• <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 ?

    Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions*

    2021-05-06 08:55:30QingYan閆青andQingFengSun孫慶豐
    Chinese Physics B 2021年4期
    關(guān)鍵詞:慶豐

    Qing Yan(閆青) and Qing-Feng Sun(孫慶豐)

    1International Center for Quantum Materials,School of Physics,Peking University,Beijing 100871,China

    2CAS Center for Excellence in Topological Quantum Computation,University of Chinese Academy of Sciences,Beijing 100190,China

    3Collaborative Innovation Center of Quantum Matter,Beijing 100871,China

    4Beijing Academy of Quantum Information Sciences,Beijing 100193,China

    Keywords: quantum computation,T gate,CNOT gate,braiding,chiral Majorana fermions

    1. Introduction

    Facing the dilemma caused by the increasing demand for data processing and the gradual failure of Moore’s law,quantum computation arises to help to break this bottleneck, that is, to compute from the basic quantum-mechanic law rather than stimulate the quantum system in a classical way.[1,2]The power of quantum computation roots in the qubit: the information contained in one qubit, defined as the superposition of two basis states, is much more than that in one classical bit,just 0 and 1;the dimension of computational space grows exponentially as the number of qubits increases due to the exotic entanglement.[3]As one of the computational models,the quantum circuit model takes up the quantum gate to manipulate the qubit based on the original proposal by Benioff that a quantum computer would be constructed by the time evolution of a quantum system.[4]Similar to the XOR and AND gates in the classical computer, a finite set of quantum gates can accurately realize the arbitrary unitary transformation, i.e., the so-called universal quantum gate set{T,H,CNOT}.[5]The design and fabrication of qubits and quantum gates have brought quantum computing into a promising and challenging research field.

    Along the way of pursuing a quantum computer, the first step is to fabricate the qubit in a physical system.Among various two-level systems, some with long coherent time have been proposed to serve as a qubit, including photons,[6]trapped atoms,[7,8]quantum dots,[9–11]superconducting Josephson junctions,[12–15]etc. Besides these conventional devices, recent interests in topology claim that a topological system owns a natural advantage of protection against local perturbations, thus opening up a research field called topological quantum computation.[16]The Majorana system,simple but nontrivial,is considered as a potential platform for fault-tolerant topological quantum computation.[17]

    In condensed matter physics, Majorana fermions represent a kind of self-conjugate quasiparticle excitations, i.e.,γ?=γ in the operator language.[18]The reality of wave function requires the phase of a Majorana fermion to be either 0 or π. A Majorana fermion is usually regarded as a half of a Dirac fermion,since an ordinary electron and a hole can be reorganized and divided into two real Majorana fermions.[19]In turn,two Majorana fermions form a nonlocal ordinary fermion level with a well-defined occupation number, which is protected by the gap. Besides, Majorana zero modes (MZMs),the zero-energy bound states with non-Abelian statistics,form the degenerate ground state within the gap, which offers the computational space for topological quantum computation.[20]MZMs follow the braiding rule of Ising anyons:after exchanging the positions of two MZMs,one of them acquires a π phase while the other does not,i.e.,γi→γj,γj→?γi.[19,21]The term“non-Abelian” refers that the braiding of γiand γjdoes not commute with the braiding of γjand γk. MZMs have been proposed as qubits,and the fermion parity of MZMs paired in a certain way is defined as the quantum basis states. Braiding MZMs means exchanging their pairing ways,i.e.,rotating the quantum state within the zero-energy degenerate ground state manifold, but keeping the total fermion parity invariant. Due to the global topology, local perturbations do not destroy the ground state,which offers the computational protection as the main advantage but also requires global operations, i.e., the braiding operations, to realize quantum gates corresponding to the Clifford algebra.

    Exploring MZMs in theory is both attractive and challenging.[22,23]Kitaev first constructed a toy model containing MZMs as the zero-dimensional end state of a 1D spinless p-wave superconducting nanowire.[24]Despite its difficulty to be realized in experiments, the spinless p-wave superconductor inspires new routines to synthesize the so-called topological superconductor (TSC), which supports MZMs at the boundary or at the vortex. With the development of topological materials[25–28]with strong spin–orbit coupling, Fu and Kane started from a 2D topological insulator, covered it with an s-wave superconductor to induce the pairing potential, and added a ferromagnetic insulator to break the timereversal symmetry so as to trap MZMs at domain walls.[29,30]MZMs also appear at the end of the 1D nanowire with strong spin–orbit coupling, when applied with a perpendicular magnetic field and covered with an s-wave superconductor.[31–33]MZMs can be induced by a small magnetic field in a hollow nanowire sandwiched between two superconductors.[34]MZMs localize at the vortices in the topological superconducting region when 3D topological insulators or 2D electron gas with Rashba spin–orbit coupling are sandwiched by an s-wave superconductor and a ferromagnetic insulator.[29,35]Besides,Tang et al. predicted the existence of the MZMs in some organic molecules(e.g.,DNA)proximity coupled by an s-wave superconductor and under the magnetic field.[36]

    Considering the experimental detection of MZMs, one of the most important theoretical proposals points out that the existence of MZMs leads to a transport outcome: a robust and quantized zero-bias conductance peak due to the perfect Andreev reflection.[37]Correspondingly,Mourik et al. in 2012 first detected the anomalous zero-bias conductance peak as the signature of MZMs locating at the end of the InAs nanowire.[38]After that, other experiments observed MZMs bound at the end of ferromagnetic iron(Fe)atomic chains on the surface of superconducting lead(Pb),[39]the vortex of the iron-based superconductor[40]as well as the interface of the helical hinge states of Bi and magnetic iron clusters on the superconducting substrate.[41]Besides, the 4π periodic fractional Josephson experiment provided compelling evidence of the charge parity conservation of MZMs.[42]

