多层网络上的离散时间量子游走

Discrete-Time Quantum Walk on Multilayer Networks.

作者信息

Jayakody Mahesh N, Pradhan Priodyuti, Ben Porath Dana, Cohen Eliahu

机构信息

Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.

networks.ai Lab, Department of Computer Science and Engineering, Indian Institute of Information Technology Raichur, Raichur 584135, Karnataka, India.

出版信息

Entropy (Basel). 2023 Nov 30;25(12):1610. doi: 10.3390/e25121610.

DOI:10.3390/e25121610

PMID:38136490

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10743082/

Abstract

A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.

摘要

多层网络是一个强大的平台，为研究具有多种关系类型的各种网络中实体之间的相互作用铺平了道路。本研究探讨了多层网络上离散时间量子行走的动力学。我们推导了具有有限数量节点的无向图上量子行走者波函数系数的递推公式。通过扩展此公式以包含额外的层，我们开发了一个模拟模型来描述多层网络上量子行走者的时间演化。利用傅里叶变换研究了量子行走者的时间平均概率和返回概率，以及多层网络上的格罗弗行走。此外，我们分析了退相干对量子输运的影响，揭示了环境相互作用如何影响多层网络结构上量子行走者的行为。