• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Robust Quantum Computing in Decoherence-Free Subspaces with Double-Dot Spin Qubits?

    2014-03-12 08:44:09FENGZhiBo馮志波ZHANGChunLi張春麗andZHOUYunQing周運清
    Communications in Theoretical Physics 2014年2期

    FENG Zhi-Bo(馮志波), ZHANG Chun-Li(張春麗),and ZHOU Yun-Qing(周運清)

    1School of Electric Engineering,Xuchang University,Xuchang 461000,China

    2Department of Physics,Zhejiang Ocean University,Zhoushan 316000,China

    1 Introduction

    With theoretical signif i cance and practical applications,quantum information processing has been a fascinating research f i eld.[1]As solid-state artif i cial atom,semiconductor quantum dot can be manipulated controllably and scaled up easily,then it is one of the most promising candidates for quantum state engineering.[2?3]Based on the electronic spin degrees of freedom,double-dot qubits have made remarkable progress on coherent manipulations and precise readouts of quantum states.[4?5]In the past few years,one-dimensional transmission line resonator(TLR)on a chip has attracted particular attention.[6?7]The quantized cavity f i eld generated by the TLR can be coupled to semiconductor quantum dots,which thus forms a circuit quantum electrodynamics(QED)device.[8?12]Very recently,the strong couplings between semiconductor quantum dots and superconducting microwave cavity have been realized experimentally,[13?16]which are very helpful to perform quantum information processing with hybrid systems.

    For semiconductor spin-based qubits,decoherence effect is still one of the main obstacles to build a quantum computer.[1,17?18]Many fault-tolerant strategies for removing noise eあects have been proposed,such as geometric quantum computing,[19]dynamical decoupling,[20]and optimal operation.[21]As a quantum error-avoiding way,decoherence-free subspace(DFS)encoding can be resistant to the collective noises according to the symmetry of system-bath interaction.[22?25]Especially,the DFS encoding may be a more robust approach to f i ght against quantum errors,when the decoherence eあects are caused mainly by the collective noises in a multiqubit system.However,how to physically perform the DFS-encoded logic gates on double-dot qubits is highly desirable for fault-tolerant quantum computing.

    In this paper,we propose a theoretical scheme for performing robust quantum gates on the DFS-encoded qubits inside a circuit QED architecture.Through the TLR-assisted interaction,the couplings between any pair of qubits can be realized controllably and selectively,by which we construct a set of universal quantum gates on the DFS-encoded qubits.It is found that the gate f i delities can be enhanced remarkably by eliminating the collective noises.The proposal may provide the potential opportunity of implementing the robust quantum computing with solid-state hybrid systems.

    The rest of paper is organized as follows.In Sec.2,many semiconductor double-dots in a circuit QED are illustrated.In Sec.3,we present the controllable interqubit couplings. Logic quantum gates on the DFS-encoded qubits are given in Sec.4.We analyze the f i delity enhancement by DFS-encoding way in Sec.5.Finally,discussion and conclusion are drawn in Sec.6.

    2 Double-Dot Qubits in a Circuit QED

    As schematically depicted in Fig.1(a),a high Q onedimensional TLR(of length Lxalong the x direction)has a single-mode frequency ωr.[9,26]Many semiconduc-tor double-dot systems are arranged along the x direction.The k-th double-dot is electrically coupled to the TLR via capacitance Ck,k=1,2,...,n.Through a capacitor Ci(Co),the TLR is connected to the input(output)wiring of the waveguide.[9?10]In the considered circuit QED device,the TLR generates a quantized standing-wave f i eld.Here the quantum dots are all situated at the antinodes to achieve the maximum coupling strengths between the dots and the cavity f i eld.Each double-dot includes two adjacent quantum dots,in which two electrons exist totally.And the double-dots are electrically biased to create potential diあerences Δ.[9,12]

    For the operated double-dot,an external f i eld Bz(≈100 mT)is applied along the z axis.The spin parallel states[|(1,1)T+〉=|↑↑〉,|(1,1)T?〉=|↓↓〉]are split from the spin antiparallel ones[|(1,1)T0〉=(|↑↓〉+|↓↑〉)/|(1,1)S〉=(| ↑↓〉? | ↓↑〉)/],where(nu,nd)denotes nu(nd)electrons localized in the up(down)dot,T±,0stand for spin-triplet states,S denotes a spin-singlet one.[9?10]The doubly occupied state|(0,2)S〉is coupled to|(1,1)S〉only,whose tunneling energy is T,see Fig.1(b),and the potential diあerence between them is Δ.Due to the Pauli spin blockade,the coupling between|(0,2)S〉and|(1,1)T0〉is suppressed eあectively.[27?28]In the considered subspace{|(1,1)S〉,|(0,2)S〉},the system Hamiltonian is reduced to[9?10]

    The eigenstates of Hamiltonian of Eq.(1)are|+〉=sinα|(0,2)S〉+cosα|(1,1)S〉and|?〉=cosα|(0,2)S〉?sinα|(1,1)S〉,with α =tan?1[?2T/(+ Δ)].The above Hamiltonian can be rewritten as H= ?ωσz/2,in which the transition frequency between|?〉and|+〉is ω(= ω?? ω+)=/?,ω?(ω+)is the eigenfrequency of the level state|?〉(|+〉),and σz=|?〉〈?|?|+〉〈+|is a Pauli operator.With the experimentally available parameters,the dependences of ωjon Δ are shown in Fig.1(c),where T/2π =1.5 GHz is f i xed,j= ?,+.At the optimal working point Δ=0,the states

    constitute the spin-based qubit states,which are insensitive to the f l uctuations of control electronics.[9]

    Fig.1 (a)Many double-dots are coupled to a one-dimensional TLR.(b)Level structure associated with spin states in a double-dot system.(c)Eigenfrequencies ωjof level states|j〉vs.potential diあerence Δ,with j= ?,+.ωjand Δ are given in units of 2π GHz.