    Then the question comes that how to braid MZMs in a real physical system and how to realize the topological quantum computation based on MZMs, facing with the difficulty that MZMs are constrained at the end or vortex of TSCs.The T junctions[43]or Y junctions[44]are theoretically proposed to move the MZM one by one by tuning the electric gate or magnetic flux, changing the topology of superconducting regions, evolving the system from one degenerate ground state to another, or pushing one MZM from one end to another end. During such evolution process, the non-Abelian Berry phase accumulates and one of the two MZMs gets a π phase, after completing the braiding process. Moreover, there is a “strange” strategy named as “braiding without braiding”,[45]which does not need to move MZMs but to measure them. When performing a physical measurement on a non-eigen superposition state, this superposition state will collapse into one of the eigenstates,corresponding to a kind of state transformations.[46]Some works based on the electronteleportation,[47]measuring the fermion parity,[48]and encoding the non-local entanglement of MZMs provide an alternative way of detecting the non-Abelian property and constructing the topologically protected quantum gates.[49]Other issues have also been considered, including the state distillation or the error correction.[50,51]However, based on the braiding of the MZMs,it is difficult to realize the T quantum gate,one of the three universal quantum gates.

    A recent experiment,inspired by the theoretical proposal of Ref.[60],reported the measurement of the chiral Majorana fermion and observed the half-integer quantized plateau of the Hall conductance.[66]However, alternative theoretical interpretations of the origin of the half-integer quantized plateau led to a skeptical or supportive attitude to the existence of the chiral Majorana fermion.[67–70]Based on the percolation model of QAHI–superconductor–QAHI junction, Huang et al.[67]showed that edge modes could transmit from left to right through the superconducting region with suitable leakage to adjacent chiral edges near the percolation threshold,giving rise to a nearly flat half-integer conductance. Ji and Wen[68]studied the contact conductance under a magnetic field and found that the half-integer conductance is a common result of a good electric contact between the integer quantum Hall insulator and superconductor films. Also, another experiment[71]studied the electric transport of a similar heterostructure of QAHI and s-wave superconductor, and they presented the half-integer quantized conductance without chiral Majorana fermions: two QAHI regions in series with wellaligned magnetization always lead to the half-integer quantized conductance because of the good contact transparency.

    Besides the interest in confirming the existence and regulating chiral Majorana fermions, some intuitive ideas turn to braiding chiral Majorana fermions with the purpose of quantum computation. Compared with MZMs, the most exciting property of chiral Majorana fermions is their natural mobility with the potential for rapid information processing.Lian et al.[72]first suggested to perform the braiding of chiral Majorana fermions with a Corbino ring junction. Zhou et al.[73]proposed the braiding-like operation of chiral Majorana fermions via the quantum dot.In addition,Beenakker et al.[74]constructed a device to braid the mobile chiral Majorana vortex around the immobile bulk vortex based on the Josephson junction. Despite these proposals of non-Abelian detections or operations, there is no scheme to implement the universal quantum computation via chiral Majorana fermions,especially the T and CNOT gates.

    In this paper,we propose the realization of arbitrary twoqubit quantum gates based on chiral Majorana fermions.Starting from the QAHI–TSC hybrid system, we first construct the elementary cell consisting of a QAHI surrounded by a TSC, which supports two chiral Majorana fermions along the boundary. Then, we introduce an electric gate on the QAHI region and a quantum-dot structure between adjacent cells to braid and partially exchange any two chiral Majorana fermions. Two chiral Majorana fermions in two edge channels within the same cell can be redistributed since the electric gate-induced dynamical phase mixes the electron and hole components. The quantum-dot structure contains two quantum dots, the central one of which allows the quantum tunneling of the chiral Majorana fermions between adjacent cells and the side dot makes up the phase to satisfy the braiding convention. Considering a single qubit defined by four chiral Majorana fermions,the electric gate can tune the trajectory of the chiral Majorana fermions so that half of each incoming chiral Majorana fermion tunnels into the opposite side and the other half keeps its own trajectory,thus realizing an expected T quantum gate. Three braiding operations via two electric gates and one quantum-dot structure achieve an H quantum gate.Based on the minimal definition of two-qubit basis states,we use six chiral Majorana fermions to construct an entangled CNOT quantum gate. Furthermore,the former single-qubit T and H quantum gates are realized within the two-qubit scheme.Besides, we show that a useful quantum Fourier transform algorithm can be decomposed into the aforementioned three quantum gates based on chiral Majorana fermions.

    This paper is organized as follows. Section 2 depicts the elementary cell supporting chiral Majorana fermions and explains the function of electric gates and quantum dots to achieve the braiding operation and the partial exchange operation. In Section 3, we construct the quantum gates of the single-qubit and two-qubit gates. In Section 4, a quantum circuit model of the two-qubit quantum Fourier transform is shown with the quantum gates realized via chiral Majorana fermions. We discuss the initialization and measurement of qubits based on chiral Majorana fermions and state the advantage of our proposal in Section 5. We summarize and discuss the further utilization of chiral Majorana fermions in Section 6.

    2. Elementary cells for the Braiding and partial exchange operations

    That is, the electric gate can regulate the outgoing trajectory of two incoming chiral Majorana fermions.[64]

    Besides the regulation of two chiral Majorana fermions in the same elementary cell,we introduce the quantum-dot structure to braid and partially exchange chiral Majorana fermions between two adjacent elementary cells. Here the magnetization orientations of two adjacent cells are set in the opposite directions,leading to the chirality of the corresponding chiral Majorana fermions being opposite,as shown in Fig.1(d). As a result,the adjacent chiral Majorana fermions from the adjacent cells have the same mobile direction,which is beneficial for their braiding. A quantum-dot structure of two quantum dots inserts between these two adjacent cells and couples with two adjacent co-propagating chiral Majorana fermions,γ2and γ3. Let us consider the central quantum dot coupling with two chiral Majorana fermions. The Hamiltonian of the chiral Majorana fermions is[73]

    Integrate x in Eq.(6)from 0?to 0+,we get

    where S denotes the scattering matrix[73]

    matching the scattering matrix via the electric gate in Eq.(1).When θ =0,the disabled quantum-dot structure has no effect on the chiral Majorana fermions. When θ =π/2,here comes γ2→γ3and γ3→?γ2,that is,the enabled quantum-dot structure completes the braiding operation B23,shown in Fig.1(e).When the relative coupling is tuned to a suitable value, the quantum-dot structure performs the partial exchange operation T23(θ): γ2→cosθγ2+sinθγ3and γ3→?sinθγ2+cosθγ3,as shown in Fig.1(f).

