1585 pairs of graphs demonstrate that our algorithm performs significantly better on both ordinary graphs and regular graphs.

scholarly journals Continuous-time quantum walks on spatially correlated noisy lattices

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Matteo A. C. Rossi ◽  
Claudia Benedetti ◽  
Massimo Borrelli ◽  
Sabrina Maniscalco ◽  
Matteo G. A. Paris
Keyword(s):  
Continuous Time ◽  
Quantum Walks ◽  
Spatially Correlated ◽  
Time Quantum

scholarly journals Transport properties of continuous-time quantum walks on Sierpinski fractals

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
Zoltán Darázs ◽  
Anastasiia Anishchenko ◽  
Tamás Kiss ◽  
Alexander Blumen ◽  
Oliver Mülken
Keyword(s):  
Transport Properties ◽  
Continuous Time ◽  
Quantum Walks ◽  
Time Quantum

scholarly journals PERFECT STATE TRANSFER, GRAPH PRODUCTS AND EQUITABLE PARTITIONS

2011 ◽  
Vol 09 (03) ◽  
pp. 823-842 ◽  
Author(s):  
YANG GE ◽  
BENJAMIN GREENBERG ◽  
OSCAR PEREZ ◽  
CHRISTINO TAMON
Keyword(s):  
Continuous Time ◽  
Quantum Walks ◽  
Perfect State ◽  
Graph Products ◽  
State Transfer ◽  
Time Quantum ◽  
Perfect State Transfer

We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on generalizations of the double cones and variants of the Cartesian graph products (which include the hypercube). We also describe a generalization of the path collapsing argument (which reduces questions about perfect state transfer to simpler weighted multigraphs) for graphs with equitable distance partitions.

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