• <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 ?

    Majorana noise model and its influence on the power spectrum

    2024-01-25 07:29:42ShumengChen陳書(shū)夢(mèng)SifanDing丁思凡ZhenTaoZhang張振濤andDongLiu劉東
    Chinese Physics B 2024年1期
    關(guān)鍵詞:思凡劉東

    Shumeng Chen(陳書(shū)夢(mèng)), Sifan Ding(丁思凡), Zhen-Tao Zhang(張振濤), and Dong E.Liu(劉東),3,4,5,?

    1State Key Laboratory of Low Dimensional Quantum Physics,Department of Physics,Tsinghua University,Beijing 100084,China

    2School of Physics Science and Information Technology,Shandong Key Laboratory of Optical Communication Science and Technology,Liaocheng University,Liaocheng 252059,China

    3Beijing Academy of Quantum Information Sciences,Beijing 100193,China

    4Frontier S

    cience Center for Quantum Information,Beijing 100084,China

    5Hefei National Laboratory,Hefei 230088,China

    Keywords: Majorana zero mode, topological quantum computation, topological devices, decoherence and noise in qubits

    1.Introduction

    Non-Abelian anyons offer a novel methodology for potentially achieving fault-tolerant quantum computation,wherein quantum information is encoded using non-local degrees of freedom and quantum operations are manipulated in a manner that is topologically protected.[1–8]Of particular interest in this context are the Majorana zero modes that can be potentially hosted by topological superconductors, which are widely regarded as the most realizable candidates for topological quantum computation.[9–24]

    Numerous theoretical proposals have been put forward regarding the readout and manipulation of Majorana qubits in superconducting nanowires.[23,25–42]In these designs, the qubit is encoded in a non-local manner using the parity of pairs of Majorana zero modes.In topological quantum computing,the readout of Majorana parity is of significant importance,and a number of methods have been proposed for this purpose.These include projective measurement schemes[28,29]and continuous measurement approaches with the use of quantum dot ancillaries,[26,43]as well as a conductance-based readout method in a dot-free configuration under a tunable magnetic flux.[30]A recent publication[44]briefly discusses the above different techniques used for Majorana parity readout.Among these methods,the use of quantum dot ancillaries for measurement displays considerable promise due to its scalability.[29]In work by Steineret al.,[43]a continuous measurement scheme employing quantum dot ancillaries is suggested to distinguish between Majorana parities.Specifically, the power spectrum of current correlation is utilized under the diffusion limit of a quantum point contact to achieve this objective.Building upon this idea, we examine the physical parameter discussed in Wiseman and Milburn’s work[45]and derive the power spectrum of current in the quantum point contact utilizing the quantum jump model.Based on this model,we then study a readout method for Majorana parities.It is suggested that Majorana readout based on the quantum jump model may be more practical for real materials and experimental devices.

    While Majorana qubits possess certain theoretical advantages, quantum information can still be affected by both internal and external noise sources.[46–53]Therefore, refining the noise model and evaluating its impact is crucial for the progress of Majorana quantum computation.The Majorana noise model was initially developed to study the impact of noise on quantum channels by Knapp and coworkers[53]In this regard, the model was used to investigate the pseudothreshold of the Majorana qubit realization of Bacon–Shor code.To further investigate the effect of noise from a quantum dynamics perspective,we proposed a concise Majorana noise model based on the master equation in Lindblad form.We combined this model with the Majorana noise model and conducted numerical research to examine the influence of noise on the readout signal.Our study yielded insights into how different types and intensities of noise affect the power spectrum and frequency curve.Based on these findings, we developed an approach for detecting noise in the Majorana qubit.We employed a quaternion array(Γ1,Γ2,εhyb,g2)to classify the noise, while peak width, peak weight, fusion point and curve structure were used to label the frequency curve as it varied with quasi-particle poisoning rate.By analyzing the characteristics of the frequency curve,we obtained crucial information about the noise,thus introducing an approach for investigating noise in the Majorana qubit.

    The present paper is structured as follows.Section 2 provides the formulation of the noise model for quasi-particle poisoning and Majorana overlapping noise based on the master equation in Lindblad form.In Section 3, we offer a comprehensive review of the Majorana parity readout technique and develop it further through the use of the quantum jump model for quantum point conduction coupled with an ancillary quantum dot.Subsequently, in Section 4, we evaluate the impact of noise on the readout signal through numerical calculations using the model presented in Section 2 and the methodology elaborated in Section 3;based on these results,we propose an approach for detecting noise in the Majorana qubit.