    Based on the braiding operation implemented via an electric gate or a quantum-dot structure, we further introduce a transfer box to connect two vertically adjacent elementary cells, as shown in Fig.2(a). Figure 2(b) draws a symbolic picture of a transfer box with four chiral Majorana fermions injecting and ejecting. The transfer box contains two electric gates and two quantum-dot structures arranged in the way shown in Fig.2(c). If the electric gates and quantum dots are disabled, the transfer box is closed, so four chiral Majorana fermions propagate in their own way, (γ1,γ2,γ3,γ4) →(γ1,γ2,γ3,γ4),i.e.,the chiral Majorana pair γ1and γ2remains in the upper cell and the pair γ3and γ4remains in the lower cell. But when the electric gates and quantum dots are tuned to the value corresponding to θ=π/2,the transfer box is open and executes the braiding operations B23,B12,B34,and B23in series.To be specific,four chiral Majorana fermions transform as follows:

    Thus, Fig.2(d) clearly shows the function of a transfer box:carry out four braiding operations, exchange of the Majorana pair γ1and γ2with the pair γ3and γ4,and transfer the Majorana pair γ3and γ4from the lower cell to the upper cell. This transfer makes possible cascading vertical cells and braiding chiral Majorana fermions on both sides to be seen in Fig.6.

    Fig.2. (a) Schematic diagram of two vertically adjacent elementary cells with a transfer box between them. (b)Symbolic picture of the transfer box.(c) The detailed structure of the transfer box with two electric gates and two quantum-dot structures. (d) Braiding diagram of operations B23, B12,B34, and B23, depicting the function of the transfer box as transferring the Majorana pair from the lower cell to the upper cell.

    3. Realization of quantum gates

    A complete quantum computation process includes three parts:input the qubit,perform the quantum gate operation,and read out the final qubit. The core of quantum computation lies in the realization of arbitrary quantum gates. The standard set of universal quantum gates is{H,T,CNOT},specifically,

    Considering the quantum states as qubits, the essence of the quantum gate is the unitary operation in the Hilbert space. In this section,we utilize chiral Majorana fermions as the qubit,use the electric gate and the quantum-dot structure to perform operations on the qubit,and construct the quantum gates in the two-qubit basis to realize any two-qubit quantum operations.

    Recalling the elementary cell device in Section 2,we have realized the braiding operation of adjacent chiral Majorana fermions via an electric gate or a quantum-dot structure. Here,we denote the braiding operator of Majorana fermions as[21]

    Express the operator in terms of the bilinear Majorana operators as follows:

    Similarly, for the partial exchange operation, we denote the operator as Ti,i+1(θ),

    and express Ti,i+1(θ)in terms of the bilinear Majorana operators

    which satisfies

    When θ =0, Ti,i+1(0)=1. When θ =π/2, Ti,i+1(π/2)=Bi,i+1,i.e.,the braiding operation represents the total exchange with a dynamical phase being π/2 or equal coupling between the quantum dot and two chiral Majorana fermions.

    Hereafter, we regard the braiding operator Bi,i+1and the partial exchange operator Ti,i+1(θ)(θ is not an integer multiple of π/2) as the elementary operations of two chiral Majorana fermions to construct the quantum gates.

    3.1. The single-qubit T and H gates

    For a single qubit, the minimal number of Majorana fermions is four,due to the fermion parity conservation.[21,76]Thus we place two column of elementary cells to construct the single-qubit quantum device,as shown in Figs.3(a)and 4(a).Four Majorana fermions are input from the lower cells A1 and A2, conveyed via two transfer boxes to the cells B1 and B2,acted on by the quantum operations in the cells B1 and B2,conveyed via two transfer boxes to the cells C1 and C2 as the output. As for the quantum gate,we focus on the core cells B1 and B2 with four incoming chiral Majorana fermions propagating upward,denoted as γ1,γ2,γ3,and γ4from left to right.

    Fig.3. Construction of the T gate. (a) The single qubit device contains two columns of elementary cells supporting four chiral Majorana fermions. The dashed rectangle emphasizes the core region which performs the T gate with an electric gate. (b)Braiding diagram of operations in(a). The dashed cross line represents the partial exchange operation of γ1 and γ2,T1,2(π/4),leading to the transformation of chiral Majorana fermions in Eq.(35).

    Fig.4. Construction of the H gate. (a) The single qubit device contains two columns of elementary cells supporting four chiral Majorana fermions. The dashed rectangle emphasizes the core region which performs the H gate with two electric gates and one quantum-dot structure.(b)Braiding diagram of operations in(a). The central cross lines represent the braiding operations of B12,B23,and B12 in series,leading to the transformation of chiral Majorana fermions in Eq.(37).

    Since Bi,i+1=Ti,i+1(π/2),here comes the matrix form of the braiding operator

    Now we construct the T quantum gate performed on the single qubit composed of four chiral Majorana fermions. The T quantum gate can not be realized by the braiding of MZMs.As shown in Fig.3(a),a gate voltage is applied to the electric gate in the convex QAHI region along the right edge of the elementary cell B1. Tune the gate voltage to achieve the partial exchange operation of chiral Majorana fermions γ1and γ2with θ=π/4,so that one half of the incoming chiral Majorana fermion γ1(γ2) stays in the original path while the other half of γ1(γ2)crosses over and merges into the opposite side[see the dashed crossing curves in Fig.3(b)]. Follow the definition of the operator T12(π/4)in Eq.(20),four chiral Majorana fermions transform as follows:

    Correspondingly,the single-qubit state basis evolves

    Then we construct the H quantum gate. Via combining the braiding operations in Eq. (34), the H gate could be decomposed into three braiding operations B12, B23, and B12in series, up to an overall phase.[49,78]We introduce two electric gates to braid chiral Majorana fermions within the elementary cell B1 and one quantum-dot structure to braid between cells B1 and B2,as shown in Fig.4(a),that is,

    Correpondingly,the single-qubit state basis evolves

    which is indeed the unitary transformation under the H gate with the definition in Eq.(16).

