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

[2] A. M. Childs, E. Farhi, S. Gutmann. An example of the difference between quantum and classical random walks. Quantum Inf. Process, 1, 35-43(2002).

[3] O. Mülken, A. Blumen. Continuous-time quantum walks: models for coherent transport on complex networks. Phys. Rep., 502, 37-87(2011).

[4] I. Buluta, F. Nori. Quantum simulators. Science, 326, 108-111(2009).

[5] I. M. Georgescu, S. Ashhab, F. Nori. Quantum simulation. Rev. Mod. Phys., 86, 153-185(2014).

[6] A. Aspuru-Guzik, P. Walther. Photonic quantum simulators. Nat. Phys., 8, 285-291(2012).

[7] J. D. Whitfield, C. A. -RosarioRodríguez, A. Aspuru-Guzik. Quantum stochastic walks: a generalization of classical random walks and quantum walks. Phys. Rev. A, 81, 022323(2010).

[8] D. N. Biggerstaff, R. Heilmann, A. A. Zecevik, M. Gräfe, M. A. Broome, A. Fedrizzi, I. Kassal. Enhancing coherent transport in a photonic network using controllable decoherence. Nat. Commun., 7, 11208(2016).

[9] H. Tang, Z. Feng, Y. H. Wang, P. C. Lai, C. Y. Wang, Z. Y. Ye, C. K. Wang, Z. Y. Shi, T. Y. Wang, Y. Chen, J. Gao, X.-M. Jin. Experimental quantum stochastic walks simulating associative memory of Hopfield neural networks. Phys. Rev. Appl., 11, 024020(2019).

[10] T. Eichelkraut, R. Heilmann, S. Weimann, S. Stützer, F. Dreisow, D. N. Christodoulides, S. Nolte, A. Szameit. Mobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun., 4, 143604(2013).

[11] Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, Y. Silberberg. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett., 100, 013906(2008).

[12] A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, C. Silberhorn. Decoherence and disorder in quantum walks: from ballistic spread to localization. Phys. Rev. Lett., 106, 180403(2011).

[13] T. Kitagawa, M. A. Broome, A. Fedrizzi, M. S. Rudner, E. Berg, I. Kassal, A. Aspuruguzik, E. Demler, A. G. White. Observation of topologically protected bound states in photonic quantum walks. Nat. Commun., 3, 882(2012).

[14] L. Banchi, D. Burgarth, M. J. Kastoryano. Driven quantum dynamics: will it blend?. Phys. Rev. X, 7, 041015(2017).

[15] H. Tang, L. Banchi, T. Y. Wang, X. W. Shang, X. Tan, W. H. Zhou, Z. Feng, A. Pal, H. Li, C. Q. Hu, M. S. Kim, X.-M. Jin. Generating Haar-uniform randomness using stochastic quantum walks on a photonic chip. Phys. Rev. Lett., 128, 050503(2022).

[16] S. D. Berry, J. B. Wang. Quantum-walk-based search and centrality. Phys. Rev. A, 82, 042333(2010).

[17] H. Schmitz, R. Matjeschk, C. Schneider, J. Glueckert, M. Enderlein, T. Huber, T. Schaetz. Quantum walk of a trapped ion in phase space. Phys. Rev. Lett., 103, 090504(2009).

[18] J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, R. Han. Experimental implementation of the quantum random-walk algorithm. Phys. Rev. A, 67, 042316(2003).

[19] M. Gong, S. Y. Wang, C. Zha. Quantum walks on a programmable two-dimensional 62-qubit superconducting processor. Science, 372, 948-952(2021).

[20] H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, Y. Silberberg. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett., 100, 170506(2008).

[21] A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismaili, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien. Quantum walks of correlated photons. Science, 329, 1500-1503(2010).

[22] A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, C. Silberhorn. A 2D quantum walk simulation of two-particle dynamics. Science, 336, 55-58(2012).

[23] Y. C. Jeong, C. Di Franco, H. T. Lim, M. S. Kim, Y. H. Kim. Experimental realization of a delayed-choice quantum walk. Nat. Commun., 4, 2471(2013).

[24] Z. Y. Shi, H. Tang, Z. Feng, Y. Wang, Z. M. Li, J. Gao, Y. J. Chang, T. Y. Wang, J. P. Dou, Z. Y. Zhang, Z. Q. Jiao, W. H. Zhou, X. M. Jin. Quantum fast hitting on glued trees mapped on a photonic chip. Optica, 7, 613-618(2020).

[25] H. Tang, X. F. Lin, Z. Feng, J. Y. Chen, J. Gao, K. Sun, C. Y. Wang, P. C. Lai, X. Y. Xu, Y. Wang, L. F. Qiao, A. L. Yang, X. M. Jin. Experimental two-dimensional quantum walk on a photonic chip. Sci. Adv., 4, eaat3174(2018).

