Acta Optica Sinica, Volume. 44, Issue 2, 0200001(2024)

Quantum Walk

Peng Xue1、* and Kunkun Wang2
Author Affiliations
  • 1Beijing Computational Science Research Center, Beijing 100084, China
  • 2School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, Anhui, China
  • show less
    References(60)

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

    [2] Ambainis A, Kempe J, Rivosh A. Coins make quantum walks faster[C], 1099-1108(2005).

    [3] Childs A M, Goldstone J. Spatial search by quantum walk[J]. Physical Review A, 70, 022314(2004).

    [4] Aaronson S, Ambainis A. Quantum search of spatial regions[C], 200-209(2003).

    [5] Ambainis A. Quantum walk algorithm for element distinctness[C], 22-31(2004).

    [6] Magniez F, Santha M, Szegedy M. Quantum algorithms for the triangle problem[J]. SIAM Journal on Computing, 37, 413-424(2007).

    [7] Saks M E, Wigderson A. Probabilistic Boolean decision trees and the complexity of evaluating game trees[C], 29-38(2008).

    [8] Farhi E, Gutmann S. Quantum computation and decision trees[J]. Physical Review A, 58, 915-928(1998).

    [9] Aharonov D, Ambainis A, Kempe J et al. Quantum walks on graphs[C], 50-59(2001).

    [10] Xue P, Zhang R, Qin H et al. Experimental quantum-walk revival with a time-dependent coin[J]. Physical Review Letters, 114, 140502(2015).

    [11] Giordani T, Polino E, Emiliani S et al. Experimental engineering of arbitrary qudit states with discrete-time quantum walks[J]. Physical Review Letters, 122, 020503(2019).

    [12] Gratsea A, Lewenstein M, Dauphin A. Generation of hybrid maximally entangled states in a one-dimensional quantum walk[J]. Quantum Science and Technology, 5, 025002(2020).

    [13] Giordani T, Innocenti L, Suprano A et al. Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics[J]. New Journal of Physics, 23, 023012(2021).

    [14] Christandl M, Datta N, Ekert A et al. Perfect state transfer in quantum spin networks[J]. Physical Review Letters, 92, 187902(2004).

    [15] 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).

    [16] Yalçınkaya İ, Gedik Z. Qubit state transfer via discrete-time quantum walks[J]. Journal of Physics A: Mathematical and Theoretical, 48, 225302(2015).

    [17] Zhan X A, Qin H, Bian Z H et al. Perfect state transfer and efficient quantum routing: a discrete-time quantum-walk approach[J]. Physical Review A, 90, 012331(2014).

    [18] Xue P, Zhang R, Bian Z H et al. Localized state in a two-dimensional quantum walk on a disordered lattice[J]. Physical Review A, 92, 042316(2015).

    [19] Rohde P P, Fitzsimons J F, Gilchrist A. Quantum walks with encrypted data[J]. Physical Review Letters, 109, 150501(2012).

    [20] Bae M, Krawec W O. Semi-source independent quantum walk random number generation[C](2021).

    [21] Panda S S, Yasir P A A, Chandrashekar C M. Quantum direct communication protocol using recurrence in k-cycle quantum walks[J]. Physical Review A, 107, 022611(2023).

    [22] Venegas-Andraca S E. Quantum walks: a comprehensive review[J]. Quantum Information Processing, 11, 1015-1106(2012).

    [23] Apers S, Chakraborty S, Novo L et al. Quadratic speedup for spatial search by continuous-time quantum walk[J]. Physical Review Letters, 129, 160502(2022).

    [24] Slate N, Matwiejew E, Marsh S et al. Quantum walk-based portfolio optimisation[J]. Quantum, 5, 513(2021).

    [25] Broome M A, Fedrizzi A, Rahimi-Keshari S et al. Photonic boson sampling in a tunable circuit[J]. Science, 339, 794-798(2013).

    [26] Tillmann M, Dakić B, Heilmann R et al. Experimental boson sampling[J]. Nature Photonics, 7, 540-544(2013).

    [27] Paparo G D, Dunjko V, Makmal A et al. Quantum speedup for active learning agents[J]. Physical Review X, 4, 031002(2014).

    [28] Izaac J A, Zhan X A, Bian Z H et al. Centrality measure based on continuous-time quantum walks and experimental realization[J]. Physical Review A, 95, 032318(2017).

    [29] Wang K K, Shi Y H, Xiao L et al. Experimental realization of continuous-time quantum walks on directed graphs and their application in PageRank[J]. Optica, 7, 1524-1530(2020).

    [30] Shenvi N, Kempe J, Whaley K B. Quantum random-walk search algorithm[J]. Physical Review A, 67, 052307(2003).

    [31] Roy S G, Chakrabarti A. A novel graph clustering algorithm based on discrete-time quantum random walk[M]. Bhattacharyya S, Maulik U, Dutta P. Quantum inspired computational intelligence, 361-389(2017).

    [32] Berry S D, Wang J B. Two-particle quantum walks: entanglement and graph isomorphism testing[J]. Physical Review A, 83, 042317(2011).