    3 Controllable Interqubit Couplings

    Through the gate capacitance Ck,the k-th double-dot situated at the antinode interacts with the quantized cavity f i eld.Under the rotating wave approximation,the interaction Hamiltonian within the basis{|+〉k,|?〉k}is given by[12,29]Hrk=?λk(a?σ?k+aσ+k),the coupling strength is λk=(eCk/2?Ckt)with Cktbeing the total capacitance of the double-dot,a?(a)denotes the creation(annihilation)operator associated with photon,σ?k=|+〉k〈?|and σ+k=|?〉k〈+|represent the level inversion operators.For simplicity,the coupling coeきcients λkare assumed to be identical hereafter,namely,λk= λ.

    Consider any two qubits,say k=1,2.The total Hamiltonian of the composite system involving the two qubits and cavity f i eld is described by HΣ=H0+H′,[29]where H0= ωra?a+ ω1σ1z/2+ ω1σ2z/2,and H′=δ12σ2z/2+ ∑k=1,2(λa?σ?ke?iδkt+H.c.),with ω1,2being the respective transition frequencies of qubits 1 and 2,a detuning is δ12= ω2? ω1,and we take ? =1.In the dispersive regions,the detunings are much larger than coupling strengths,δ1r,2r(=|ω1,2? ωr|)? λ.Given the cavity f i eld is initially in the vacuum state,H′can be further transformed into the eあective Hamiltonian[30]

    where the coupling strength isJ12= λ2(δ1r+δ2r)/(2δ1rδ2r).Through the cavity-mediated interaction,the interqubit coupling can be realized eあectively.

    The states of qubits 1 and 2 span a product space as{|jj′〉},with j′=+,?.For an arbitrary state vector,it can be expressed as ψ(t)= ∑ Cjj′|jj′〉,where Cjj′ are the normalization coeきcients.The time evolution of ψ(t)is governed by the diあerential equation,i(dψ(t)/dt)=Heあψ(t).We focus on the dependence of coherent transition between|+?〉and|?+〉on the detuning δ12.Physically,with the f i xed transition frequency ω1,the changeable parameter δ12can be obtained only by tuning ω2.

    Utilizing the experimentally feasible parameters,ω1/2π =5 GHz, ωr/2π =6.75 GHz[15]and λ/2π =0.125 GHz,[9]we numerically calculate the occupied probabilities of states|+?〉and|?+〉versus the detuning δ12.Note that we consider the maximum probability of|?+〉and the minimum one of|+?〉,and postulate that the initial state is|+ ?〉.After a specif i c evolution time tn(=π/2J12)=28 ns,the occupied probabilities of|+?〉and|? +〉,as represented in Fig.2,depend on the detuning δ12remarkably.When δ12=0,the system is in|?+〉completely.The probability of|?+〉will be reduced greatly with increasing δ12.As demonstrated in the subf i gure,the probability of|?+〉is less than 4.25×10?3when δ12is in the large detuning region(δ12/2π ≥ 0.3 GHz).

    From the viewpoint of coherent control,the interqubit coupling can be switchable eあectively by adjusting the detuning δ12.[31]When the transition frequencies are resonant with each other,the interqubit coupling exists.On the other hand,the coupling gets vanished at the large detuning δ12.At the same time,we can operate qubits selectively.Towards the practical quantum computing,the controllable and selective interqubit coupling is desirable to f l exibly manipulate the multiqubit system.

    Fig.2 The occupied probabilities of states|?+〉and|+ ?〉as functions of detuning δ12for a given evolution time,the unit of δ12is 2π GHz.

    4 Quantum Gates on DFS-Encoded Qubits

    As mentioned before,the two qubits 1 and 2 span a Hilbert space{|jj′〉},from which we select a subspace{|+ ?〉,|? +〉},and encode the logic qubit states as|0〉L=|+ ?〉and|1〉L=|? +〉,respectively.Owing to the symmetry of system-bath interaction,the subspace can be insensitive to certain collective noises,[22]which is thus referred to as decoherence-free subspace(DFS).The considered DFS{|+ ?〉,|? +〉}is immune to σz-type collective noises.[32]Energy relaxation and dephasing are two factors that induce qubit decoherence.It is found that the dephasing eあect is dominant over the energy relaxation for the semiconductor spin qubit.Generally,the f l uctuations of nucleus spin and external f i elds with low frequencies give rise to the dephasing eあect.[30,33]The present DFS-encoded approach is just helpful to avoid the dephasing eあects caused by the collective noises.

    In the following,taking advantages of the controllable interqubit coupling,we construct the universal logic gates on the DFS-encoded qubits.Firstly,we perform singlelogic-qubit gates.Adjust ω2to make ω2= ω1,and therefore the detuning is δ12=0.From Eq.(3),the evolution operator in the logic qubit basis{|0〉L,|1〉L}is obtained as[32]

    where the identical phase factors e?iJ12tregarding|0〉Land|1〉Lhave been left out.Obviously,two noncommutable single-logic-qubit gates can be achieved by controlling the diあerent evolution times.