    3.2. The two-qubit CNOT gate

    where the central qubit labeled by M serves as the ancillary qubit to balance the fermion parity.

    where I2is a 2-by-2 identity matrix. These four matrices are not entangled since they can be decomposed into the direct product of single-qubit matrices.[1]However, considering the braiding operator of γ3and γ4, the matrix form is derived as follows:Noticeably,the braiding operator B34is an entangled operator since the matrix ρt[B34] cannot be decomposed in the direct product form.

    Fig.5. Construction of the CNOT gate. (a)The two-qubit device contains three columns of elementary cells supporting six chiral Majorana fermions. The dashed rectangle emphasizes the core region which performs the CNOT gate with five electric gates and two quantum-dot structures. (b)Braiding diagram of operations in(a). The central cross lines represent the braiding operations of B34,B45,B56,,B34,B45,B34 in series, leading to the transformation of chiral Majorana fermions in Eq. (48). Note here the is the inverse braiding of γ1 and γ2,realized by an opposite value of the gate voltage corresponding to B12.

    The entangled operator is vital in the quantum computation since it introduces the entanglement into the quantum state.One of the famous entangled quantum gates is the CNOT gate(the controlled-NOT gate)performing a conditional operation on the two-qubit state [see the matrix form of CNOT gate in Eq. (16)]. After a CNOT gate, the control qubit remains while the target qubit transforms according to the state of the control qubit: if the control qubit is 1, the target qubit reverses its state;if the control qubit is 0,the target qubit keeps its state.

    Combining the basic braiding operators in two-qubit basis,the CNOT gate is decomposed into seven braiding operations up to an overall phase as follows:[76]

    We construct a device to realize the CNOT gate via five electric gates and two quantum-dot structures, as shown in Fig.5(a). The effect of seven braiding operations from Eq. (47) in series on the six chiral Majorana fermions of cells B1,B2,and B3 is

    3.3. The T and H gates in the two-qubit basis

    Fig.6. H gate acting on the left qubit in the two-qubit basis. (a)The two-qubit device contains three columns of elementary cells supporting six chiral Majorana fermions. The colorful electric gates and quantum dots are enabled while the gray ones are disabled. The H gate acting on the left qubit is realized when opening electric gates and quantum dots of cells B4 and B5. Besides,other single-qubit gates or CNOT gate can be realized when enabling other cells in the same was as core regions in Figs.3–5. (b)Braiding diagram of operations in(a). The central cross lines represent the braiding operations of B12,B23 and B12 in series,leading to the same transformation of chiral Majorana fermions in Eq.(37).

    To realize the H gate on the left qubit HL, we construct the device as shown in Fig.6(a). Two cells, B4 and B5,are crucial to perform the HLgate. Two electric gates and one quantum-dot structure achieve the braiding operations B12, B23, and B12. Multiplying the matrices of these operators in Eq.(43)gives the HLgate up to an overall phase,

    Correspondingly,Fig.6(b)depicts the braiding of γ1and γ2,γ2and γ3,γ1and γ2in series.

    Based on quantum gates HL, HR, TL, and TR, all nonentangled single-qubit gates could be achieved. Easily to see,the CNOT gate is compatible with the device in Fig.6(a).Combined with HL, HR, TL, TR, and CNOT, arbitrary twoqubit gate can be constructed. Thus, the device plotted in Fig.6(a)can perform arbitrary two-qubit quantum gate based on six chiral Majorana fermions.

    4. The quantum circuit of the quantum Fourier transform

    After the realization of quantum gates T, H, and CNOT,as an example,we state that the algorithm of quantum Fourier transform (QFT) can be realized via the two-qubit device of chiral Majorana fermions shown in Fig.6(a).

    As for the realization of quantum gates in the QFT circuit, the single-qubit H gate acting on either qubit has been discussed in Subsection 3.3. The two-qubit CS gate can be decomposed as CS=CNOT·(I ?T?1)·CNOT·(T?T)[see the equivalent circuit in Fig.7(b)].[1]Similarly,the T?1can be realized by inversing the sign of the gate voltage corresponding to the T quantum gate.

    Fig.7. (a)A two-qubit quantum circuit realizes the quantum Fourier transform. (b) The controlled-S gate is decomposed into the quantum gates CNOT and T. T?1 denotes the inverse of T gate, realizable by an opposite gate voltage of T gate.

    5. Discussion on initialization and readout of qubits

    Besides the quantum gates proposed above to realize quantum operations on qubits,here we briefly discuss the initialization and measurement of qubits based on chiral Majorana fermions.

    Considering the conventional physical qubits, information is encoded in the degree of freedom such as photons,spin,or the electric charge. For the photon qubit,[3,6]the initialization is to create single photon states by attenuating laser light and drive them into certain polarization through optical polarizers and the measurement is to detect single photons,e.g.,by a photomultipler tube.For qubits realized by nuclear magnetic resonance,[79]the initial state is prepared in a strong magnetic field to polarize the spins and the readout process is to measure the voltage signal induced by precessing magnetic moment.As to the charge qubit based on the superconducting Josephson junctions[15]or the singly charged quantum dot pair,[10]the electron number is used as the basis state of qubit. These charge qubits can be initialized by electron injection via a current pulse or voltage pulse and the electronic charge state is straightforward to be measured by the quantum point contact or another quantum dots due to their high sensitivity to the conductance response to the applied gate voltage.[12,80,81]

    Here it is worth mentioning that the partial exchange operation of the chiral Majorana fermions via these electric gates is not topologically protected. But it can be well controlled within the time scale ps, presenting the faster speed of information processing than physically moving or measuring Majorana zero modes. Except the gate operating region,the propagation of chiral Majorana fermions is topologically protected with no backscattering and no additional complex phase. Thus, our proposal owns the advantage of quantum computations based on chiral Majorana fermions: the fast speed of quantum computation well preserves and it partially displays the topological protection.