    2.Majorana noise model

    The issue of noise in Majorana qubits has been extensively discussed in previous works such as Refs.[29,46,47,50,51,53,54].As a complement to these discussions,this section presents a mathematical formulation in Lindblad form to model the effects of quasi-particle poisoning noise and Majorana overlapping with fluctuations.

    2.1.Single quasi-particle poisoning event

    Quasi-particle poisoning represents a major source of noise in Majorana qubits.

    This phenomenon is primarily attributed to the presence of superfluous electrons within the device, as well as the ensnarement of those single electrons by the Majorana wave function.The creation of those single electrons is generally provoked by thermal excitation or radiationinduced excitement of Cooper pairs within the superconducting material.[47,53]Because quasi-particle poisoning can directly change the parity state of a Majorana qubit, it can lead to either qubit error or leakage,causing the Majorana qubit to deviate from its original computational subspace,resulting in negative impacts on the storage and retrieval of information for topological quantum bits.

    In this section,we adopt the quantum trajectory approach outlined in Refs.[55,56] to construct our noise model.Our starting point is the simplest noise event,namely,a Majorana quasi-particle poisoning event, denoted as ?γ1, that occurs in one of the Majorana zero modes.We assume that the quasiparticle poisoning rate,denoted asΓ1,remains constant and is entirely determined by the environment, i.e., independent of the system state.At timet,the quasi-particle poisoning event dN(t)=1 occurs with a probability ofp1=Γ1dtduring the time interval dt.Here,N(t) represents the number of quasiparticle poisoning events up to timet.The operator associated with this event can be expressed as

    such that

    Then, by the conservation of probability, we can define the operator when no event happens ?A0by

    then

    Thus,we can get the state for both evolutions.For dN(t)=1,

    For dN(t)=0,

    Then,the stochastic Schr¨odinger equation is

    Then by Ito rules and taking averageE[dN]=Γ1dt, we can get the master equation of quasi-particle poisoning

    whereρMpresent the density matrix of the Majorana qubit.The noise model can also be obtained when a quasi-particle poisoning event affects the whole Majorana zero mode in the same way,

    In order to obtain an estimate of the quasi-particle rateΓi,we can make use of the values reported in Refs.[47,51].These values take into account all potential sources of uncorrelated quasi-particle poisoning events that contribute toΓi.

    2.2.Overlapping with fluctuation

    Taking into account the finite size of nanowires,the effective Hamiltonian for the Majorana system takes the form[9,37]

    Here,the value ofεhybwas discussed in Refs.[9,37,54].However, we assume that the hybridization energy may exhibit fluctuations, leading to a corresponding fluctuating Hamiltonian given by

    In this expression, the termgξ(t) represents the fluctuation contribution and we assume that it follows Gaussian statistics such that

    Here,grepresents the intensity of the noise and dWdenotes the Wiener increment.Using these assumptions,we can obtain the following property forδε(t):

    For Gaussian white noise,

    whereδ(t ?τ)is the Dirac function.Then

    With certain encoding, we can have iγ1γ2=σzunder a qubit basis.Then,by Ito rules,we can get the propagator

    Then,by taking the average of stochastic wave function increment dρ=d(|ψ〉〈ψ|),we can get the master equation for the fluctuating hybridization energy.

    So far, we have obtained the master equation for Majorana overlapping with Gaussian fluctuation.

    3.Majorana parity readout by continuous measurement

    Several proposals for Majorana readout methods utilizing quantum dot ancillaries have been presented in the literature.[26,28,29,57]In contrast,Steineret al.[43]introduced a novel technique that relies on continuous measurement.This method utilizes the power spectrum of current correlation in a quantum point contact, in conjunction with a quantum dot,to differentiate between different Majorana parities.A recent review article[44]provides a succinct overview of various Majorana readout approaches.We begin by introducing the effective tunneling Hamiltonian for a Majorana coupled with quantum dots[30]

    The Majorana parity-dependent effective tunneling amplitude,denoted bytp,is given bytp=t1?ipt2.Alternatively,we can expresstpin terms of the phase difference betweent1andt2astp=|t1|(1?i eiθ pλ),whereλ=|t2|/|t1|andθ=Arg(t2/t1).This expression serves as the fundamental premise for all Majorana parity readout techniques that employ quantum dot ancillaries.

    The article[29]discusses three methods for measuring the parity-dependent tunneling amplitude in a Majorana system.The first method involves energy-level spectroscopy,whereby the ground-state energy difference is measured.The second and third methods rely on the measurement of the differential capacitance and the average dot occupation number, respectively.

