Order from chaos in quantum walks on cyclic graphs

It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein...

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Published inarXiv.org
Main Authors Panda, Abhisek, Benjamin, Colin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.06.2021
Subjects
Computer Science - Neural and Evolutionary Computing
Mathematics - Quantum Algebra
Physics - Chaotic Dynamics
Physics - Disordered Systems and Neural Networks
Physics - Quantum Physics
Random walk
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Abstract It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.
AbstractList Phys. Rev. A 104, 012204 (2021) It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.
It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.
Author Panda, Abhisek
Benjamin, Colin
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BackLink https://doi.org/10.48550/arXiv.2008.00316$$DView paper in arXiv
https://doi.org/10.1103/PhysRevA.104.012204$$DView published paper (Access to full text may be restricted)
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Snippet It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog...
Phys. Rev. A 104, 012204 (2021) It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this...
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SubjectTerms Computer Science - Neural and Evolutionary Computing
Mathematics - Quantum Algebra
Physics - Chaotic Dynamics
Physics - Disordered Systems and Neural Networks
Physics - Quantum Physics
Random walk
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