Quantum transport on large-scale sparse regular networks by using continuous-time quantum walk

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.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[2]  Ching-Nung Yang,et al.  Quantum Relief algorithm , 2018, Quantum Information Processing.

[3]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[4]  E. Farhi,et al.  Quantum computation and decision trees , 1997, quant-ph/9706062.

[5]  Alexander Blumen,et al.  Asymmetries in symmetric quantum walks on two-dimensional networks (9 pages) , 2005 .

[6]  Maxim Dolgushev,et al.  Universality at Breakdown of Quantum Transport on Complex Networks. , 2015, Physical review letters.

[7]  Walter T. Strunz,et al.  Continuous-time quantum walks on multilayer dendrimer networks. , 2016, Physical review. E.

[8]  Christino Tamon,et al.  One-Dimensional Continuous-Time Quantum Walks , 2004, Quantum Inf. Process..

[9]  M. B. Plenio,et al.  Dephasing-assisted transport: quantum networks and biomolecules , 2008, 0807.4902.

[10]  Alexander Blumen,et al.  Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks , 2011, 1101.2572.

[11]  Colin P. Williams.  Explorations in Quantum Computing, Second Edition , 2011, Texts in Computer Science.

[12]  Matthias Christandl,et al.  Perfect state transfer in quantum spin networks. , 2004, Physical review letters.

[13]  E. Agliari,et al.  Dynamics of continuous-time quantum walks in restricted geometries , 2008, 0810.1184.

[14]  D. Cvetkovic,et al.  Spectra of Graphs: Theory and Applications , 1997 .

[15]  Ching-Nung Yang,et al.  An Efficient and Secure Arbitrary N-Party Quantum Key Agreement Protocol Using Bell States , 2018 .

[16]  Wenjie Liu,et al.  A Quantum-Based Database Query Scheme for Privacy Preservation in Cloud Environment , 2019, Secur. Commun. Networks.

[17]  A. Hora,et al.  Quantum Probability and Spectral Analysis of Graphs , 2007 .

[18]  Volker Pernice,et al.  Quantum transport on small-world networks: a continuous-time quantum walk approach. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  B. McKay.  The expected eigenvalue distribution of a large regular graph , 1981 .

[20]  Piet Van Mieghem,et al.  Graph Spectra for Complex Networks , 2010 .

[21]  Andrew M. Childs,et al.  Spatial search by quantum walk , 2003, quant-ph/0306054.

[22]  Yong Xu,et al.  Multiparty quantum sealed-bid auction using single photons as message carrier , 2016, Quantum Inf. Process..

[23]  Wenjie Liu,et al.  A Unitary Weights Based One-Iteration Quantum Perceptron Algorithm for Non-Ideal Training Sets , 2019, IEEE Access.

[24]  Xinping Xu,et al.  Exact analytical results for quantum walks on star graphs , 2009, 0903.1149.

[25]  X. P. Xu,et al.  Coherent exciton transport on scale-free networks , 2008 .

[26]  Andrew M. Childs,et al.  Universal computation by quantum walk. , 2008, Physical review letters.