    Reference [28] proposes a Majorana readout method based on the direct measurement of the parity-dependent Rabi-oscillation frequency, which originates from the paritydependent tunneling amplitude.However, this method requires a fast projective measurement of the quantum dot,which poses experimental challenges.Therefore, Ref.[43]suggests a continuous measuring approach to overcome these challenges.In this approach, the Rabi-oscillation frequency is obtained by measuring the current correlation in a quantum point contact coupled to the quantum dot ancillary.The setup for continuous measuring is shown in Fig.1.As discussed in Refs.[45,55,58–61], two models describe the current in a quantum point contact.In addition, Ref.[43] employs the diffusive model.Here,by considering the discussion in Refs.[45,62],we explore the quantum jump model as a suitable framework for simulating scenarios that involve a photon number detector.

    Fig.1.Setup for continuous measurement of Majorana parity.

    Subsequently, the following Hamiltonian for the perfect Majorana island connected to a quantum dot is introduced:

    In the low-temperature regime and under the strong magnetic field required for a topological phase,[11,20]the effective Hamiltonian for a single spinless fermion level can be approximated for the quantum dot

    whereε1is the dot level andis the particle number operator for the electron of the quantum dot.In the work by Karziget al.,[29]the charging energy terms of the quantum dot and the superconducting island are taken into consideration.By employing the parameter transformation method discussed in Ref.[57], the mutual charging energy term and the dot level term are effectively combined into a single charging energy term,which can be expressed as ?HC+QD=εC(?n1?n1g)2,where ?n1represents the particle number operator of the quantum dot andn1gis the quantum dot’s ground state occupation number.The parameterεCdenotes the effective dimensionless gate voltage of the superconductor–quantum dot system and the effective charging energy.The detailed treatment can be found in the appendix of Ref.[57].As the system operates in the resonance regime,where the energy of the quantum dot is approximately equal to the charging energy of the superconductor,for simplicity,the authors useε1as the effective tuning parameter and express the effective Hamiltonian of the quantum dot asε1?n1.This simplification does not affect the matrix form or the measurement result.

    Subsequently, the quantum point contact is integrated as a dot occupation number monitor in the subsequent stage,enabling the extraction of parity information from the current flowing through the quantum point contact.We follow a strategy similar to that used for a double quantum dot[60,61,63,64]and obtain the dynamics for the Majorana–quantum dot setup

    The Hamiltonian for the quantum point contact can be expressed as follows:

    where ?cLk, ?cRkandωLk,ωRkare, respectively, the electron annihilation operators and the energy levels for the left and right reservoir states at wave numberk.Tkqis the tunneling amplitude for the corresponding tunneling channel.The Hamiltonian describing the interaction between the quantum dot and quantum point contact is given as

    When the quantum dot is occupied,the effective tunneling amplitude of quantum point contact changes fromTkq →Tkq+χkq.Next,we follow the approach presented in Refs.[55,63]and obtain the conditional current in the quantum point contact based on the quantum jump model

    The two values currently depend on the dot occupation number.The reduced two-time-correlation function is defined as

    where E[]present the ensemble average.

    In the general case, it is preferable to conduct numerical investigations onR(τ).However,in the case whereε1=0,an analytical expression is available, the current correlation for Majorana coupled to the quantum dot is

    Then

    whereS0=e2(D'+D)represents the shot noise.Thus we can distinguish between different Majorana parities by the power spectrum of the current in quantum point contact.Figure 2 shows the numerical simulation of the power spectrum for different Majorana parity values.

    Fig.2.Power spectrum for different Majorana parity values.The normalized power spectrum, as defined here, is represented by SN =,where the parameters are specified as follows:λ =1,θ=π/4,κ =0.2|t1|,and|t1|=?.It is worth noting that ? serves as the reference frequency unit here.

    4.Noise influence on parity readout

    The scheme presented in Ref.[43] posits a power spectrum current correlation technique for ideal Majorana qubits,featuring zero noise, as a means of Majorana parity readout.In this scenario,the current correlation can be computed from the fixed parity subspace, much akin to the double quantum dot system with a constant tunneling amplitudet1+ipt2.This approach remains valid for other parity readout methods for Majorana qubits, such as measuring the average occupation number of the quantum dot,for which only the subspace warrants consideration.Nevertheless, when probing the impact of Majorana noise, comprehensive consideration of the full Hilbert space, inclusive of both the Majorana qubit and the quantum dot,becomes indispensable.

    For quasi-particle poisoning,we can get the dynamics of a Majorana coupled with a quantum dot

    For Majorana overlapping,we can get

    For Majorana overlapping with fluctuation,we can get

    As the analytical solution to the aforementioned master equation is considerably intricate,our discussion primarily focuses on the numerical outcomes.

