Growing Random Graphs with Quantum Rules

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.

arXiv commentIn Proceedings QSQW 2020, arXiv:2004.01061

References in corpus (6)

• Emergence of scaling in random networks
• Spatial search by quantum walk
• Identification of clusters of investors from their real trading activity in a financial market
• Quantum walks public key cryptographic system
• From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
• Dynamical Triangulation Induced by Quantum Walk