    Next we execute a two-logic-qubit conditional gate.Choosing other two physical qubits 3 and 4,we encode similarly the logic-qubit states as|0〉L=|+ ?〉and|1〉L=|? +〉.Thus the DFS-encoded logic-qubit states are|00〉LL=|+ ?〉|+ ?〉,|01〉LL=|+ ?〉|? +〉,|10〉LL=|? +〉|+ ?〉,and|11〉LL=|? +〉|? +〉.By means of an auxiliary state|+〉5of qubit 5,we can perform a controlled-phase gate on the selected logic-qubits.[34]When the transition frequencies satisfy ω5= ω3= ω1,the eあective Hamiltonian of the three-qubit system is expressed as[34]

    where the coupling strengths are J(=J13=J15=J35).According to Hamiltonian(5),the auxiliary qubit 5 is decoupled from the other qubits after a duration time tcp=2π/3J.Then the controlled-phase gate on the logic qubits is achieved as[32]

    with ?00= ?01= ?10=0 and ?11= ?2π/3.

    So far,by virtue of the controllable interqubit couplings,we have obtained a set of universal logic gates on the DFS-encoded qubits,containing two noncommutative single-logic-qubit gates and a two-logic-qubit conditional gate.

    5 Fidelity Enhancement by DFS-Encoding Qubits

    In the multiqubit system,environmental noises acting upon qubits can be usually divided into the individual noises and the collective ones.[32]Since the DFS-encoded qubits are immune to the collective noises,the corresponding decoherence eあects can be eliminated naturally,which is extremely useful to obtain the fault-tolerant gate operations.The decoherence eあects on qubits can be simulated numerically by gate f i delity.As in Ref.[35],we have the f idelity F=where|ψi〉is an ideal output state without the noise eあects,ρ =|ψ〉〈ψ|indicates the reduced density matrix associated with a realistic state|ψ〉.And the time evolution of the density matrix can be addressed by the quantum theory of damping.

    Here take the not-gate as an example to consider the robustness of the DFS-encoded way.The dynamical evolution of the reduced density matrix ρ is described by the Lindblad-type master equation,[36]

    in which Heあis the Hamiltonian of(3)with δ12=0, γkandˉγkφare the relaxation and total dephasing rates of qubit k,respectively,D[L]ρ =(2LρL??L?Lρ?ρL?L)/2,with L=σ?kand σkz.We haveˉγkφ=γkφin the DFS case.Diあerently,the two qubits in the non-DFS case are aあected by both the individual noises and the collective ones,and thenˉγkφ=γkφ+γφ,where γφis the collective dephasing rate for qubits 1 and 2.Due to the virtual exchange of photons,the eあects of the photon leakages on the evolution processes can be neglected safely.[12,37]Theoretically,the DFS-encoded scheme is not aあected by the σz-type collective noises,which is the pivotal reason for performing robust quantum gates.

    Fig.3 The dependence of the not-gate f i delity on γkand γφ in the DFS case(a),and in the non-DFS case(b).The f i delity enhancement ΔF as a function of γkand γφ in(c).Here γkand γφ are given in units of 2π MHz.

    Through calculating Eq.(7)with diあerentˉγkφ,the dependences of the f i delities Fdand Fnon the individual γkand the collective γφare given in Figs.3(a)and 3(b),respectively,here we assume γ1= γ2(= γk)and γ1φ= γ2φ(=2π × 0.2 MHz).In the DFS-encoded case,Fddecreases with the increase of γk,but does not change with γφ,which means that Fdis aあected by the individual noises only,see Fig.3(a).However,the f i delity Fnin the non-DFS case is dependent on both the individual noises and the collective ones,i.e.,Fndecreases as increasing either γkor γφ.To demonstrate explicitly the fi delity enhancement by the DFS encoding,the diあerence ΔF=Fd?Fnis plotted in Fig.3(c).It is clear that ΔF increases with increasing γφ,and ΔF can reach up to 3.22%when γφ/2π =1.0 MHz.[30]Moreover,we can estimate that the f i delity enhancement for the controlledphase gate may be larger than 6.44%since the required time tcpis longer than tn.

    6 Discussion and Conclusion

    Through the TLR in circuit QED setup,the selective and controllable interqubit couplings can be realized only by adjusting the detuning between transition frequencies of qubits,which thus provide the preferable conditions to construct the scalable quantum information processing.[1]Diあerent from the previous case,[37]the noise eあects on semiconductor spin qubits in the present scheme are the pure dephasing mainly.[10,17]The DFS-encoded protocol is just useful to eliminate the dephasing eあects originated from the σz-type collective noises,and therefore the gate f i delities can be enhanced signif i cantly.Additionally,with the interaction Hamiltonian of Eq.(3),many important quantum information tasks with double-dots could be performed,such as quantum state transfer and entanglement.[30]However,as an open question,how to make the collective noises dominant over the individual ones in the multiqubit system needs to be studied further,which is crucial for building the more robust quantum computing in the DFS-encoded scenario.