    6. Conclusion

    We have constructed the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions. The elementary cell which consists of a quantum anomalous Hall insulator surrounded by a topological superconductor with some electric gates and quantum-dot structures realizes the braiding operation and the partial exchange operation. Single-qubit operations,T and H quantum gates,are completed via one partial exchange and three braiding operations among four chiral Majorana fermions.An entangled two-qubit gate,the CNOT gate,is achieved via braiding six chiral Majorana fermions.We also show a design which can perform several quantum gate operations in series. These two-qubit quantum gates are used to the quantum circuit model of a simple quantum Fourier transform. This proposed device could be used for more interesting algorithm.

    猜你喜歡
    慶豐
    Photoinduced valley-dependent equal-spin Andreev reflection in Ising superconductor junction
    最美慶豐湖
    上海慶豐彩印有限公司
    綠色包裝(2022年9期)2022-10-12 12:18:10
    給父親做一回“父親”
    A NEW ALGORITHM FOR MONOTONE INCLUSION PROBLEMS AND FIXED POINTS ON HADAMARD MANIFOLDS WITH APPLICATIONS?
    金慶豐3D 硬金新展廳隆重開業(yè)
    中國寶玉石(2018年2期)2018-04-11 07:43:26
    山東慶豐餐飲公司侵害“慶豐”商標(biāo)及不正當(dāng)競爭
    “慶豐包子”案翻天大逆轉(zhuǎn)
    人民周刊(2017年10期)2017-08-04 21:31:40
    從“慶豐包子”看時(shí)評(píng)對(duì)新聞的點(diǎn)化魅力
    新聞傳播(2015年6期)2015-07-18 11:13:15
    AltBOC navigation signal quality assessment and measurement*
    在线天堂中文资源库| 亚洲国产欧美在线一区| 亚洲 欧美一区二区三区| 一边摸一边抽搐一进一出视频| 午夜精品国产一区二区电影| 91精品三级在线观看| 丝瓜视频免费看黄片| 欧美变态另类bdsm刘玥| 欧美在线一区亚洲| av又黄又爽大尺度在线免费看| 久久青草综合色| 曰老女人黄片| 亚洲精品久久成人aⅴ小说| 久久中文字幕一级| 性少妇av在线| 久久人人爽av亚洲精品天堂| 亚洲色图综合在线观看| 国产人伦9x9x在线观看| 免费av中文字幕在线| 中文字幕高清在线视频| 国产一区二区三区视频了| 午夜福利一区二区在线看| 亚洲av第一区精品v没综合| 精品国产一区二区久久| 一级毛片精品| 99久久人妻综合| 亚洲精品美女久久av网站| 国产精品 国内视频| 亚洲第一欧美日韩一区二区三区 | 老汉色∧v一级毛片| 久久精品国产亚洲av香蕉五月 | 日本vs欧美在线观看视频| 精品国内亚洲2022精品成人 | 亚洲全国av大片| 亚洲成av片中文字幕在线观看| 最近最新免费中文字幕在线| 亚洲国产欧美在线一区| 色婷婷久久久亚洲欧美| av在线播放免费不卡| 久久人妻福利社区极品人妻图片| 久久久久视频综合| 国产老妇伦熟女老妇高清| 在线观看一区二区三区激情| 亚洲人成77777在线视频| 精品熟女少妇八av免费久了| 丁香六月欧美| 午夜精品国产一区二区电影| 国产精品av久久久久免费| 中文字幕人妻熟女乱码| 亚洲av片天天在线观看| 999久久久国产精品视频| 亚洲精品久久成人aⅴ小说| 男女下面插进去视频免费观看| 夜夜夜夜夜久久久久| 亚洲成人手机| videos熟女内射| 一个人免费在线观看的高清视频| 免费不卡黄色视频| 超碰成人久久| 两个人免费观看高清视频| 国产成人精品无人区| 自拍欧美九色日韩亚洲蝌蚪91| 日韩免费高清中文字幕av| 十八禁高潮呻吟视频| 久久精品人人爽人人爽视色| 十分钟在线观看高清视频www| netflix在线观看网站| 