    [33] Štefanák M, Kiss T, Jex I et al. The meeting problem in the quantum walk[J]. Journal of Physics A: Mathematical and General, 39, 14965-14983(2006).

    [34] Hoyer S, Meyer D A. Faster transport with a directed quantum walk[J]. Physical Review A, 79, 024307(2009).

    [35] Qu D K, Marsh S, Wang K K et al. Deterministic search on star graphs via quantum walks[J]. Physical Review Letters, 128, 050501(2022).

    [36] Childs A M. Universal computation by quantum walk[J]. Physical Review Letters, 102, 180501(2009).

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

    [38] Lovett N B, Cooper S, Everitt M et al. Universal quantum computation using the discrete-time quantum walk[J]. Physical Review A, 81, 042330(2010).

    [39] 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).

    [40] Zhan X, Xiao L, Bian Z H et al. Detecting topological invariants in nonunitary discrete-time quantum walks[J]. Physical Review Letters, 119, 130501(2017).

    [41] Wang K K, Qiu X Z, Xiao L et al. Simulating dynamic quantum phase transitions in photonic quantum walks[J]. Physical Review Letters, 122, 020501(2019).

    [42] Qiu X Z, Deng T S, Hu Y et al. Fixed points and dynamic topological phenomena in a parity-time-symmetric quantum quench[J]. iScience, 20, 392-401(2019).

    [43] Wang K K, Qiu X Z, Xiao L et al. Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics[J]. Nature Communications, 10, 2293(2019).

    [44] Xiao L, Deng T S, Wang K K et al. Non-Hermitian bulk-boundary correspondence in quantum dynamics[J]. Nature Physics, 16, 761-766(2020).

    [45] Xiao L, Deng T S, Wang K K et al. Observation of non-Bloch parity-time symmetry and exceptional points[J]. Physical Review Letters, 126, 230402(2021).

    [46] Wang K K, Li T Y, Xiao L et al. Detecting non-Bloch topological invariants in quantum dynamics[J]. Physical Review Letters, 127, 270602(2021).

    [47] Wang K K, Xiao L, Budich J C et al. Simulating exceptional non-Hermitian metals with single-photon interferometry[J]. Physical Review Letters, 127, 026404(2021).

    [48] Lin Q, Li T Y, Xiao L et al. Observation of non-Hermitian topological Anderson insulator in quantum dynamics[J]. Nature Communications, 13, 3229(2022).

    [49] Lin Q A, Li T Y, Xiao L et al. Topological phase transitions and mobility edges in non-Hermitian quasicrystals[J]. Physical Review Letters, 129, 113601(2022).

    [50] Bian Z H, Li J A, Qin H et al. Realization of single-qubit positive-operator-valued measurement via a one-dimensional photonic quantum walk[J]. Physical Review Letters, 114, 203602(2015).

    [51] Zhan X A, Zhang X, Li J A et al. Realization of the contextuality-nonlocality tradeoff with a qubit-qutrit photon pair[J]. Physical Review Letters, 116, 090401(2016).

    [52] Zhan X A, Cavalcanti E G, Li J A et al. Experimental generalized contextuality with single-photon qubits[J]. Optica, 4, 966-971(2017).

    [53] Zhan X A, Kurzyński P, Kaszlikowski D et al. Experimental detection of information deficit in a photonic contextuality scenario[J]. Physical Review Letters, 119, 220403(2017).

    [54] Wang K K, Emary C, Zhan X A et al. Enhanced violations of Leggett-Garg inequalities in an experimental three-level system[J]. Optics Express, 25, 31462-31470(2017).

    [55] Wang K K, Knee G C, Zhan X A et al. Optimal experimental demonstration of error-tolerant quantum witnesses[J]. Physical Review A, 95, 032122(2017).

    [56] Wang K K, Emary C, Xu M Y et al. Violations of a Leggett-Garg inequality without signaling for a photonic qutrit probed with ambiguous measurements[J]. Physical Review A, 97, 020101(2018).

    [57] Lovett N B, Crosnier C, Perarnau-Llobet M et al. Differential evolution for many-particle adaptive quantum metrology[J]. Physical Review Letters, 110, 220501(2013).

    [58] Motes K R, Olson J P, Rabeaux E J et al. Linear optical quantum metrology with single photons: exploiting spontaneously generated entanglement to beat the shot-noise limit[J]. Physical Review Letters, 114, 170802(2015).

    [59] Annabestani M, Hassani M, Tamascelli D et al. Multiparameter quantum metrology with discrete-time quantum walks[J]. Physical Review A, 105, 062411(2022).

    [60] Wang K K, Wang X P, Zhan X A et al. Entanglement-enhanced quantum metrology in a noisy environment[J]. Physical Review A, 97, 042112(2018).

    Tools

    Get Citation

    Copy Citation Text

    Peng Xue, Kunkun Wang. Quantum Walk[J]. Acta Optica Sinica, 2024, 44(2): 0200001

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category: Reviews

    Received: May. 5, 2023

    Accepted: Jul. 11, 2023

    Published Online: Dec. 29, 2023

    The Author Email: Xue Peng (gnep.eux@gmail.com)

    DOI:10.3788/AOS230929

    CSTR:32393.14.AOS230929

    Topics