    In summary,we have theoretically proposed a scheme to perform the robust quantum gates on the DFS-encoded double-dot spin qubits.Many double-dots are connected to a common TLR via gate capacitances.In the dispersive regimes,the controllable and selective interqubit couplings can be realized only by tuning the qubit transition frequencies.Based on the desirable interqubit couplings,we have constructed a set of universal logic gates on the DFS-encoded qubits.It is found that the σz-type collective noises can be eliminated eあectively,and then the fi delity enhancements can be obtained numerically with the accessible parameters.So,the proposed scheme may provide a potential approach towards the scalable robust gates with hybrid quantum circuits.

    [1]T.D.Ladd,F.Jelezko,R.Laf l amme,Y.Nakamura,C.Monroe,and J.L.′OBrien,Nature(London)464(2010)45.

    [2]I.Fushman,D.Euglund,A.Faraon,N.Stoltz,P.Petroあ,and J.Vuˇckovi′c,Science 320(2008)769.

    [3]N.T.T.Nguyen and S.D.Sarma,Phys.Rev.B 83(2011)235322.

    [4]S.M.Clark,K.M.C.Fu,Q.Zhang,T.D.Ladd,C.Stanley,and Y.Yamamoto,Phys.Rev.Lett.102(2009)247601.

    [5]J.Medford,L.Cywi′nski,C.Barthel,C.M.Marcus,M.P.Hanson,and A.C.Gossard,Phys.Rev.Lett.108(2012)086802.

    [6]A.Wallraあ,D.I.Schuster,A.Blais,L.Frunzio,R.S.Huang,J.Majer,S.Kumar,S.M.Girvin,and R.J.Schoelkopf,Nature(London)431(2004)162.

    [7]J.D.Teufel,D.Li,M.S.Allman,K.Cicak,A.J.Sirois,J.D.Whittaker,and R.W.Simmonds,Nature(London)471(2011)204.

    [8]M.Trif,V.N.Golovach,and D.Loss,Phys.Rev.B 77(2008)045434.

    [9]Z.R.Lin,G.P.Guo,T.Tu,F.Y.Zhu,and G.C.Guo,Phys.Rev.Lett.101(2008)230501.

    [10]P.Xue,Phys.Lett.A 374(2010)2601.

    [11]P.Pei,C.Li,J.S.Jin,and H.S.Song,J.Phys.B:At.Mol.Opt.Phys.44(2011)035501.

    [12]Z.B.Feng,Phys.Rev.A 85(2012)014302.

    [13]K.D.Petersson,L.W.McFaul,M.D.Schroer,M.Jung,J.M.Taylor,A.A.Houck,and J.R.Petta,Nature(London)490(2012)380.

    [14]P.Q.Jin,M.Marthaler,A.Shnirman,and G.Sch¨on,Phys.Rev.Lett.108(2012)190506.

    [15]T.Frey,P.J.Leek,M.Beck,A.Blais,T.Ihn,K.Ensslin,and A.Wallraあ,Phys.Rev.Lett.108(2012)046807.

    [16]H.Toida,T.Nakajima,and S.Komiyama,arXiv:condmat/1206.0674v1.

    [17]W.M.Witzel,X.Hu,and S.D.Sarma,Phys.Rev.B 76(2007)035212.

    [18]Y.Hu,F.Kuemmeth,C.M.Lieber,and C.M.Marcus,Nat.Nanotechnol.7(2012)47.

    [19]V.N.Golovach,M.Borhani,and D.Loss,Phys.Rev.A 81(2010)022315.

    [20]C.Barthel,J.Medford,C.M.Marcus,M.P.Hanson,and A.C.Gossard,Phys.Rev.Lett.105(2010)266808.

    [21]M.D.Grace,J.Dominy,W.M.Witzel,and M.S.Carroll,Phys.Rev.A 85(2012)052313.

    [22]L.M.Duan and G.C.Guo,Phys.Rev.Lett.79(1997)1953.

    [23]X.L.Zhang,M.Feng,and K.L.Gao,Quantum Inf.Comput.8(2008)96.

    [24]Z.Y.Xue,S.L.Zhu,and Z.D.Wang,Eur.Phys.J.D 55(2009)223.

    [25]S.L.Wu,L.C.Wang,and X.X.Yi,J.Phys.A:Math.Theor.45(2012)405305.

    [26]Z.B.Feng,Phys.Rev.A 78(2008)032325.

    [27]A.Pfund,I.Shorubalko,K.Ensslin,and R.Leturcq,Phys.Rev.B 76(2007)161308(R).

    [28]J.R.Petta,J.M.Taylor,A.C.Johnson,A.Yacoby,M.D.Lukin,C.M.Marcus,M.P.Hanson,and A.C.Gossard,Phys.Rev.Lett.100(2008)067601.

    [29]J.W.Li,C.W.Wu,and H.Y.Dai,Chin.Phys.Lett.28(2011)090302.

    [30]G.P.Guo,H.Zhang,Y.Hu,T.Tu,and G.C.Guo,Phys.Rev.A 78(2008)020302(R).

    [31]A.Blais,J.Gambetta,A.Wallraあ,D.I.Schuster,S.M.Girvin,M.H.Devoret,and R.J.Schoelkopf,Phys.Rev.A 75(2007)032329.

    [32]Z.B.Feng,H.L.Wang,H.Han,and R.Y.Yan,Phys.Lett.A 374(2010)539.

    [33]X.Hu and S.D.Sarma,Phys.Rev.Lett.96(2006)100501.

    [34]C.Wu,X.L.Feng,X.X.Yi,I.M.Chen,and C.H.Oh,Phys.Rev.A 78(2008)062321.

