论文标题
从经典到量子步行，随机重置网络
From classical to quantum walks with stochastic resetting on networks
论文作者
论文摘要
随机步行是随机过程的基本模型，在包括物理，生物学和计算机科学在内的各个领域的应用。我们在随机重置对任意网络的影响下研究经典和量子随机步行。基于量子随机步行的数学形式主义，我们提供了一个经典和量子步行的框架，其进化是由图形拉普拉斯人决定的。我们通过在经典和量子状态之间插值来研究量子效应对固定和长时间平均概率分布的影响。我们将有关固定和长期平均概率分布的分析结果与不同网络上的数值模拟进行了比较，从而揭示了重置影响经典和量子步行的采样属性的差异。
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.
