• Chinese Optics Letters
  • Vol. 18, Issue 5, 052701 (2020)
Gaoyan Zhu1、2, Lei Xiao1、2, Bingzi Huo2, and Peng Xue2、*
Author Affiliations
  • 1Department of Physics, Southeast University, Nanjing 211189, China
  • 2Beijing Computational Science Research Center, Beijing 100084, China
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    DOI: 10.3788/COL202018.052701 Cite this Article Set citation alerts
    Gaoyan Zhu, Lei Xiao, Bingzi Huo, Peng Xue. Photonic discrete-time quantum walks [Invited][J]. Chinese Optics Letters, 2020, 18(5): 052701 Copy Citation Text show less

    Abstract

    Quantum walks, a counterpart of classical random walks, have many applications due to their neoteric features. Since they were first proposed, quantum walks have been explored in many fields theoretically and have also been demonstrated experimentally in various physical systems. In this paper, we review the experimental realizations of discrete-time quantum walks in photonic systems with different physical structures, such as bulk optics and time-multiplexed framework. Then, some typical applications using quantum walks are introduced. Finally, the advantages and disadvantages of these physical systems are discussed.
    U^=S^C^,(1)

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    |Ψt=U^t|Ψin.(2)

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    |ΨinU^12(||1||1)U^12[(||2||)|0+||2]U^122(||3+||1+||12||1||3).(3)

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    ||0,(4)

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    12(||1||1).(5)

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    12[(||2||)|0+||2].(6)

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    122(||3+||1+||12||1||3).(7)

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    |,mq-plate|,m+1,|,mq-plate|,m1.(8)

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    |H,0=|R+L2,0,(9)

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    |ΨinU^12(||1||1)U^12[(||2||)|0+||2]U^122(||3+||1+||12||1||3),(10)

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    |H12(|H+|V),|V12(|H|V).(11)

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    |H,iBD|H,i1,|V,iBD|V,i1.(12)

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    Δt=Δl/c,(13)

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    (N1)(l1+l)<N(l2+l),(14)

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    CEOM(x)=(eiϕH(x)00eiϕV(x)),(15)

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    H=(1111)/2,(16)

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    Sx=i,jZ|i1,jWi,j||0C0|+|i+1,jWi,j||1C1|,(17)

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    Sy=i,jZ|i,j1Wi,j||0C0|+|i,j+1Wi,j||1C1|,(18)

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    H=(1111111111111111)/2,(19)

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    Sx=i,jZ|i1,j1Wi,j||0C0|+|i1,j+1Wi,j||1C1|+|i+1,j1Wi,j||2C2|+|i+1,j+1Wi,j||3C3|.(20)

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    U=TyR(θ2)TxR(θ1),(21)

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    Tx=x|x+1x|||+|x1x|||,Ty=y|y+1y|||+|y1y|||.(22)

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    U=eiH(θ1θ2)t/.(23)

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    U(θ1,θ2)=TR(θ2)T+R(θ1),(24)

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    Gaoyan Zhu, Lei Xiao, Bingzi Huo, Peng Xue. Photonic discrete-time quantum walks [Invited][J]. Chinese Optics Letters, 2020, 18(5): 052701
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