Quantum transport on large-scale sparse regular networks by using continuous-time quantum walk
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Quantum transport on large-scale sparse regular networks by using continuous-time quantum walk Xi Li1 · Hanwu Chen2,3 · Mingyou Wu1 · Yue Ruan4 · Zhihao Liu2,3 · Jianing Tan3 Received: 30 January 2019 / Accepted: 16 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A large-scale sparse regular network (LSSRN) is a type of sparse regular graph that has been broadly studied in the field of complex networks. The conventional approach of eigendecomposition cannot be used to achieve quantum transport based on continuous-time quantum walks (CTQW) on LSSRNs. This work proposes a new approach, namely the counting of walks on an LSSRN, to investigate the characteristics of quantum transport based on CTQW. The estimations of transport probability indicate that (1) it is more likely for a node to return to itself in quantum transport than in classical transport, (2) with the increase in the network degree, the return probability decays more quickly and (3) the transport probability starting from a given vertex to another vertex decreases when the distance between them increases.
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Hanwu Chen [email protected] Zhihao Liu [email protected] Xi Li [email protected] Mingyou Wu [email protected] Yue Ruan [email protected] Jianing Tan [email protected]
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School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China
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Key Laboratory of Computer Network and Information Integration in Southeast University, Ministry of Education, Nanjing 210096, China
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School of Computer Science and Engineering, Southeast University, Nanjing 210096, China
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School of Computer Science, Anhui University of Technology, Maanshan 243005, People’s Republic of China 0123456789().: V,-vol
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X. Li et al.
Keywords Continues-time quantum walk · Random walk · Complex network · Sparse regular graph
1 Introduction With the development of quantum computation and quantum information [1,2], a growing number of applications, from algorithms to secure protocols, have adopted quantum information technology [3–7], and the transport of the quantum state on complex networks is one such application [8–10]. The complex network model has attracted a significant amount of attention and has been widely applied to various types of practical problems in the past two decades, including the Internet, the World Wide Web, biological networks, utility networks (including the transmission of energy, waste, water, etc.), social networks, human brain networks, etc [11]. The transfer of energy or matter over a complex network is the basis of various physical, chemical and biological processes [8]. The dynamics of the transport process depend on both the transport models and the network topology. Different transport models have different transport characteristics when applied on the same network. Two transport model types are considered in this work, namely classical transport based on the classical continuous-time random walk (CTRW) and coherent exciton transport based on the continuous-time quan
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