[26] H. Tang, C. Di Franco, Z. Y. Shi, T. S. He, Z. Feng, J. Gao, Z. M. Li, Z. Q. Jiao, T. Y. Wang, M. S. Kim, X. M. Jin. Experimental quantum fast hitting on hexagonal graphs. Nat. Photonics, 12, 754-758(2018).

[27] X. Y. Xu, X. W. Wang, D. Y. Chen, C. M. Smith, X.-M. Jin. Quantum transport in fractal networks. Nat. Photonics, 15, 703-710(2021).

[28] D. H. Dunlap, V. M. Kenkre. Dynamic localization of a charged particle moving under the influence of an electric field. Phys. Rev. B, 34, 3625-3633(1986).

[29] K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, M. G. Raizen. Dynamical Bloch band suppression in an optical lattice. Phys. Rev. Lett., 81, 5093-5096(1998).

[30] A. Eckardt, M. Holthaus, H. Lignier, A. Zenesini, D. Ciampini, O. Morsch, E. Arimondo. Exploring dynamic localization with a Bose-Einstein condensate. Phys. Rev. A, 79, 013611(2009).

[31] S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, V. Foglietti. Observation of dynamic localization in periodically curved waveguide arrays. Phys. Rev. Lett., 96, 243901(2006).

[32] A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, Y. S. Kivshar. Polychromatic dynamic localization in curved photonic lattices. Nat. Phys., 5, 271-275(2009).

[33] E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett., 42, 673-676(1979).

[34] V. M. Kenkre, S. Raghavan. Dynamic localization and related resonance phenomena. J. Opt. B, 2, 686-693(2000).

[35] S. Raghavan, V. M. Kenkre, A. R. Bishop. Dynamic localization in spin systems. Phys. Rev. B, 61, 5864-5867(2000).

[36] G. S. Agarwal, W. Harshawardhan. Realization of trapping in a two-level system with frequency-modulated fields. Phys. Rev. A, 50, R4465-R4467(1994).

[37] S. Longhi. Self-imaging and modulational instability in an array of periodically curved waveguides. Opt. Lett., 30, 2137-2139(2005).

[38] I. L. Garanovich, S. Longhi, A. A. Sukhorukov, Y. S. Kivshar. Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep., 518, 1-79(2009).

[39] A. A. Sukhorukov, Y. S. Kivshar. Generation and stability of discrete gap solitons. Opt. Lett., 28, 2345-2347(2003).

[40] Y. Chen, J. Gao, Z. Q. Jiao, K. Sun, L. F. Qiao, H. Tang, X. F. Lin, X. M. Jin. Mapping twisted light into and out of a photonic chip. Phys. Rev. Lett., 121, 233602(2018).

[41] Y. Wang, J. Gao, X. L. Pang, Z. Q. Jiao, H. Tang, Y. Chen, L. F. Qiao, Z. W. Gao, J. P. Dou, A. L. Yang, X. M. Jin. Experimental parity-induced thermalization gap in disordered ring lattices. Phys. Rev. Lett., 122, 013903(2019).

[42] Z. Feng, Z. W. Gao, L. A. Wu, H. Tang, K. Sun, C. Q. Hu, Y. Wang, Z. M. Li, X. W. Wang, Y. Chen, E. Z. Zhang, Z. Q. Jiao, X. Y. Xu, J. Gao, A. L. Yang, X. M. Jin. Photonic Newton’s cradle for remote energy transport. Phys. Rev. Appl., 11, 044009(2019).

[43] Y. Wang, Y. H. Lu, F. Mei, J. Gao, Z. M. Li, H. Tang, S. L. Zhu, S. T. Jia, X.-M. Jin. Direct observation of topology from single-photon dynamics on a photonic chip. Phys. Rev. Lett., 122, 193903(2019).

[44] Y. Wang, Y. H. Lu, J. Gao, Y. J. Chang, R. J. Ren, Z. Q. Jiao, Z. Y. Zhang, X. M. Jin. Topologically protected polarization quantum entanglement on a photonic chip authors. Chip, 1, 100003(2022).

[45] J. Gao, X. W. Wang, W. H. Zhou, Z. Q. Jiao, R. J. Ren, Y. X. Fu, L. F. Qiao, X. Y. Xu, C. N. Zhang, X. L. Pang, H. Li, Y. Wang, X. M. Jin. Quantum advantage with membosonsampling. Chip, 1, 100007(2022).

[46] Y. Wang, Y. H. Lu, J. Gao, K. Sun, Z. Q. Jiao, H. Tang, X.-M. Jin. Quantum topological boundary states in quasi-crystal. Adv. Mater., 31, 1905624(2019).

[47] K. Sun, J. Gao, M. M. Cao, Z. Q. Jiao, Y. Liu, Z. M. Li, E. Poem, A. Eckstein, R. J. Ren, X. L. Pang, H. Tang, I. A. Walmsley, X.-M. Jin. Mapping and measuring large-scale photonic correlation with single-photon imaging. Optica, 6, 244-249(2019).

[48] Y. H. Kim. Quantum interference with beamlike type-II spontaneous parametric down-conversion. Phys. Rev. A, 68, 013804(2003).