Generalized open quantum walks on Apollonian networks

Abstract

We introduce the model of generalized open quantum walks on networks using the Transition Operation Matrices formalism. We focus our analysis on the mean first passage time and the average return time in Apollonian networks. These results differ significantly from a classical walk on these networks. We show a comparison of the classical and quantum behaviour of walks on these networks.

23 pages, 8 figures

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Cited by in corpus (11)

• Complex Quantum Networks: a Topical Review
• Central limit theorem for reducible and irreducible open quantum walks
• Quantum Hidden Markov Models based on Transition Operation Matrices
• Quantum Markov chains: recurrence, Schur functions and splitting rules
• Lively quantum walks on cycles
• Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator
• Mean hitting times of quantum Markov chains in terms of generalized inverses
• Quantum walks on hypergraphs
• Mean hitting time formula for positive maps
• Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks
• Characterizing several properties of high-dimensional random Apollonian networks