[1] |
SHOR P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer[J]. SIAM Review, 1999, 41(2):303-332.
|
[2] |
GROVER L K. A fast quantum mechanical algorithm for database search[C]// Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, 1996:212-219.
|
[3] |
KADIAN K, GARHWAL S, KUMAR A. Quantum walk and its application domains: a systematic review[J]. Computer Science Review, 2021,41:100419.
|
[4] |
VENEGAS-ANDRACA S E. Quantum walks: a comprehensive review[J]. Quantum Information Processing, 2012, 11(5):1015-1106.
|
[5] |
SHAO C, LI Y, LI H. Quantum algorithm design: techniques and applications[J]. Journal of Systems Science and Complexity, 2019, 32(1):375-452.
|
[6] |
KENDON V. Decoherence in quantum walks-a review[J]. Mathematical Structures in Computer Science, 2007, 17(6):1169-1220.
|
[7] |
PEARSON K. The problem of the random walk[J]. Nature, 1905, 72(1865):294-294.
|
[8] |
PAGE L, BRIN S, MOTWANI R, et al. The pagerank citation ranking: bringing order to the web[R]. Stanford InfoLab, 1999.
|
[9] |
SHEN J, DU Y, WANG W, et al. Lazy random walks for superpixel segmentation[J]. IEEE Transactions on Image Processing, 2014, 23(4):1451-1462.
|
[10] |
SARKAR P, MOORE A W. Random walks in social networks and their applications: a survey[M]//Social Network Data Analytics. Springer, Boston, MA, 2011:43-77.
|
[11] |
AHARONOV Y, DAVIDOVICH L, ZAGURY N. Quantum random walks[J]. Physical Review A, 1993, 48(2):1687.
|
[12] |
STRAUCH F W. Connecting the discrete-and continuous-time quantum walks[J]. Physical Review A, 2006, 74(3):030301.
|
[13] |
KEMPE J. Quantum random walks: an introductory overview[J]. Contemporary Physics, 2003, 44(4):307-327.
|
[14] |
PORTUGAL R. Quantum walks and search algorithms[M]. Springer, 2018.
|
[15] |
SZEGEDY M. Quantum speed-up of Markov chain based algorithms[C]// 45th Annual IEEE Symposium on Foundations of Computer Science. IEEE, 2004:32-41.
|
[16] |
MAGNIEZ F, NAYAK A, ROLAND J, et al. Search via quantum walk[J]. SIAM Journal on Computing, 2011, 40(1):142-164.
|
[17] |
MAGNIEZ F, NAYAK A, RICHER P C, et al. On the hitting times of quantum versus random walks[J]. Algorithmica, 2012, 63(1):91-116.
|
[18] |
KROVI H, MAGNIEZ F, OZOLS M, et al. Quantum walks can find a marked element on any graph[J]. Algorithmica, 2016, 74(2):851-907.
|
[19] |
DOHOTARU C, HØYER P. Controlled quantum amplification[C]// 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), 2017.
|
[20] |
AMBAINIS A, KEMPE J, RIVOSH A. Coins make quantum walks faster. 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 2005:1099-1108.
|
[21] |
AARONSON S, AMBAINIS A. Quantum search of spatial regions[C]// 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings. IEEE, 2003:200-209.
|
[22] |
CHILDS A M, GOLDSTONE J. Spatial search by quantum walk[J]. Physical Review A, 2004, 70(2):022314.
|
[23] |
TULSI A. Faster quantum-walk algorithm for the two-dimensional spatial search[J]. Physical Review A, 2008, 78(1):012310.
|
[24] |
HOYER P, KOMEILI M. Efficient qantum walk on the grid with multiple marked elements[C]// 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017), 2017.
|
[25] |
AMBAINIS A, GILYÉN A, JEFFERY S, et al. Quadratic speedup for finding marked vertices by quantum walks[C]// Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020:412-424.
|
[26] |
RHODES M L, WONG T G. Quantum walk search on the complete bipartite graph[J]. Physical Review A, 2019, 99(3):032301.
|
[27] |
RHODES M L, WONG T G. Search by lackadaisical quantum walks with nonhomogeneous weights[J]. Physical Review A, 2019, 100(4):042303.
|
[28] |
WONG T G, WÜNSCHER K, LOCKHART J, et al. Quantum walk search on Kronecker graphs[J]. Physical Review A, 2018, 98(1):012338.
|
[29] |
TANAKA H, SABRI M, PORTUGAL R. Spatial search on Johnson graphs by discrete-time quantum walk[J]. Journal of Physics A: Mathematical and Theoretical, 2022.
|
[30] |
JANMARK J, MEYER D A, WONG T G. Global symmetry is unnecessary for fast quantum search[J]. Physical Review Letters, 2014, 112(21):210502.
|
[31] |
BUHRMAN H, DURR C, HEILIGMAN M, et al. Quantum algorithms for element distinctness[C]// Proceedings 16th Annual IEEE Conference on Computational Complexity. IEEE, 2001:131-137.
|
[32] |
AARONSON S, SHI Y. Quantum lower bounds for the collision and the element distinctness problems[J]. Journal of the ACM (JACM), 2004, 51(4):595-605.
|
[33] |
AMBAINIS A. Quantum walk algorithm for element distinctness[J]. SIAM Journal on Computing, 2007, 37(1):210-239.
|
[34] |
MAGNIEZ F, SANTHA M, SZEGEDY M. Quantum algorithms for the triangle problem[J]. SIAM Journal on Computing, 2007, 37(2):413-424.