    [35]D.Parodi,M.Sassetti,P.Solinas,P.Zanardi,and N.Zanghi,Phys.Rev.A 73(2006)052304.

    [36]D.Walls and G.Milburn,Quantum Optics,Springer,Berlin(1994).

    [37]Z.B.Feng,R.Y.Yan,C.Zhang,and L.Fan,Int.J.Theor.Phys.51(2012)2282.

    97热精品久久久久久| 99热精品在线国产| 级片在线观看| 99国产精品一区二区蜜桃av| 我要搜黄色片| 欧美xxxx黑人xx丫x性爽| 九九热线精品视视频播放| 哪个播放器可以免费观看大片| 国产精品av视频在线免费观看| АⅤ资源中文在线天堂| 国产一区二区激情短视频| 日日摸夜夜添夜夜爱| 亚洲四区av| 国产中年淑女户外野战色| 亚洲欧美日韩高清专用| 成人二区视频| 成人综合一区亚洲| 麻豆一二三区av精品| 婷婷亚洲欧美| 男人舔奶头视频| 久久亚洲精品不卡| 青青草视频在线视频观看| 九九热线精品视视频播放| 一进一出抽搐动态| 日韩在线高清观看一区二区三区| 国产极品天堂在线| 免费看美女性在线毛片视频| 国产精品伦人一区二区| 亚洲精品成人久久久久久| 成年女人永久免费观看视频| 国产精品美女特级片免费视频播放器| 联通29元200g的流量卡| 国产精品1区2区在线观看.| av在线蜜桃| 欧美日本亚洲视频在线播放| 国产一区亚洲一区在线观看| 99riav亚洲国产免费| 亚洲va在线va天堂va国产| 听说在线观看完整版免费高清| 精华霜和精华液先用哪个| 不卡一级毛片| 中文亚洲av片在线观看爽| 日日摸夜夜添夜夜添av毛片| 精品久久久噜噜| 又黄又爽又刺激的免费视频.| 精品久久久久久成人av| 午夜激情欧美在线| 国产老妇伦熟女老妇高清| 毛片一级片免费看久久久久| 国产精品国产三级国产av玫瑰| 看非洲黑人一级黄片| 亚洲av中文av极速乱| 国产精品.久久久| 国产成人精品久久久久久| 亚洲精品自拍成人| 亚洲av男天堂| 综合色av麻豆| 国模一区二区三区四区视频| 国产精品美女特级片免费视频播放器| 高清在线视频一区二区三区 | 亚洲av成人av| 成人午夜高清在线视频| 久久久久性生活片| 精品国内亚洲2022精品成人| 国产老妇女一区| 22中文网久久字幕| 美女大奶头视频| av免费在线看不卡| 天堂√8在线中文| 精品免费久久久久久久清纯| 能在线免费看毛片的网站| 青青草视频在线视频观看| 亚洲欧洲国产日韩| 亚洲激情五月婷婷啪啪| 国产精品综合久久久久久久免费| 国产又黄又爽又无遮挡在线| 久久精品国产亚洲网站| 一本一本综合久久| 亚洲最大成人手机在线| 春色校园在线视频观看| 中国国产av一级| 我要看日韩黄色一级片| 波多野结衣高清作品| 亚洲中文字幕一区二区三区有码在线看| 欧美区成人在线视频| 白带黄色成豆腐渣| 婷婷精品国产亚洲av| 白带黄色成豆腐渣| 波野结衣二区三区在线| 99精品在免费线老司机午夜| 欧美色欧美亚洲另类二区| 国产淫片久久久久久久久| 精品一区二区三区视频在线| 免费搜索国产男女视频| 91久久精品国产一区二区成人| 一本久久精品| 亚洲婷婷狠狠爱综合网| 久久99热6这里只有精品| 久久久久久久久久久丰满| 欧美成人免费av一区二区三区| 久久久精品大字幕| 免费av不卡在线播放| 欧美xxxx性猛交bbbb| 乱码一卡2卡4卡精品| 亚洲成人av在线免费| 亚洲精品自拍成人| 亚洲欧洲国产日韩| 久久久精品94久久精品| 激情 狠狠 欧美| 美女xxoo啪啪120秒动态图| 免费观看的影片在线观看| 99在线视频只有这里精品首页| 国产麻豆成人av免费视频| 免费在线观看成人毛片| 丝袜喷水一区| 中文资源天堂在线| 少妇高潮的动态图| 日韩一本色道免费dvd| 成人国产麻豆网| 国产精品日韩av在线免费观看| 能在线免费看毛片的网站| 欧美3d第一页| 日韩大尺度精品在线看网址| 在线观看66精品国产| 亚洲成人精品中文字幕电影| 中文精品一卡2卡3卡4更新| av视频在线观看入口| 老司机福利观看| 国语自产精品视频在线第100页| 我的女老师完整版在线观看| 久久人人爽人人片av| 欧美人与善性xxx| 少妇丰满av| 亚洲国产色片| 欧美不卡视频在线免费观看| 日日撸夜夜添| 久久精品夜色国产| 久久久久久久久中文| 久久人人精品亚洲av| 久久6这里有精品| 国产亚洲av片在线观看秒播厂 | 中文字幕精品亚洲无线码一区| 