From classical to quantum walks with stochastic resetting on networks
- URL: http://arxiv.org/abs/2008.00510v2
- Date: Mon, 14 Dec 2020 05:55:02 GMT
- Title: From classical to quantum walks with stochastic resetting on networks
- Authors: Sascha Wald and Lucas B\"ottcher
- Abstract summary: We study classical and quantum random walks under the influence of resetting on arbitrary networks.
Based on the mathematical formalism of quantum walks, we provide a framework of classical and quantum walks.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Random walks are fundamental models of stochastic processes with applications
in various fields including physics, biology, and computer science. We study
classical and quantum random walks under the influence of stochastic resetting
on arbitrary networks. Based on the mathematical formalism of quantum
stochastic walks, we provide a framework of classical and quantum walks whose
evolution is determined by graph Laplacians. We study the influence of quantum
effects on the stationary and long-time average probability distribution by
interpolating between the classical and quantum regime. We compare our
analytical results on stationary and long-time average probability
distributions with numerical simulations on different networks, revealing
differences in the way resets affect the sampling properties of classical and
quantum walks.
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