[1] Guillotin-Plantard N, Schott R[M]. Dynamic random walks: theory and applications, 18-35(2006).
[2] Aharonov Y, Davidovich L, Zagury N. Quantum random walks[J]. Physical Review. A, Atomic, Molecular, and Optical Physics, 48, 1687-1690(1993).
[3] Ambainis A. Quantum walks and their algorithmic applications[J]. International Journal of Quantum Information, 1, 507-518(2003).
[4] Childs A M, Cleve R, Deotto E et al. Exponential algorithmic speedup by a quantum walk[C], 59-68(2003).
[5] Reitzner D, Hillery M, Koch D. Finding paths with quantum walks or quantum walking through a maze[J]. Physical Review A, 96, 032323(2017).
[6] Wong T G, Philipp P. Engineering the success of quantum walk search using weighted graphs[J]. Physical Review A, 94, 022304(2016).
[7] Kempe J. Quantum random walks: an introductory overview[J]. Contemporary Physics, 44, 307-327(2003).
[8] Childs A M. Universal computation by quantum walk[J]. Physical Review Letters, 102, 180501(2009).
[9] He Y F, Yang M M, Li Z et al. E-payment protocols based on quantum walk[J]. Acta Optica Sinica, 43, 0527001(2023).
[10] Zhao Y Y, Yu N K, Kurzyński P et al. Experimental realization of generalized qubit measurements based on quantum walks[J]. Physical Review A, 91, 042101(2015).
[11] Štefaňák M, Skoupý S. Perfect state transfer by means of discrete-time quantum walk search algorithms on highly symmetric graphs[J]. Physical Review A, 94, 022301(2016).
[12] Kurzyński P, Wójcik A. Quantum walk as a generalized measuring device[J]. Physical Review Letters, 110, 200404(2013).
[13] Xiao L, Zhan X, Bian Z H et al. Observation of topological edge states in parity-time-symmetric quantum walks[J]. Nature Physics, 13, 1117-1123(2017).
[14] Barkhofen S, Nitsche T, Elster F et al. Measuring topological invariants in disordered discrete-time quantum walks[J]. Physical Review A, 96, 033846(2017).
[15] Zhang W W, Goyal S K, Simon C et al. Decomposition of split-step quantum walks for simulating Majorana modes and edge states[J]. Physical Review A, 95, 052351(2017).
[16] Ionicioiu R, Terno D R. Proposal for a quantum delayed-choice experiment[J]. Physical Review Letters, 107, 230406(2011).
[17] Peruzzo A, Shadbolt P, Brunner N et al. A quantum delayed-choice experiment[J]. Science, 338, 634-637(2012).
[18] Kendon V, Sanders B C. Complementarity and quantum walks[J]. Physical Review A, 71, 022307(2005).
[19] Brun T A, Carteret H A, Ambainis A. Quantum to classical transition for random walks[J]. Physical Review Letters, 91, 130602(2003).
[20] Xue P, Sanders B C. Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin[J]. Physical Review A, 87, 022334(2013).
[21] Brun T A, Carteret H A, Ambainis A. Quantum random walks with decoherent coins[J]. Physical Review A, 67, 032304(2003).
[22] Kendon V, Tregenna B. Decoherence can be useful in quantum walks[J]. Physical Review A, 67, 042315(2003).
[23] Peng Y G. Nuclear-magnetic-resonance-based physical realization of quantum Toffoli gate[J]. Laser & Optoelectronics Progress, 60, 0727002(2023).
[24] Douglas B L, Wang J B. Efficient quantum circuit implementation of quantum walks[J]. Physical Review A, 79, 052335(2009).
[25] Georgopoulos K, Emary C, Zuliani P. Comparison of quantum-walk implementations on noisy intermediate-scale quantum computers[J]. Physical Review A, 103, 022408(2021).
[26] Chong B, Wang J Y, Chen B Y et al. Mixed entanglement of three qubit pure states[J]. Laser & Optoelectronics Progress, 59, 1127001(2022).
[27] Flurin E, Ramasesh V V, Hacohen-Gourgy S et al. Observing topological invariants using quantum walks in superconducting circuits[J]. Physical Review X, 7, 031023(2017).
[28] Dahan R, Gorlach A, Haeusler U et al. Imprinting the quantum statistics of photons on free electrons[J]. Science, 373, eabj7128(2021).