    4.1.Quasi-particle poisoning

    For quasi-particle poisoning, the following special scenarios are first considered: whenΓ1=Γ2, whenΓ1/=0 andΓ2=0, and whenΓ1=0 andΓ2/=0.The first situation describes a homogeneous environment,whereas the second and third cases represent specific instances of an inhomogeneous noise environment.This study chiefly examines three parameter regions concerning the quasi-particle rate: (1) when the quasi-particle poisoning rate is significantly smaller than the Rabi oscillation frequency,(2)when the quasi-particle poisoning rate is of the same order of magnitude as the Rabi oscillation frequency,and(3)when the quasi-particle poisoning rate is much greater than the Rabi oscillation frequency.

    In the context of homogeneous quasi-particle poisoning noise, we can denote the noise intensity byΓ=Γ1=Γ2.As demonstrated in Fig.3(a), when the quasi-particle poisoning rate is very small (Γ ?|t1|), the peak frequency exhibits an insignificant shift.This indicates that the parity measurement result can be obtained with high precision under such a noise intensity.As the quasi-particle poisoning rate increases, the two peaks move towards each other, accompanied by an increase in peak width,and eventually merge into a single peak at the Rabi oscillation frequency(Γ ≈|t1|).This implies that,in this range, the two peaks cannot be distinguished and the Majorana parity cannot be obtained from the measurement.As the quasi-particle rate further increases, the merged peak shifts its frequency to zero.This implies that when the quasiparticle poisoning rate is much larger than the Rabi oscillation frequency,the current in QPC is described by shot noise,which is similar to the behavior observed in coupled quantum dots whenκ ?4?.Here,κ=|?χ|2represents the coupling strength between the quantum dot and QPC,and?represents the coupling strength between quantum dots.In this case,the electron will be localized in the quantum dot, a phenomenon also referred to as the quantum Zeno effect.Figures 3(b)–3(d)illustrate the power spectrum at different levels of noise intensity.

    Subsequently, an observation was made that the power spectrum’s structure changes in the presence of quasi-particle poisoning.As depicted in Figs.4(a) and 4(b), a secondary peak emerges at the location of the opposite parity with a comparatively smaller weight for each parity.Here, weight corresponds to the area enclosed by the corresponding peak.The secondary peak remains negligible under a relatively low quasi-particle poisoning rate but becomes noticeable at a magnitude proximate to the Rabi frequency.As the noise intensity rises, the weight of the secondary peak increases.The primary and secondary peaks merge into a single peak with an increase in noise intensity.This phenomenon is attributed to the quasi-particle poisoning event’s alteration of the Majorana parity and the effective tunneling amplitude,resulting in the emergence and amplification of the secondary peak.The double-peak configuration of the power spectrum with a noise intensity ofΓ/?=0.5 is visually demonstrated in Fig.4(c).

    Subsequently,we present a discussion on inhomogeneous quasi-particle noise.Firstly, we consider the special cases whereΓ1/= 0 andΓ2= 0, as well asΓ1= 0 andΓ2/= 0.These cases correspond to the scenario where only one Majorana zero mode undergoes a quasi-particle poisoning event.Forλ=1, the power spectrum is indistinguishable betweenΓ1/= 0,Γ2= 0 andΓ1= 0,Γ2/= 0.By comparing Figs.5 and 3, the most conspicuous dissimilarity between inhomogeneous quasi-particle noise and homogeneous quasi-particle noise is that for noise intensities much greater than the Rabi oscillation frequency;the fused frequency tends to zero in the former,whereas it tends to|t1|(also equal to|t2|)in the latter.

    Fig.3.(a)Peak frequency curve of different parity under quasi-particle noise intensities(Γ/?)ranging from 10?3 to 101,with λ =1,θ =π/4,κ =0.002|t1|, and |t1|=?.The corresponding Rabi oscillation frequency,denoted as ωR,is associated with the peak.The error bar in the figures represents the peak width and the main peak of each parity state is shown.The values of κ and θ are held constant throughout the remaining images.(b) Power spectrum for Γ/? =0.01.(c) Power spectrum for Γ/? =1.6.(d)Power spectrum for Γ/? =10.

    Fig.4.(a) Peak frequency curve for even parity under quasi-particle noise intensity ranging from 10?3 to 101,where the color bar presents the relative weight of the peaks.(b)Peak frequency for odd parity under quasi-particle noise intensity ranging from 10?3 to 101.(c)Power spectrum for Γ/? =0.5.

