Clustering quantum Markov chains on trees associated with open quantum random walks

Luigi Accardi; Amenallah Andolsi; Farrukh Mukhamedov; Mohamed Rhaima; Abdessatar Souissi; Luigi Accardi; Amenallah Andolsi; Farrukh Mukhamedov; Mohamed Rhaima; Abdessatar Souissi

doi:10.3934/math.20231170

AIMS Mathematics

2023, Volume 8, Issue 10: 23003-23015. doi: 10.3934/math.20231170

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Research article

Clustering quantum Markov chains on trees associated with open quantum random walks

1.
Centro Vito Volterra, Università di Roma "Tor Vergata", Roma I-00133, Italy
2.
Nuclear Physics and High Energy Physics Research Unit, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis 2092, Tunisia
3.
Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, United Arab Emirates
4.
Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
5.
Mathematical Physics, Quantum Modeling and Mechanical Design, University of Carthage, Carthage 1054, Tunisia

Received: 14 May 2023 Revised: 15 June 2023 Accepted: 19 June 2023 Published: 19 July 2023
MSC : 35Qxx, 60Jxx, 81-XX

In networks, the Markov clustering (MCL) algorithm is one of the most efficient approaches in detecting clustered structures. The MCL algorithm takes as input a stochastic matrix, which depends on the adjacency matrix of the graph network under consideration. Quantum clustering algorithms are proven to be superefficient over the classical ones. Motivated by the idea of a potential clustering algorithm based on quantum Markov chains, we prove a clustering property for quantum Markov chains (QMCs) on Cayley trees associated with open quantum random walks (OQRW).
- Markov chains,
- quantum theory,
- clustering, Cayley tree,
- random walks
Citation: Luigi Accardi, Amenallah Andolsi, Farrukh Mukhamedov, Mohamed Rhaima, Abdessatar Souissi. Clustering quantum Markov chains on trees associated with open quantum random walks[J]. AIMS Mathematics, 2023, 8(10): 23003-23015. doi: 10.3934/math.20231170

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Abstract

In networks, the Markov clustering (MCL) algorithm is one of the most efficient approaches in detecting clustered structures. The MCL algorithm takes as input a stochastic matrix, which depends on the adjacency matrix of the graph network under consideration. Quantum clustering algorithms are proven to be superefficient over the classical ones. Motivated by the idea of a potential clustering algorithm based on quantum Markov chains, we prove a clustering property for quantum Markov chains (QMCs) on Cayley trees associated with open quantum random walks (OQRW).

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