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Generalized Open Quantum Walks on Apollonian Networks.
Łukasz Pawela1, Piotr Gawron1, Jarosław Adam Miszczak1
1Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland.
Plos One
|July 16, 2015
Summary
We present a new model for generalized open quantum walks on networks. Our findings reveal distinct quantum behaviors in Apollonian networks compared to classical walks, particularly in passage and return times.
Area of Science:
- Quantum mechanics
- Network theory
- Complex systems
Background:
- Quantum walks offer a quantum analogue to classical random walks.
- Understanding quantum dynamics on complex networks is crucial for quantum information processing.
Purpose of the Study:
- To introduce a model for generalized open quantum walks on networks.
- To analyze quantum walk behavior on Apollonian networks, focusing on key metrics.
Main Methods:
- Utilized the Transition Operation Matrices formalism.
- Calculated mean first passage time and average return time for quantum walks.
- Compared quantum walk dynamics with classical random walks on Apollonian networks.
Main Results:
- Generalized open quantum walks exhibit significantly different behaviors than classical walks on Apollonian networks.
- Quantified differences in mean first passage and average return times.
Conclusions:
- The study highlights the unique properties of quantum walks in complex network structures.
- Provides a comparative analysis of classical versus quantum transport phenomena on Apollonian networks.
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