    Fig.5.(a) Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ1/?, which varies from 10?3 to 101.Additionally, Γ2/? =0 and the value of λ is set to 1.The frequency diagram exhibits symmetry across the ωR =0 axis.Therefore, in (a), to provide a clearer demonstration, we only display even parity for ωR >0 and only odd parity for ωR <0.Otherwise, the even and odd parity would overlap, decreasing the picture’s clarity.(b) Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ2/?,which varies from 10?3 to 101, while Γ1 =0 and λ =1.Similar to (a), only odd parity is presented for ωR >0 and only even parity for ωR <0 to enhance clarity.Due to the symmetry of the frequency diagram by the axis ωR=0,(a)and(b)are identical.(c)Power spectrum for Γ1/? =0.5.

    By comparing Figs.5 and 3,we observe the difference between inhomogeneous quasi-particle noise and homogeneous quasi-particle noise,but we are unable to differentiate between a single quasi-particle ?γ1(Γ1/=0,Γ2=0),and a single quasiparticle, ?γ2(Γ2/=0,Γ1=0).This lack of distinction is expected because atλ=1, the Majorana modes ?γ1and ?γ2possess full symmetry and thus it is not possible to distinguish between them.If we desire to distinguish between ?γ1and ?γ2in real space, we can set|t1|/=|t2|and break the symmetry between the noise effects ofΓ1andΓ2.For instance,whenλ=0.5,that is|t1|=2|t2|, we can define ?γ1and ?γ2in real space, resulting in different spectra for the two types of noise.Additionally,in the high noise region(i.e.,≥101),single quasi-particle noise exhibits distinct behavior from homogeneous quasi-particle noise: the Rabi-oscillation frequency no longer tends to zero but converges to 2|t1|forΓ2=0 and to 2|t2|forΓ1=0.

    Fig.6.(a) Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ1/?, which varies from 10?3 to 101.Additionally,Γ2/? =0 and the value of λ is set to 0.5.For the sake of enhancing visual clarity, only the width of the peak with a weight greater than 10?3 is displayed and only odd parity is displayed for ωR >0.Both parities have the same configuration but with different weights, both are symmetry curves along axis ωR=0 as displayed in Figs.4(a)and 4(b),to have a better comparison,only half of each parity is displayed.(b)Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ2/?, which varies from 10?3 to 101.Additionally, Γ1/? =0 and the value of λ is set to 0.5.(c) Power spectrum for Γ1/? =10 Here the curve of even parity is almost covered by the curve of odd parity,since they have the same configuration.This situation is the same for(d)and other figures.(d)Power spectrum for Γ2/? =10.

    Fig.7.(a) Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ2/?, which varies from 10?3 to 101.Additionally,Γ1/? =0.1 and the value of λ is set to 0.5.(b)Peak frequency curve under the influence of quasi-particle noise with intensity represented by Γ2/?,which varies from 10?3 to 101.Additionally,Γ1/? =0.5 and the value of λ is set to 0.5.

    Subsequently, we explore the case where bothΓ1andΓ2are non-zero and not equal.Specifically,we consider the range ofΓ1/?to be between 10?3and 101, whileΓ2remains constant.Moreover, we can setΓ1=x+C1withx ∈[10?3,101]andΓ2=C2, or conversely,Γ2=x+C2withx ∈[10?3,101]andΓ1=C1, following the approach proposed in Ref.[52].This yields the possibility of discerning the prevailing quasiparticle noise situation(represented byC1andC2)in the Majorana qubit by observing different behaviors of the power spectrum concerning the variablex.As such, we present a method for detecting noise in the Majorana qubit, with the numerical results serving as a reliable reference for experimental investigations.We demonstrate the peak frequency diagram as an illustrative example in Figs.7(a) and 7(b).Notably, distinct quasi-particle poisoning leads to different behaviors ofωR.Specifically, the peak width forΓ1/?=0.1 is considerably narrower than that ofΓ1/?=0.5 at the sameΓ2value.Both peak widths increase withΓ2before the fusion point, corresponding to the rising dissipation effect proportional to the total noise rate (Γ1+Γ2).Additionally, we observe that the fusion points for different noise intensities also differ.We denote the fusion point asF= (ΓF,ωRF),with the value ofΓFforΓ1/?=0.5 being larger than that forΓ1/?=0.1,and the value ofωRFforΓ1/?=0.5 being greater than the value forΓ1/?=0.1.Furthermore,forΓ1/?=0.1,the frequency curves approach zero before fusing,whereas forΓ1/?=0.5,the frequency curve fuses directly,indicating different fusion points.The weight of the secondary peak forΓ1/?=0.5 is also greater than the weight of the secondary peak forΓ1/?=0.1.Overall, the fusion point, peak width and peak weight serve as reliable indicators for distinguishing different noise types and intensities.Therefore,the theoretical results presented in this study can aid in detecting noise in the Majorana qubit.