国产精品伦人一区二区| 久久久久久久亚洲中文字幕| 国产精品伦人一区二区| 成人美女网站在线观看视频| 久久久久免费精品人妻一区二区| 欧美三级亚洲精品| av国产免费在线观看| 欧美一区二区国产精品久久精品| 国模一区二区三区四区视频| 国产一级毛片在线| 欧美日本视频| 边亲边吃奶的免费视频| 菩萨蛮人人尽说江南好唐韦庄 | eeuss影院久久| 偷拍熟女少妇极品色| 国产精品久久久久久精品电影小说 | 免费看日本二区| 国产精品一区二区三区四区免费观看| 中文精品一卡2卡3卡4更新| 久久九九热精品免费| 小蜜桃在线观看免费完整版高清| 丰满的人妻完整版| 麻豆精品久久久久久蜜桃| 欧美激情久久久久久爽电影| 国产av不卡久久| 99热这里只有是精品在线观看| 色综合色国产| 国产精品日韩av在线免费观看| 国产精品久久久久久久久免| 欧美区成人在线视频| 欧美性猛交黑人性爽| 99久国产av精品| 插逼视频在线观看| 综合色丁香网| 国产成人精品一,二区 | 久久久精品大字幕| 亚洲欧美日韩无卡精品| av女优亚洲男人天堂| 国产伦在线观看视频一区| 国产伦精品一区二区三区视频9| 麻豆成人午夜福利视频| 免费av不卡在线播放| 久久久久久国产a免费观看| 亚洲av不卡在线观看| 成人特级黄色片久久久久久久| 成年女人永久免费观看视频| 中文字幕人妻熟人妻熟丝袜美| 在线观看av片永久免费下载| 一区二区三区免费毛片| 国产精品不卡视频一区二区| 亚州av有码| 麻豆精品久久久久久蜜桃| 一级黄色大片毛片| 超碰av人人做人人爽久久| 国产av一区在线观看免费| 91午夜精品亚洲一区二区三区| 91在线精品国自产拍蜜月| 成人美女网站在线观看视频| 久久精品夜夜夜夜夜久久蜜豆| 日韩高清综合在线| 久久久久国产网址| 久久久久久大精品| 老女人水多毛片| 欧美日本亚洲视频在线播放| 久久久国产成人免费| 特级一级黄色大片| 久久精品综合一区二区三区| 欧洲精品卡2卡3卡4卡5卡区| 国产精品久久久久久久电影| 狠狠狠狠99中文字幕| 国产综合懂色| 亚洲国产精品sss在线观看| 成人无遮挡网站| 看黄色毛片网站| 看非洲黑人一级黄片| 日韩亚洲欧美综合| 欧美+日韩+精品| 国产伦精品一区二区三区视频9| 亚洲国产精品成人久久小说 | 高清毛片免费观看视频网站| 亚洲人成网站在线观看播放| 免费电影在线观看免费观看| 亚洲人与动物交配视频| 免费av不卡在线播放| 国产一区二区在线av高清观看| 成人鲁丝片一二三区免费| 精品不卡国产一区二区三区| 少妇的逼好多水| 狂野欧美白嫩少妇大欣赏| 欧美+日韩+精品| 深夜精品福利| 又爽又黄a免费视频| 午夜福利在线在线| 午夜免费激情av| 伦精品一区二区三区| 亚洲国产欧洲综合997久久,| 国内久久婷婷六月综合欲色啪| 日产精品乱码卡一卡2卡三| 男人的好看免费观看在线视频| 国产精品99久久久久久久久| 国国产精品蜜臀av免费| 国产高清三级在线| 少妇被粗大猛烈的视频| 国产精品久久久久久精品电影小说 | 日本-黄色视频高清免费观看| 免费大片18禁| 麻豆一二三区av精品| 丰满的人妻完整版| 精品久久久久久成人av| 91av网一区二区| 日本欧美国产在线视频| 欧美日韩综合久久久久久| 乱人视频在线观看| 亚洲人成网站在线观看播放| 色吧在线观看| 免费黄网站久久成人精品| 在线观看av片永久免费下载| 99在线视频只有这里精品首页| 久久久久久久久久久免费av| 中国国产av一级| 成人综合一区亚洲| 亚州av有码| 女人被狂操c到高潮| 国内精品美女久久久久久| 久久6这里有精品| 中文字幕av在线有码专区| 色综合亚洲欧美另类图片| 一级av片app| 边亲边吃奶的免费视频| 99久国产av精品国产电影| 人妻制服诱惑在线中文字幕| 我要搜黄色片| 亚洲精华国产精华液的使用体验 | 久久久久网色| 看十八女毛片水多多多| 日本爱情动作片www.