Continuous regulation from quantum walk to classical walk

doi:10.3969/j.issn.1007-5461.2023.06.011

Abstract

Abstract: In order to deeply understand the wave particle duality of microscopic particles, explore the transitions between wave state and particle state, and prepare the coexistence states of multi-path wave state and particle state, a theoretical scheme to realize the continuous transition from wave- to particlestate in quantum walks by introducing quantum control is proposed. The variation of the position distribution and variance of quantum walks with auxiliary bit coefficients is calculated respectively. It is shown that quantum control can make the walker not only in the mixed state of wave and particle, but also in the coherent superposition state. The continuous morphing from wave state to particle state is displayed by the position variance in both the coherent way and the mixed way, and the difference between the mixed state control and the coherent state control is also demonstrated. Quantum walks provide a useful platform for in-depth study on the wave-particle duality of microscopic particles.

Key words: quantum optics, quantum walks, quantum control, coherent superposition

CLC Number:

O431.2

CHEN Bin# , CHEN Tianhao# , ZHANG Rong . Continuous regulation from quantum walk to classical walk[J]. Chinese Journal of Quantum Electronics, 2023, 40(6): 917-923.

References

[1]Motwani R, Raghavan P.Randomized algorithms [M]. Cambridge university press, 1995.
[2]Aharonov Y, Davidovich L, Zagury N.Quantum random walks[J].Physical Review A, 1993, 48(2):1687-1690
[3]Guillotin-Plantard N, Schott R.Dynamic random walks: Theory and applications [M]. Elsevier, 2006.
[4]Childs A M.Universal computation by quantum walk[J].Physical Review Letters, 2009, 102(18):180501-
[5]Venegas-Andraca S E .Quantum walks: a comprehensive review[J].Quantum Information Processing, 2012, 11(5):1015-1106
[6]Ambainis A.Quantum walks and their algorithmic applications[J].International Journal of Quantum Information, 2003, 1(04):507-518
[7]Childs A M, Cleve R, Deotto E, et al.Exponential algorithmic speedup by a quantum walk [C] //Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. 2003: 59-68.
[8]Shenvi N, Kempe J, Whaley K B.Quantum random-walk search algorithm[J].Physical Review A, 2003, 67(5):052307-
[9]Shantanav, Chakraborty, Leonardo, et al..Spatial search by quantum walk is optimal for almost all graphs[J].Physical review letters, 2016, 116(10):100501-
[10]Karski M, F?rster L, Choi J M, et al.Quantum walk in position space with single optically trapped atoms[J].Science, 2009, 325(5937):174-177
[11]Schmitz H, Matjeschk R, Schneider C, et al.Quantum walk of a trapped ion in phase space[J].Physical review letters, 2009, 103(9):090504-
[12]Sansoni L, Sciarrino F, Vallone G, et al.Two-particle bosonic-fermionic quantum walk via integrated photonics[J].Physical review letters, 2012, 108(1):010502-
[13]Ionicioiu R, Terno D R.Proposal for a quantum delayed-choice experiment[J].Physical Review Letters, 2011, 107(23):230406-
[14]Peruzzo A, Shadbolt P, Brunner N, et al.A quantum delayed-choice experiment[J].Science, 2012, 338(6107):634-637
[15]Tang J S, Li Y L, Xu X Y, et al.Realization of quantum Wheeler's delayed-choice experiment[J].Nature Photonics, 2012, 6(9):600-604
[16]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, 2013, 87(2):022334-
[17]Brun T A, Carteret H A, Ambainis A.Quantum to classical transition for random walks[J].Physical review letters, 2003, 91(13):130602-
[18]Kendon V, Sanders B C.Complementarity and quantum walks[J].Physical Review A, 2005, 71(2):022307-
[19]Schreiber A, Cassemiro K N, Poto?ek V, et al.Decoherence and disorder in quantum walks: from ballistic spread to localization[J].Physical review letters, 2011, 106(18):180403-
[20]Arapat Ablimit, YANG Fan, Dildar Hitjan, Aynisa Yasin, BAI Huiting, Aziza Abdukerim, Ahmad Abliz.Quantum coherence evolution of Heisenberg XXZ spin chain within non-Markovian environment[J].Chinese Journal of Quantum Electronics, 2021, 38(3):341-345
[21]阿拉帕提·阿不力米提, 杨帆, 迪丽达尔·海依提江, 阿依尼沙·牙生, 白慧婷, 艾则孜姑丽·阿不都克热木, 艾合买提·阿不力孜.非马尔科夫环境中海森堡自旋链的量子相干演化特性[J].量子电子学报, 2021, 38(3):341-345
[22]GAO Deying, LI Ning.Dynamics and conservation of quantum coherence in a two-body system[J].Chinese Journal of Quantum Electronics, 2021, 38(4):444-453
[23]高德营, 李宁.两体系统量子相干性的动力学和守恒[J].量子电子学报, 2021, 38(4):444-453