    4.2.Overlapping with fluctuation

    This section explores the effects of overlapping and fluctuations on the power spectrum of the Majorana readout.Firstly, we analyze the impact of pure Majorana overlapping.The Hamiltonian governing the coupling between a Majorana mode and a quantum dot under the particle number basis,with pure Majorana overlapping,can be expressed as

    Based on the Hamiltonian derived earlier,it is evident that pure Majorana overlapping introduces a 2εhybenergy level space,as expected.The even parity and odd parity of the Majorana are denoted as|0〉tand|1〉t,respectively.In an infinitely long nanowire,ideal zero energy degeneracy can be achieved,where the energy level for|0〉tand|1〉tis zero.However,Majorana overlapping leads to a splitting of the degenerate energy level, where the energy level for|0〉tis?εhyb, and for|1〉tisεhyb.Denoting|0〉 and|1〉 as the dot occupation number of the quantum dot, we use|01〉to represent|0〉?|1〉t.The energy level for|01〉 isεhyb, for|10〉 it is?εhyb, for|00〉 it is also?εhyband for|11〉 it isεhyb.Therefore, the diagonal elements of the matrix can be obtained.The effective Rabi oscillation frequency can be calculated asIt is observed that forεhyb<10?1,pure Majorana overlapping has a negligible influence.Forεhyb≥1, the peak frequency increases almost linearly withεhyband the distance between the two parities decreases, while the peak width remains almost unchanged.This indicates that pure Majorana overlapping causes minimal dissipation,which is in accordance with expectations, as illustrated in Fig.8(a).The influence ofεhybon the power spectrum can be observed from Fig.8.Asεhybincreases, the weight of the Rabi oscillation peak decreases while the weight of the zero-frequency peak increases.This indicates that Majorana overlapping leads to the shot noise effect.It should be noted that the main difference between pure Majorana overlapping and Majorana overlapping with fluctuation is the width of the peak,which is caused by fluctuation.

    Fig.8.(a) Peak frequency curve for the scenario of pure Majorana overlapping.It is notable that the diagram possesses a symmetry with respect to ωR=0;therefore,solely the portion corresponding to ωR ≥0 is depicted.(b) Peak frequency curve for Majorana overlapping with fluctuation g2=0.1εhyb.

    In Subsection 4.2, the frequency behavior of overlapping and quasi-particle poisoning noise is discussed by varying the quasi-particle injection rate.The proposed approach suggests that the noise in the Majorana qubit can be uniquely identified and labeled by a quaternion array consisting of(Γ1,Γ2,εhyb,g2), which we refer to as the characteristic array for noise.By analyzing the peak width, fusion point,frequency under the quasi-particle poisoning rate limit and curve structure of the frequency curve, we can describe the behavior of the frequency curve.The establishment of a map between the characteristic array for noise and the frequency curve enables theoretical simulations to provide valuable guidance for the detection and characterization of noise in Majorana qubits.In Fig.9,a comparison is made between different noise parameters.It is observed that, withεhyb/?=1, the frequency under a low quasi-particle poisoning rate is higher than the case without Majorana overlapping.Additionally,differences in peak width and weight are visible for Majorana overlapping noise with and without quasi-particle poisoning(Γ2/?=0.5)under a low quasi-particle poisoning rate(Γ1/? ?1).ForΓ1/? ≈1, it is found that, before fusion,the primary peak frequency decreases but does not reach zero forεhyb/?=1,g2=0.1εhyb, whereas it does reach zero forεhyb/?=1,g2=0.1εhyb,Γ2/?=0.5.After fusion, the primary and secondary peaks are in the fused state forεhyb/?=1,g2=0.1εhyb,but forεhyb/?=1,g2=0.1εhyb,Γ2/?=0.5,there is a non-vanishing space between the primary and secondary peaks.While the physical mechanisms underlying these complex curve behaviors are still not fully understood,the differences between the curves offer a promising approach to identifying and characterizing noise in Majorana qubits.

    Fig.9.(a) Peak frequency curve for εhyb/? =1, g2 =0.1εhyb and λ = 0.5.(b) Peak frequency curve for Γ2/? = 0.5, εhyb/? = 1,g2=0.1εhyb and λ/? =0.5.