在线观看| 免费人成在线观看视频色| 久久这里只有精品中国| 精品无人区乱码1区二区| 亚洲第一区二区三区不卡| 亚洲七黄色美女视频| 中文字幕av在线有码专区| 亚州av有码| 国产久久久一区二区三区| 欧美日韩在线观看h| 麻豆成人午夜福利视频| 亚洲色图av天堂| 亚洲国产欧美人成| 欧美极品一区二区三区四区| 老熟妇乱子伦视频在线观看| 美女大奶头视频| 精品久久久久久久末码| 99久久人妻综合| 国产成人精品久久久久久| 亚洲欧洲日产国产| 亚洲成a人片在线一区二区| 日本熟妇午夜| 国产精品av视频在线免费观看| 亚洲欧美清纯卡通| 国产伦精品一区二区三区四那| 只有这里有精品99| 亚洲av熟女| 国产乱人偷精品视频| 国产高潮美女av| 中文字幕熟女人妻在线| 蜜桃亚洲精品一区二区三区| 插逼视频在线观看| 国产成年人精品一区二区| 女人被狂操c到高潮| 人体艺术视频欧美日本| 亚洲国产欧美人成| 人妻久久中文字幕网| 国产成人精品久久久久久| 国模一区二区三区四区视频| 日本成人三级电影网站| 亚洲五月天丁香| 精品少妇黑人巨大在线播放 | 非洲黑人性xxxx精品又粗又长| 亚洲成人久久性| 毛片女人毛片| 你懂的网址亚洲精品在线观看 | 精品久久久久久久久久久久久| 91av网一区二区| 亚洲成a人片在线一区二区| 欧美+亚洲+日韩+国产| 午夜精品在线福利| 12—13女人毛片做爰片一| 亚洲va在线va天堂va国产| 免费av不卡在线播放| 色播亚洲综合网| 久久鲁丝午夜福利片| 一个人免费在线观看电影| 在线国产一区二区在线| 青春草亚洲视频在线观看| 欧美潮喷喷水| 色噜噜av男人的天堂激情| 成人av在线播放网站| 不卡一级毛片| 男女视频在线观看网站免费| 97超碰精品成人国产| 麻豆国产97在线/欧美| 成人综合一区亚洲| 精品久久国产蜜桃| 久久这里有精品视频免费| 99在线人妻在线中文字幕| av在线老鸭窝| 国产成年人精品一区二区| 国产 一区 欧美 日韩| 男女做爰动态图高潮gif福利片| 欧美成人精品欧美一级黄| 国产 一区精品| 久久久国产成人精品二区| 最好的美女福利视频网| 非洲黑人性xxxx精品又粗又长| 日韩av不卡免费在线播放| 国产成人aa在线观看| 1000部很黄的大片| 亚洲欧美中文字幕日韩二区| 男的添女的下面高潮视频| 老司机影院成人| 亚洲电影在线观看av| 日韩欧美精品免费久久| 国产亚洲精品久久久久久毛片| 一边摸一边抽搐一进一小说| 国产亚洲精品久久久久久毛片| 一边摸一边抽搐一进一小说| 午夜福利在线观看免费完整高清在 | 欧美日韩国产亚洲二区| 一级毛片久久久久久久久女| 久久久久国产网址| 亚洲高清免费不卡视频| 夜夜看夜夜爽夜夜摸| 99久久精品国产国产毛片| 中文亚洲av片在线观看爽| 高清毛片免费观看视频网站| 国内精品美女久久久久久| 男人和女人高潮做爰伦理| 三级国产精品欧美在线观看| 成人性生交大片免费视频hd| 99国产极品粉嫩在线观看| 三级毛片av免费| 亚洲精品久久久久久婷婷小说 | 午夜久久久久精精品| 精品一区二区免费观看| 亚洲在线自拍视频| 久久精品综合一区二区三区| 91狼人影院| 18禁在线播放成人免费| 九草在线视频观看| 69av精品久久久久久| 黄色一级大片看看| 亚洲精品影视一区二区三区av| 在线观看66精品国产| 久久久久九九精品影院| 色哟哟哟哟哟哟| 精品一区二区三区视频在线| 久久欧美精品欧美久久欧美| 国产精品伦人一区二区| 久久婷婷人人爽人人干人人爱| 天堂影院成人在线观看| 久久精品影院6| 成人午夜精彩视频在线观看| 最近视频中文字幕2019在线8| 亚洲精华国产精华液的使用体验 | 精品不卡国产一区二区三区| 亚洲欧美日韩高清专用| 神马国产精品三级电影在线观看| 久久草成人影院| 精品国产三级普通话版| 又黄又爽又刺激的免费视频.| 国产亚洲91精品色在线| kizo精华| 天美传媒精品一区二区| 99久久九九国产精品国产免费| 免费搜索国产男女视频| 亚洲第一区二区三区不卡| 在线免费十八禁| 日韩人妻高清精品专区| 非洲黑人性xxxx精品又粗又长| 亚洲欧美精品专区久久| 亚洲精品乱码久久久v下载方式| 久久久久久伊人网av| 亚洲在线观看片| 97在线视频观看| 国产成人一区二区在线| 一个人观看的视频www高清免费观看| 精品不卡国产一区二区三区| 国产真实乱freesex| 欧美一区二区精品小视频在线| 欧美xxxx性猛交bbbb| 亚洲欧美精品专区久久| 别揉我奶头 嗯啊视频| 久久久久久久久大av| 啦啦啦观看免费观看视频高清| 成人特级av手机在线观看| 亚洲成av人片在线播放无| 亚洲av一区综合| 免费无遮挡裸体视频| 日本一二三区视频观看| 亚洲精品亚洲一区二区| 老司机福利观看| 日日撸夜夜添| 国产在线男女| 日本av手机在线免费观看| 黄色日韩在线| 国产精品嫩草影院av在线观看| 男人舔奶头视频| 嘟嘟电影网在线观看| 久久99热这里只有精品18| 国产日韩欧美在线精品| 综合色av麻豆| 伦理电影大哥的女人| 国产精华一区二区三区| 男人舔奶头视频| 晚上一个人看的免费电影| 日日撸夜夜添| 波多野结衣巨乳人妻| 一夜夜www| 亚洲av二区三区四区| 久久久色成人| 亚洲真实伦在线观看| 