[1] Guillotin-Plantard N, Schott R. Dynamic random walks: Theory and application［M］. Amsterdam: Elsevier, 2006.

[2] Aharonov Y, Davidovich L, Zagury N. Quantum random walks［J］. Phys Rev A, 1993, 48(2): 1687-1690.

[3] Ambainis A. Quantum walks and their algorithmic applications［J］. International Journal of Quantum Information, 2003, 1(4): 507-518.

[4] Childs A M, Cleve R, Deotto E, et al. Quantum walks on graphs［C］. Proc 35th ACM Symposium on Theory of Computing (STOC), 2003: 59-68.

[5] Shenvi N, Kempe J. Quantum random-walk search algorithm［J］. Phys Rev A, 2003, 67(5): 052307.

[6] Kempe J. Quantum random walks: An introductory overview［J］. Contemporary Physics, 2003, 44(4), 307-327.

[7] Oliveira A C, Portugal R, Donangelo R. Decoherence in two-dimensional quantum walks［J］. Phys Rev A, 2006, 74(1): 012312.

[8] Brun T A, Carteret H A, Ambainis A. Quantum to classical transition for random walks［J］. Phys Rev Lett, 2003, 91(13): 130602.

[9] Crespi A, Osellame R, Ramponi R, et al. Anderson localization of entangled photons in an integrated quantum walk［J］. Nature Photonics, 2013, 7(4), 322-328.

[10] Kitagawa T, Rudner M S, Berg E, et al. Exploring topological phases with quantum walks［J］. Phys Rev A, 2010, 82(3): 033429.

[11] Kitagawa T, Broome M A, Fedrizzi A, et al. Observation of topologically protected bound states in photonic quantum walks［J］. Nature Communications, 2012, 3: 882.

[12] Childs A M. Universal computation by quantum walk［J］. Phys Rev Lett, 2009, 102(18): 180501.

[13] Childs A M, Gosset D, Webb Z. Universal computation by multiparticle quantum walk［J］. Science, 2013, 339(6121): 791-794.

[14] Lovett N B, Cooper S, Everitt M, et al. Universal quantum computation using the discrete-time quantum walk［J］. Phys Rev A, 2010, 81(4): 042330.

[15] Kurzyński P, Wòjcik A. Discrete-time quantum walk approach to state transfer［J］. Phys Rev A, 2011, 83(6): 062315.

[16] Du J, Li H, Xu X, et al. Experimental implementation of the quantum random-walk algorithm［J］. Phys Rev A, 2003, 67(4): 042316.

[17] Ryan C A, Laforest M, Boileau J C, et al. Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor［J］. Phys Rev A, 2005, 72(6): 062317.

[18] Lu D, Zhu J, Zou P, et al. Experimental implementation of a quantum random-walk search algorithm using strongly dipolar coupled spins［J］. Phys Rev A, 2010, 81(2): 022308.

[19] Zahringer F, Kirchmair G, Gerritsma R, et al. Realization of a quantum walk with one and two trapped ions［J］. Phys Rev Lett, 2010, 104(10): 100503.

[20] Schmitz H, Matjeschk R, Schneider Ch, et al. Quantum walk of a trapped ion in phase space［J］. Phys Rev Let, 2009, 103(9): 090504.

[21] Broome M A, Fedrizzi A, Lanyon B P, et al. Discrete single-photon quantum walks with tunable decoherence［J］. Phys Rev Lett, 2010, 104(15): 153602.

[22] Schreiber A, Cassemiro K N, Potocek V, et al. Photons walking the line: A quantum walk with adjustable coin operations［J］. Phys Rev Lett, 2010, 104(5): 050502.

[23] Schreiber A, Cassemiro K N, Potocek V, et al. Decoherence and disorder in quantum walks: From ballistic spread to localization［J］. Phys Rev Lett, 2011, 106(18): 180403.

[24] Peruzzo A, Lobino M, Matthews J C F, et al. Quantum walks of correlated photons［J］. Science, 2010, 329(5998): 1500-1503.

[25] Schreiber A, Gábris A, Rohde P, et al. A 2D quantum walk simulation of two-particle dynamics［J］. Science, 2012, 336(6077): 55-58.

[26] Crespi A, Osellame R, Ramponi R, et al. Anderson localization of entangled photons in an integrated quantum walk［J］. Nature Photonics, 2013, 7(4): 322-328.

[27] Owens J O, Broome M A, Biggerstaff N, et al. Two-photon quantum walks in an elliptical direct-write waveguide array［J］. New Journal of Physics, 2011, 13(7): 075003.

[28] Huang Jiang, Xie Qin, Zhou Kaiwei, et al. Sudden death and sudden birth of bound entanglement［J］. Laser & Optoelectronics Progress, 2015, 52(4): 042701.

[29] Lu Daoming. Time evolution of chaotic field in diffusion process［J］. Laser & Optoelectronics Progress, 2015, 52(4): 042702.

[30] Sansoni L, Sciarrino F, Vallone G, et al. Two-particle bosonic-fermionic quantum walk via integrated photonics［J］. Phys Rev Lett, 2012, 108(1): 010502.

[31] Zhang R, Xue P. Two-dimensional quantum walk with position-dependent phase defects［J］. Quantum Information Processing, 2014, 13(8): 1825-1839.

[32] Xue P, Sanders B C, Leibfried D. Quantum walk on a line for a trappedion［J］. Phys Rev Lett, 2009, 103(18): 183602.

[33] Wòjcik A, uczak T, Kurzyński P, et al. Trapping a particle of a quantum walk on the line［J］. Phys Rev A, 2012, 85(1): 012329.

[34] Segev M, Silberberg Y, Christodoulides D N. Anderson localization of light［J］. Nature Photonics, 2013, 7(3): 197-204.

[35] Li Z J, Izaac J A, Wang J B. Position-defect-induced reflection, trapping, transmission, and resonance in quantum walks［J］. Phys Rev A, 2013, 87(1): 012314.

[36] Lu Daoming. Solution of master equation of density matrix in interaction system of atom with thermal reservoir［J］. Laser & Optoelectronics Progress, 2016, 53(9): 092701.