    5.Summary and outlook

    In this paper, we present a comprehensive analysis of noise in Majorana qubits, wherein we construct a Majorana noise model that incorporates quasi-particle poisoning and Majorana overlapping with fluctuation.Subsequently,we develop a method for continuous Majorana parity measurement,which relies on the quantum jump model.Furthermore, we examine the impact of noise on the readout signal and propose a new approach for detecting the noise situation in Majorana qubits.Our future work aims to expand upon our current findings and refine the mapping between noise parameters and signal curve characteristics,thereby enhancing the rigor of the Majorana noise detection method.

    Acknowledgements

    We would like to express our gratitude for the valuable discussions with Li Chen, Feng-Feng Song, Gu Zhang and Zhenhua Zhu.This work was supported by the Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302400), the National Natural Science Foundation of China (Grants No.11974198), and the Natural Science Foundation of Shandong Province of China (Grant No.ZR2021MA091).

    猜你喜歡
    思凡劉東
    # 你會(huì)把相機(jī)借給別人嗎?#
    攝影之友(2022年10期)2022-10-22 02:15:48
    #“海鮮市場(chǎng)”上購(gòu)買二手器材如何避免被坑?#
    攝影之友(2022年6期)2022-06-30 13:54:00
    池塘里的歌手
    一間老房子
    昆劇折子戲《思凡》研究評(píng)述
    Max講故事——思凡
    領(lǐng)個(gè)女人回家
    人身上的尺子
    冷湖
    飛天(2009年6期)2009-09-02 01:46:04
    養(yǎng)小鳥(niǎo)
    国产色婷婷99| ponron亚洲| 91av网一区二区| 免费不卡的大黄色大毛片视频在线观看 | 日本三级黄在线观看| 国产午夜精品论理片| 成年女人看的毛片在线观看| 日韩三级伦理在线观看| 99久久精品国产国产毛片| 成年av动漫网址| 亚洲性久久影院| 久久热精品热| 免费高清视频大片| 欧美成人一区二区免费高清观看| 天堂影院成人在线观看| 亚洲专区国产一区二区| 搡女人真爽免费视频火全软件 | 国产欧美日韩精品一区二区| 日韩av不卡免费在线播放| 精品午夜福利在线看| 日韩欧美精品免费久久| 亚洲人成网站在线播| 熟妇人妻久久中文字幕3abv| 亚洲精品成人久久久久久| 美女xxoo啪啪120秒动态图| 51国产日韩欧美| 午夜精品一区二区三区免费看| 国产高清不卡午夜福利| 在线免费观看的www视频| 久久天躁狠狠躁夜夜2o2o| 久久草成人影院| 色5月婷婷丁香| 嫩草影视91久久| 99在线人妻在线中文字幕| 久久午夜福利片| 九九爱精品视频在线观看| 久久鲁丝午夜福利片| 国产一区二区三区av在线 | 麻豆av噜噜一区二区三区| 久久久久久久久中文| 亚洲成人久久性| 精品午夜福利在线看| 给我免费播放毛片高清在线观看| 青春草视频在线免费观看| 亚洲第一区二区三区不卡| 99久久中文字幕三级久久日本| 午夜福利在线观看吧| 欧美高清性xxxxhd video| 黄色配什么色好看| 菩萨蛮人人尽说江南好唐韦庄 | 国产一区二区在线观看日韩| 婷婷色综合大香蕉| 日本黄色片子视频| 亚洲欧美中文字幕日韩二区| h日本视频在线播放| 成人高潮视频无遮挡免费网站| 中文亚洲av片在线观看爽| 