丝袜喷水一区| 欧美性猛交黑人性爽| 天天一区二区日本电影三级| 亚洲欧美清纯卡通| 午夜福利在线在线| 欧美高清性xxxxhd video| 黑人高潮一二区| 在线国产一区二区在线| 99久久无色码亚洲精品果冻| 成人毛片60女人毛片免费| 热99re8久久精品国产| 午夜福利视频1000在线观看| 欧美高清成人免费视频www| 一边亲一边摸免费视频| 国产 一区 欧美 日韩| 男女做爰动态图高潮gif福利片| 如何舔出高潮| 国产精品福利在线免费观看| 非洲黑人性xxxx精品又粗又长| 22中文网久久字幕| 久久久国产成人免费| 亚洲中文字幕一区二区三区有码在线看| 97热精品久久久久久| av福利片在线观看| 日韩av在线大香蕉| 黄色配什么色好看| 在线观看美女被高潮喷水网站| 国产午夜精品论理片| 美女xxoo啪啪120秒动态图| 国产av麻豆久久久久久久| 免费不卡的大黄色大毛片视频在线观看 | 大型黄色视频在线免费观看| 亚洲欧美中文字幕日韩二区| 欧美最新免费一区二区三区| 国产极品天堂在线| 亚洲高清免费不卡视频| 夫妻性生交免费视频一级片| 午夜免费激情av| 亚洲成人久久性| 国产黄色视频一区二区在线观看 | 特级一级黄色大片| 久久人人爽人人爽人人片va| 麻豆一二三区av精品| 久久综合国产亚洲精品| 日韩在线高清观看一区二区三区| 日本免费a在线| .国产精品久久| 午夜精品在线福利| 亚洲激情五月婷婷啪啪| a级毛色黄片| eeuss影院久久| 国产av一区在线观看免费| 久久久久久久久大av| 天堂网av新在线| 国产高清视频在线观看网站| 99热这里只有是精品50| 黑人高潮一二区| 国产在线精品亚洲第一网站| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 人妻久久中文字幕网| avwww免费| 亚洲精品乱码久久久v下载方式| 草草在线视频免费看| 午夜福利成人在线免费观看| 久久亚洲精品不卡| 精品人妻一区二区三区麻豆| 久久中文看片网| 中文字幕久久专区| 亚洲国产欧洲综合997久久,| 国产探花在线观看一区二区| 国产一区二区亚洲精品在线观看| 亚洲精华国产精华液的使用体验 | 色5月婷婷丁香| 日日干狠狠操夜夜爽| 亚洲色图av天堂| 插阴视频在线观看视频| 不卡一级毛片| 非洲黑人性xxxx精品又粗又长| 亚洲自拍偷在线| 亚洲av电影不卡..在线观看| 99久久中文字幕三级久久日本| 尤物成人国产欧美一区二区三区| 免费不卡的大黄色大毛片视频在线观看 | 亚洲成人久久性| 国产成年人精品一区二区| 内地一区二区视频在线| 丰满的人妻完整版| 成人一区二区视频在线观看| 亚洲av一区综合| 欧美日韩综合久久久久久| 国产人妻一区二区三区在| 国产真实伦视频高清在线观看| 内地一区二区视频在线| 亚洲精品色激情综合| 精品久久久噜噜| 国产精品精品国产色婷婷| 国产精品.久久久| 亚洲最大成人手机在线| 男人舔奶头视频| 国产精品伦人一区二区| 男女做爰动态图高潮gif福利片| 老师上课跳d突然被开到最大视频| 日韩精品有码人妻一区| 亚洲在线观看片| 听说在线观看完整版免费高清| h日本视频在线播放| 男人和女人高潮做爰伦理| 最好的美女福利视频网| 亚洲国产精品国产精品| 精品久久久久久久久av| 久久精品国产亚洲av涩爱 | 天天一区二区日本电影三级| 性色avwww在线观看| 国产精品久久久久久久电影| 亚洲成人久久爱视频| 亚洲欧美日韩无卡精品| 99久久成人亚洲精品观看| 看非洲黑人一级黄片| 国产亚洲av片在线观看秒播厂 | 久久久a久久爽久久v久久| 中文字幕熟女人妻在线| 国产精品一区二区三区四区免费观看| 春色校园在线视频观看| 神马国产精品三级电影在线观看| 午夜福利成人在线免费观看| 久久中文看片网| 国产精品人妻久久久久久| 国产成人a∨麻豆精品| 人妻夜夜爽99麻豆av| 干丝袜人妻中文字幕| 国产精品,欧美在线| 18+在线观看网站| 久久韩国三级中文字幕| 国产女主播在线喷水免费视频网站 | 99久久久亚洲精品蜜臀av| 亚洲一区高清亚洲精品| 婷婷六月久久综合丁香| 99久久精品一区二区三区| 青青草视频在线视频观看| 欧美日韩综合久久久久久| 国产真实乱freesex| 亚洲精品日韩av片在线观看| 精品久久久久久久久久久久久| 国产精品日韩av在线免费观看| 欧美日本视频| 插阴视频在线观看视频| 自拍偷自拍亚洲精品老妇| 国产在视频线在精品| 久久久久久国产a免费观看| 伦理电影大哥的女人| 亚洲av免费高清在线观看| 久久欧美精品欧美久久欧美|