好男人电影高清在线观看| 国产欧美亚洲国产| 久久天躁狠狠躁夜夜2o2o| 一级片'在线观看视频| 老司机深夜福利视频在线观看| 国产男靠女视频免费网站| 90打野战视频偷拍视频| 免费不卡黄色视频| 黄色视频在线播放观看不卡| 宅男免费午夜| 免费人妻精品一区二区三区视频| 黑人猛操日本美女一级片| 麻豆成人av在线观看| 国产真人三级小视频在线观看| 天堂中文最新版在线下载| 亚洲成国产人片在线观看| 一区二区三区乱码不卡18| 国产在线一区二区三区精| videosex国产| 久久久久视频综合| 一级a爱视频在线免费观看| 久久久精品免费免费高清| a级毛片在线看网站| 搡老乐熟女国产| 亚洲五月色婷婷综合| 91麻豆精品激情在线观看国产 | 天天添夜夜摸| 久久久久国产一级毛片高清牌| 亚洲专区字幕在线| kizo精华| 欧美日韩一级在线毛片| 香蕉久久夜色| 国产淫语在线视频| 麻豆av在线久日| svipshipincom国产片| 黄色成人免费大全| 一二三四社区在线视频社区8| 青草久久国产| 丝袜美足系列| 日韩欧美一区视频在线观看| 亚洲色图 男人天堂 中文字幕| 色视频在线一区二区三区| 国产无遮挡羞羞视频在线观看| 亚洲久久久国产精品| 后天国语完整版免费观看| 精品少妇久久久久久888优播| 久久婷婷成人综合色麻豆| 午夜福利,免费看| 香蕉国产在线看| 精品国内亚洲2022精品成人 | 国产又爽黄色视频| 久久九九热精品免费| 免费在线观看日本一区| 丝袜喷水一区| 高清黄色对白视频在线免费看| 2018国产大陆天天弄谢| 国产无遮挡羞羞视频在线观看| 国产三级黄色录像| 欧美日韩一级在线毛片| 手机成人av网站| 精品视频人人做人人爽| 视频在线观看一区二区三区| 国产免费视频播放在线视频| 女人高潮潮喷娇喘18禁视频| 日韩欧美免费精品| 在线播放国产精品三级| 亚洲美女黄片视频| 久久精品成人免费网站| 日日爽夜夜爽网站| h视频一区二区三区| 国产黄色免费在线视频| 亚洲中文日韩欧美视频| 色在线成人网| 久久午夜亚洲精品久久| 女人爽到高潮嗷嗷叫在线视频| 欧美av亚洲av综合av国产av| 啪啪无遮挡十八禁网站| 脱女人内裤的视频| 巨乳人妻的诱惑在线观看| 亚洲精品美女久久久久99蜜臀| 国产福利在线免费观看视频| 久9热在线精品视频| 午夜久久久在线观看| 热re99久久国产66热| 新久久久久国产一级毛片| 亚洲国产精品一区二区三区在线| 国产99久久九九免费精品| 新久久久久国产一级毛片| 精品福利永久在线观看| 精品少妇内射三级| 欧美变态另类bdsm刘玥| 99久久精品国产亚洲精品| 国产精品久久久久久精品电影小说| 久久天堂一区二区三区四区| 免费在线观看黄色视频的| 无限看片的www在线观看| 他把我摸到了高潮在线观看 | 伊人久久大香线蕉亚洲五| 日韩视频一区二区在线观看| 亚洲国产中文字幕在线视频| 黑人巨大精品欧美一区二区蜜桃| 久久久久国内视频| 大片免费播放器 马上看| 日韩 欧美 亚洲 中文字幕| 91国产中文字幕| av国产精品久久久久影院| 精品亚洲乱码少妇综合久久| 国产精品偷伦视频观看了| 免费在线观看日本一区| 一区二区日韩欧美中文字幕| 欧美精品一区二区免费开放| 女人爽到高潮嗷嗷叫在线视频| 国产av一区二区精品久久| 波多野结衣一区麻豆| 啦啦啦中文免费视频观看日本| 日韩成人在线观看一区二区三区| 老鸭窝网址在线观看| 国产在线精品亚洲第一网站| 免费黄频网站在线观看国产| 桃红色精品国产亚洲av| 美国免费a级毛片| 精品视频人人做人人爽| 亚洲国产av影院在线观看| 女性被躁到高潮视频| 亚洲久久久国产精品| 亚洲免费av在线视频| 777久久人妻少妇嫩草av网站| 人妻 亚洲 视频| 久久午夜亚洲精品久久| 色婷婷久久久亚洲欧美| 色94色欧美一区二区| 午夜激情久久久久久久| 三上悠亚av全集在线观看| 欧美激情高清一区二区三区| 天堂8中文在线网| 亚洲少妇的诱惑av| 国产黄频视频在线观看| 欧美 亚洲 国产 日韩一| 午夜福利一区二区在线看| 视频区图区小说| 欧美精品亚洲一区二区| 俄罗斯特黄特色一大片| 91老司机精品| 少妇精品久久久久久久| 别揉我奶头~嗯~啊~动态视频| 国产成+人综合+亚洲专区| 国产不卡av网站在线观看| 国产欧美日韩综合在线一区二区| 亚洲熟女毛片儿| 99国产综合亚洲精品| 夫妻午夜视频| 国产亚洲精品第一综合不卡| 如日韩欧美国产精品一区二区三区| 99九九在线精品视频| 亚洲精品一二三| 国产欧美日韩一区二区精品| 一二三四在线观看免费中文在| 亚洲精品美女久久久久99蜜臀| 91麻豆av在线| 在线观看www视频免费| 久久av网站| 日韩中文字幕视频在线看片| 欧美 日韩 精品 国产| 香蕉丝袜av| 黄色a级毛片大全视频| 精品亚洲成a人片在线观看| 在线观看免费日韩欧美大片| 超碰成人久久| 亚洲人成77777在线视频| 搡老乐熟女国产| 亚洲成人免费av在线播放| 1024视频免费在线观看| 精品卡一卡二卡四卡免费| 少妇被粗大的猛进出69影院| 一区二区av电影网| 飞空精品影院首页| 男女下面插进去视频免费观看| 一级毛片精品| 亚洲成av片中文字幕在线观看| 婷婷丁香在线五月| 建设人人有责人人尽责人人享有的| 成人亚洲精品一区在线观看| 啦啦啦中文免费视频观看日本| 午夜福利乱码中文字幕| 亚洲第一欧美日韩一区二区三区 | 视频在线观看一区二区三区| 757午夜福利合集在线观看| 深夜精品福利| 黑人猛操日本美女一级片| 十八禁高潮呻吟视频| 久久九九热精品免费| 亚洲一区中文字幕在线| 天天添夜夜摸| 一区二区三区国产精品乱码| 亚洲成av片中文字幕在线观看| 欧美日韩亚洲国产一区二区在线观看 | www.