Growing Random Graphs with Quantum Rules

• URL: http://arxiv.org/abs/2004.01331v1
• Date: Fri, 3 Apr 2020 01:51:43 GMT
• Title: Growing Random Graphs with Quantum Rules
• Authors: Hamza Jnane (T\'el\'ecom Paris, LTCI, Palaiseau, France), Giuseppe Di Molfetta (Universit\'e publique, CNRS, LIS, Marseille, France, and Quantum Computing Center, Keio University), Filippo M. Miatto (T\'el\'ecom Paris, LTCI, Palaiseau, France)
• Abstract summary: We propose two variations of a model to grow random graphs and trees based on continuous-time quantum walks on the graphs. We investigate several rates of this spontaneous collapse for an individual quantum walker and for two non-interacting walkers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more established techniques. We propose two variations of a model to grow random graphs and trees, based on continuous-time quantum walks on the graphs. After a random characteristic time, the position of the walker(s) is measured and new nodes are attached to the nodes where the walkers collapsed. Such dynamical systems are reminiscent of the class of spontaneous collapse theories in quantum mechanics. We investigate several rates of this spontaneous collapse for an individual quantum walker and for two non-interacting walkers. We conjecture (and report some numerical evidence) that the models are scale-free.

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