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 Transport Efficiency of Continuous-Time Quantum Walks on Graphs

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 85
Author(s):  
Luca Razzoli ◽  
Matteo G. A. Paris ◽  
Paolo Bordone
Keyword(s):  
Transport Properties ◽  
Continuous Time ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Transport Processes ◽  
Initial State ◽  
Transport Efficiency ◽  
Harvesting Systems ◽  
Time Quantum ◽  
Modeling Transport

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex that is accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but, in general, they are uncorrelated.

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 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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