精华液| 在线观看66精品国产| 18禁国产床啪视频网站| 亚洲精品自拍成人| 久久久久久久久免费视频了| 午夜视频精品福利| 日本黄色日本黄色录像| 日本av免费视频播放| 亚洲欧美日韩高清在线视频 | 18禁美女被吸乳视频| 精品久久蜜臀av无| 欧美日韩av久久| a级片在线免费高清观看视频| 国产黄频视频在线观看| 丁香六月欧美| 丁香欧美五月| 视频在线观看一区二区三区| 50天的宝宝边吃奶边哭怎么回事| 国产欧美日韩一区二区三区在线| 亚洲人成77777在线视频| 少妇的丰满在线观看| 久久久久精品人妻al黑| 国产精品美女特级片免费视频播放器 | 蜜桃在线观看..| 高清黄色对白视频在线免费看| 久久久精品94久久精品| 久热爱精品视频在线9| 国产精品麻豆人妻色哟哟久久| 男女免费视频国产| 国产片内射在线| 亚洲欧美精品综合一区二区三区| 亚洲成av片中文字幕在线观看| 一进一出抽搐动态| 香蕉久久夜色| 国产精品久久久人人做人人爽| 桃红色精品国产亚洲av| 免费在线观看日本一区| 少妇精品久久久久久久| 丝袜人妻中文字幕| 久久99热这里只频精品6学生| 日韩制服丝袜自拍偷拍| 国产成人精品无人区| 黄色丝袜av网址大全| 成人特级黄色片久久久久久久 | 国产av又大| 亚洲中文日韩欧美视频| 久久狼人影院| 久9热在线精品视频| 国产在视频线精品| 日韩欧美一区视频在线观看| 国产欧美日韩一区二区精品| 国产精品熟女久久久久浪| 亚洲男人天堂网一区| 国产成人欧美在线观看 | 丝袜美足系列| 国产精品国产av在线观看| 日韩人妻精品一区2区三区| 高潮久久久久久久久久久不卡| 女人被躁到高潮嗷嗷叫费观| videosex国产| 久久久久视频综合| 在线 av 中文字幕| 国产午夜精品久久久久久| √禁漫天堂资源中文www| 人人妻,人人澡人人爽秒播| 夜夜爽天天搞| 久久99热这里只频精品6学生| 亚洲国产毛片av蜜桃av| 夜夜爽天天搞| 少妇猛男粗大的猛烈进出视频| 无遮挡黄片免费观看| 高清毛片免费观看视频网站 | 午夜免费鲁丝| 少妇精品久久久久久久| 国产欧美日韩一区二区精品| 亚洲一区中文字幕在线| 亚洲成人国产一区在线观看| 一区二区av电影网| 水蜜桃什么品种好| 亚洲精品国产精品久久久不卡| 老鸭窝网址在线观看| 色综合婷婷激情| 搡老岳熟女国产| 女人久久www免费人成看片| 中国美女看黄片| 一区二区三区乱码不卡18| 日韩视频在线欧美| 国产成人影院久久av| 午夜福利影视在线免费观看| 久久人人97超碰香蕉20202| 欧美精品人与动牲交sv欧美| 久久人人爽av亚洲精品天堂| 极品少妇高潮喷水抽搐| 后天国语完整版免费观看| av不卡在线播放| 国产精品九九99| 老司机午夜十八禁免费视频| 在线观看免费高清a一片| 老熟女久久久| 露出奶头的视频| 久久久国产成人免费| 无限看片的www在线观看| 黄片小视频在线播放| 国产国语露脸激情在线看| 国产无遮挡羞羞视频在线观看| 亚洲国产精品一区二区三区在线| 亚洲国产中文字幕在线视频| 蜜桃国产av成人99| 啦啦啦 在线观看视频| 大码成人一级视频| 免费日韩欧美在线观看| 一边摸一边做爽爽视频免费| 久久国产精品大桥未久av| 亚洲国产中文字幕在线视频| 久久久久久人人人人人| 国产三级黄色录像| 一二三四社区在线视频社区8| 后天国语完整版免费观看| 真人做人爱边吃奶动态| 99re在线观看精品视频| a在线观看视频网站| 国产高清国产精品国产三级| 亚洲精品中文字幕在线视频| 老司机影院毛片| 日本一区二区免费在线视频| 黄色视频在线播放观看不卡| 久久久国产精品麻豆| 亚洲欧洲精品一区二区精品久久久| 日韩成人在线观看一区二区三区| 两性夫妻黄色片| 热99国产精品久久久久久7| 国产午夜精品久久久久久| 欧美中文综合在线视频| 99国产极品粉嫩在线观看| 大型av网站在线播放| 午夜福利视频精品| 久久精品aⅴ一区二区三区四区| 久久亚洲真实| 国产亚洲精品一区二区www | 日韩欧美一区二区三区在线观看 | 亚洲精品自拍成人| 日韩免费高清中文字幕av| 在线天堂中文资源库| 丰满人妻熟妇乱又伦精品不卡| 久久久国产欧美日韩av| 国产黄频视频在线观看| 亚洲色图av天堂| 俄罗斯特黄特色一大片| 极品教师在线免费播放| 亚洲国产欧美在线一区| 天堂俺去俺来也www色官网| 露出奶头的视频| 一级毛片精品| 国产不卡av网站在线观看| 久久久久久亚洲精品国产蜜桃av| av在线播放免费不卡| 一边摸一边抽搐一进一小说 | 精品国产一区二区久久| 一边摸一边抽搐一进一出视频| 成人亚洲精品一区在线观看| 淫妇啪啪啪对白视频| 美女午夜性视频免费| 99香蕉大伊视频| 中文亚洲av片在线观看爽 | 啪啪无遮挡十八禁网站| 欧美日韩国产mv在线观看视频| 1024香蕉在线观看| 国产97色在线日韩免费| 999久久久国产精品视频| 久久性视频一级片| 