|
[35] |
FEYNMAN R P. Quantum mechanical computers[J]. Optics News, 1985, 11(2):11-20.
|
[36] |
CHILDS A M. Universal computation by quantum walk[J]. Physical Review Letters, 2009, 102(18):180501.
|
[37] |
CHILDS A M, GOSSET D, WEBB Z. Universal computation by multiparticle quantum walk[J]. Science, 2013, 339(6121):791-794.
|
[38] |
LOVETT N B, COOPER S, EVERITT M, et al. Universal quantum computation using the discrete-time quantum walk[J]. Physical Review A, 2010, 81(4):042330.
|
[39] |
UNDERWOOD M S, FEDER D L. Universal quantum computation by discontinuous quantum walk[J]. Physical Review A, 2010, 82(4):042304.
|
[40] |
KURZYŃSKI P, WÓJCIK A. Quantum walk as a generalized measuring device[J]. Physical Review Letters, 2013, 110(20):200404.
|
[41] |
ZHAO Y, YU N, KURZYŃSKI P, et al. Experimental realization of generalized qubit measurements based on quantum walks[J]. Physical Review A, 2015, 91(4):042101.
|
[42] |
BIAN Z, LI J, QIN H, et al. Realization of single-qubit positive-operator-valued measurement via a one-dimensional photonic quantum walk[J]. Physical Review Letters, 2015, 114(20):203602.
|
[43] |
LI Z, ZHANG H, ZHU H. Implementation of generalized measurements on a qudit via quantum walks[J]. Physical Review A, 2019, 99(6):062342.
|
[44] |
HOU Z, TANG J F, SHANG J, et al. Deterministic realization of collective measurements via photonic quantum walks[J]. Nature Communications, 2018, 9(1):1-7.
|
[45] |
WANG Y, SHANG Y, XUE P. Generalized teleportation by quantum walks[J]. Quantum Information Processing, 2017, 16(9):1-13.
|
[46] |
CHATTERJEE Y, DEVRARI V, BEHERA B K, et al. Experimental realization of quantum teleportation using coined quantum walks[J]. Quantum Information Processing, 2020, 19(1):1-14.
|
[47] |
LI H J, CHEN X B, WANG Y L, et al. A new kind of flexible quantum teleportation of an arbitrary multi-qubit state by multi-walker quantum walks[J]. Quantum Information Processing, 2019, 18(9):1-16.
|
[48] |
YALÇINKAYA İ, GEDIK Z. Qubit state transfer via discrete-time quantum walks[J]. Journal of Physics A: Mathematical and Theoretical, 2015, 48(22):225302.
|
[49] |
ZHAN X, QIN H, BIAN Z, et al. Perfect state transfer and efficient quantum routing: a discrete-time quantum-walk approach[J]. Physical Review A, 2014, 90(1):012331.
|
[50] |
SHANG Y, WANG Y, LI M, et al. Quantum communication protocols by quantum walks with two coins[J]. EPL (Europhysics Letters), 2019, 124(6):60009.
|
[51] |
SHANG Y, LI M. Experimental realization of state transfer by quantum walks with two coins[J]. Quantum Science and Technology, 2019, 5(1):015005.
|
[52] |
ŠTEFAŇÁK M, SKOUPÝ S. Perfect state transfer by means of discrete-time quantum walk search algorithms on highly symmetric graphs[J]. Physical Review A, 2016, 94(2):022301.
|
[53] |
ŠTEFAŇÁK M, SKOUPÝ S. Perfect state transfer by means of discrete-time quantum walk on complete bipartite graphs[J]. Quantum Information Processing, 2017, 16(3):1-14.
|
[54] |
SANTOS R A M. Quantum state transfer on the complete bipartite graph[J]. Journal of Physics A: Mathematical and Theoretical, 2022, 55(12):125301.
|
[55] |
SKOUPÝ S, ŠTEFAŇÁK M. Quantum-walk-based state-transfer algorithms on the complete M-partite graph[J]. Physical Review A, 2021, 103(4):042222.
|
[56] |
LI M, SHANG Y. Entangled state generation via quantum walks with multiple coins[J]. npj Quantum Information, 2021, 7(1):1-8.
|
[57] |
CHEN C, DING X, QIN J, et al. Observation of topologically protected edge states in a photonic two-dimensional quantum walk[J]. Physical Review letters, 2018, 121(10):100502.
|
[58] |
TANG H, LIN X F, FENG Z, et al. Experimental two-dimensional quantum walk on a photonic chip[J]. Science Advances, 2018, 4(5):eaat3174.
|
[59] |
QIANG X, LOKE T, MONTANARO A, et al. Efficient quantum walk on a quantum processor[J]. Nature Communications, 2016, 7(1):1-6.
|
[60] |
XUE P, SANDERS B C, LEIBFRIED D. Quantum walk on a line for a trapped ion[J]. Physical Review Letters, 2009, 103(18):183602.
|
[61] |
YAN Z, ZHANG Y R, GONG M, et al. Strongly correlated quantum walks with a 12-qubit superconducting processor[J]. Science, 2019, 364(6442):753-756.
|
[62] |
GONG M, WANG S, ZHA C, et al. Quantum walks on a programmable two-dimensional 62-qubit superconducting processor[J]. Science, 2021, 372(6545):948-952.
|
[63] |
KARSKI M, FÖRSTER L, CHOI J M, et al. Quantum walk in position space with single optically trapped atoms[J]. Science, 2009, 325(5937):174-177.
|