Wald Sascha, Böttcher Lucas
Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany.
Department of Computational Medicine, University of California, Los Angeles, California 90024, USA.
Phys Rev E. 2021 Jan;103(1-1):012122. doi: 10.1103/PhysRevE.103.012122.
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.
随机游走是随机过程的基本模型，在包括物理、生物和计算机科学在内的各个领域都有应用。我们研究了在随机重置影响下任意网络上的经典和量子随机游走。基于量子随机游走的数学形式，我们提供了一个经典和量子游走的框架，其演化由图拉普拉斯算子决定。我们通过在经典和量子区域之间进行插值，研究了量子效应在平稳和长时间平均概率分布上的影响。我们将关于平稳和长时间平均概率分布的分析结果与不同网络上的数值模拟进行比较，揭示了重置影响经典和量子游走采样特性方式的差异。