97人妻天天添夜夜摸| 色94色欧美一区二区| 日本av手机在线免费观看| 少妇被粗大的猛进出69影院| 亚洲第一欧美日韩一区二区三区 | 国产亚洲欧美在线一区二区| 免费在线观看视频国产中文字幕亚洲| 日日爽夜夜爽网站| 午夜福利一区二区在线看| 首页视频小说图片口味搜索| 自线自在国产av| 欧美成狂野欧美在线观看| 色老头精品视频在线观看| 国产有黄有色有爽视频| 午夜福利视频精品| 国产精品二区激情视频| 成人18禁在线播放| 日韩成人在线观看一区二区三区| 国产成人av教育| 午夜视频精品福利| 久久午夜亚洲精品久久| 欧美成人午夜精品| 亚洲av欧美aⅴ国产| 免费在线观看视频国产中文字幕亚洲| 久久精品人人爽人人爽视色| 久久青草综合色| 国产不卡av网站在线观看| 日本av手机在线免费观看| 免费高清在线观看日韩| 老熟妇乱子伦视频在线观看| 国产av又大| 国产在线一区二区三区精| 成人三级做爰电影| 欧美黑人欧美精品刺激| 丰满少妇做爰视频| 久久天躁狠狠躁夜夜2o2o| 美女视频免费永久观看网站| 最新在线观看一区二区三区| 国产精品久久久人人做人人爽| 日本av手机在线免费观看| 黑丝袜美女国产一区| 亚洲自偷自拍图片 自拍| 麻豆av在线久日| 女人被躁到高潮嗷嗷叫费观| 中文字幕色久视频| 久久精品aⅴ一区二区三区四区| 91老司机精品| 久久人妻福利社区极品人妻图片| 麻豆成人av在线观看| 亚洲人成电影免费在线| tube8黄色片| 国产人伦9x9x在线观看| 国产免费现黄频在线看| 欧美日韩av久久| 波多野结衣一区麻豆| 丁香六月天网| 中文字幕最新亚洲高清| 亚洲av电影在线进入| 曰老女人黄片| 男人操女人黄网站| 丁香六月天网| 国产精品一区二区在线不卡| 成人免费观看视频高清| 在线 av 中文字幕| 免费观看a级毛片全部| 97在线人人人人妻| 正在播放国产对白刺激| 午夜福利免费观看在线| 国产精品98久久久久久宅男小说| 桃红色精品国产亚洲av| 免费看a级黄色片| 久久久精品94久久精品| 久久久国产精品麻豆| 激情在线观看视频在线高清 | 国产欧美日韩综合在线一区二区| 啦啦啦免费观看视频1| 久久人人爽av亚洲精品天堂| 国内毛片毛片毛片毛片毛片| 黄网站色视频无遮挡免费观看| 久久这里只有精品19| 久久精品aⅴ一区二区三区四区| 99精品在免费线老司机午夜| 少妇裸体淫交视频免费看高清 | 自拍欧美九色日韩亚洲蝌蚪91| 免费在线观看完整版高清| 9191精品国产免费久久| 亚洲七黄色美女视频| 另类精品久久| 十分钟在线观看高清视频www| kizo精华| 一区二区三区乱码不卡18| 丝袜人妻中文字幕| 97在线人人人人妻| 久久午夜综合久久蜜桃| 国产一区二区激情短视频| 亚洲 欧美一区二区三区| 日本黄色日本黄色录像| 波多野结衣一区麻豆| 人人妻人人添人人爽欧美一区卜| 国产精品香港三级国产av潘金莲| 大码成人一级视频| 巨乳人妻的诱惑在线观看| 自拍欧美九色日韩亚洲蝌蚪91| 国产又爽黄色视频| 国产激情久久老熟女| 久久亚洲精品不卡| 久久久久精品国产欧美久久久| 欧美老熟妇乱子伦牲交| 青青草视频在线视频观看| 国产在线视频一区二区| 国产成人免费无遮挡视频| 国产精品九九99| 黑人操中国人逼视频| 久久人妻熟女aⅴ| 免费在线观看视频国产中文字幕亚洲| 亚洲精品中文字幕一二三四区 | 国产午夜精品久久久久久| 99国产精品99久久久久| 极品教师在线免费播放| 欧美精品啪啪一区二区三区| 日韩欧美免费精品| 欧美激情久久久久久爽电影 | 91麻豆av在线| 久久精品国产亚洲av香蕉五月 | 免费一级毛片在线播放高清视频 | 亚洲色图综合在线观看| 夜夜爽天天搞| 午夜免费成人在线视频| 9色porny在线观看| 亚洲精品中文字幕一二三四区 | 日韩中文字幕视频在线看片| 国产欧美日韩精品亚洲av| av不卡在线播放| 亚洲一卡2卡3卡4卡5卡精品中文| 午夜福利乱码中文字幕| 色播在线永久视频| 男女边摸边吃奶| 免费看a级黄色片| 91老司机精品| 人成视频在线观看免费观看| www.自偷自拍.com| 久久影院123| 视频区欧美日本亚洲| av免费在线观看网站| 日本撒尿小便嘘嘘汇集6| 午夜福利,免费看| 欧美精品啪啪一区二区三区| 99热国产这里只有精品6| 在线永久观看黄色视频| 大片免费播放器 马上看| 一区二区三区精品91| 91成人精品电影| 国产精品一区二区免费欧美| 亚洲一码二码三码区别大吗| www.自偷自拍.com| 欧美久久黑人一区二区| 亚洲av日韩在线播放| 久久人人97超碰香蕉20202| 成人影院久久| 亚洲精品中文字幕一二三四区 | 高清av免费在线| 人人妻人人澡人人爽人人夜夜| 曰老女人黄片| 操美女的视频在线观看| 精品人妻熟女毛片av久久网站| 欧美精品亚洲一区二区| 女人精品久久久久毛片| 另类亚洲欧美激情| 一级片'在线观看视频| 亚洲男人天堂网一区| 亚洲午夜精品一区,二区,三区| 国产一区二区在线观看av| 久热这里只有精品99| 日韩免费高清中文字幕av| 亚洲一卡2卡3卡4卡5卡精品中文| 国产免费av片在线观看野外av| 国产成+人综合+亚洲专区| 最黄视频免费看| 午夜福利一区二区在线看| 无限看片的www在线观看| 99热国产这里只有精品6| 国产精品免费一区二区三区在线 |