日韩人妻高清精品专区| 国产免费一级a男人的天堂| 国产乱人视频| 久久婷婷人人爽人人干人人爱| 亚洲av成人av| 搡女人真爽免费视频火全软件 | 久久99热6这里只有精品| 两个人视频免费观看高清| 日日摸夜夜添夜夜爱| a级毛色黄片| 国产精品久久久久久久久免| 久久精品国产鲁丝片午夜精品| 内射极品少妇av片p| 欧美+亚洲+日韩+国产| 国产欧美日韩精品亚洲av| 99九九线精品视频在线观看视频| 久久九九热精品免费| 在线免费观看不下载黄p国产| 一级黄片播放器| 国产乱人偷精品视频| 国产亚洲精品av在线| 国产视频一区二区在线看| 国产三级在线视频| 色综合亚洲欧美另类图片| 久久久久久大精品| 在现免费观看毛片| 欧美丝袜亚洲另类| 人妻丰满熟妇av一区二区三区| 伦理电影大哥的女人| 1000部很黄的大片| 日韩精品有码人妻一区| 噜噜噜噜噜久久久久久91| 国产精品嫩草影院av在线观看| 色尼玛亚洲综合影院| 青春草视频在线免费观看| 99视频精品全部免费 在线| 亚洲美女黄片视频| 在线免费观看的www视频| 一个人免费在线观看电影| 一进一出抽搐动态| 蜜桃久久精品国产亚洲av| 天堂网av新在线| 看免费成人av毛片| 日韩人妻高清精品专区| 一a级毛片在线观看| 久久久久久国产a免费观看| 午夜老司机福利剧场| 老司机午夜福利在线观看视频| 精品久久久噜噜| 伦理电影大哥的女人| 欧美日本亚洲视频在线播放| av免费在线看不卡| 成人漫画全彩无遮挡| 春色校园在线视频观看| 桃色一区二区三区在线观看| 久久久久精品国产欧美久久久| 日日摸夜夜添夜夜添av毛片| 国产视频一区二区在线看| 日日啪夜夜撸| 亚洲国产欧洲综合997久久,| 日日干狠狠操夜夜爽| 欧美色欧美亚洲另类二区| 国产精品一区二区免费欧美| 1024手机看黄色片| 晚上一个人看的免费电影| 国产精品野战在线观看| 夜夜看夜夜爽夜夜摸| 在线观看一区二区三区| 亚洲国产欧美人成| 禁无遮挡网站| 日本黄色片子视频| 国产探花在线观看一区二区| 波野结衣二区三区在线| 亚洲乱码一区二区免费版| 免费不卡的大黄色大毛片视频在线观看 | 神马国产精品三级电影在线观看| 国产精品人妻久久久影院| 国产黄色小视频在线观看| 可以在线观看的亚洲视频| 最近最新中文字幕大全电影3| 国内久久婷婷六月综合欲色啪| 一级a爱片免费观看的视频| 国产精品人妻久久久影院| 亚洲精品影视一区二区三区av| 日本黄色片子视频| 在线国产一区二区在线| 精品福利观看| 美女大奶头视频| 色哟哟·www| 毛片女人毛片| 亚洲欧美精品综合久久99| 国产精品不卡视频一区二区| 精品一区二区三区人妻视频| 久久亚洲精品不卡| 亚洲性夜色夜夜综合| 最近在线观看免费完整版| 久久久久精品国产欧美久久久| 大香蕉久久网| 午夜影院日韩av| 一级毛片电影观看 | 免费一级毛片在线播放高清视频| 国产熟女欧美一区二区| 婷婷六月久久综合丁香| 美女xxoo啪啪120秒动态图| 国产麻豆成人av免费视频| 成人欧美大片| 12—13女人毛片做爰片一| 国产精品国产三级国产av玫瑰| 国产黄色视频一区二区在线观看 | 少妇的逼水好多| 亚洲欧美日韩无卡精品| 99在线视频只有这里精品首页| 日韩在线高清观看一区二区三区| 高清日韩中文字幕在线| 亚洲精品456在线播放app| 亚洲专区国产一区二区| 久久综合国产亚洲精品| 国内精品久久久久精免费| 日本五十路高清| 国产成人a∨麻豆精品| 精品一区二区三区av网在线观看| 成人三级黄色视频| 亚洲va在线va天堂va国产| a级一级毛片免费在线观看| 亚洲欧美日韩无卡精品| 国产精品一区www在线观看| 91狼人影院| 久久精品国产亚洲av香蕉五月| 国模一区二区三区四区视频| 搞女人的毛片| 久久久久久久久大av| 毛片一级片免费看久久久久| 人妻久久中文字幕网| 日本在线视频免费播放| 美女黄网站色视频| 欧美激情在线99| 在线播放国产精品三级| 国产成人精品久久久久久| 91麻豆精品激情在线观看国产| 成人午夜高清在线视频| 国产91av在线免费观看| 国产伦一二天堂av在线观看| 久久人人精品亚洲av| 99热网站在线观看| 最后的刺客免费高清国语| 成人美女网站在线观看视频| 一进一出抽搐gif免费好疼| 亚洲18禁久久av| 熟女人妻精品中文字幕| 少妇熟女aⅴ在线视频| 3wmmmm亚洲av在线观看| 性色avwww在线观看| 久久久a久久爽久久v久久| 老熟妇仑乱视频hdxx| 99在线人妻在线中文字幕| 国产成人aa在线观看| 亚洲av电影不卡..在线观看| 一个人看的www免费观看视频| 久久婷婷人人爽人人干人人爱| 麻豆国产av国片精品| 久久久久久久久中文| 男女啪啪激烈高潮av片| 激情 狠狠 欧美| 国产视频内射| 精品久久久久久久久久久久久| 一级黄色大片毛片| eeuss影院久久| 99国产精品一区二区蜜桃av| 如何舔出高潮| 日本熟妇午夜| 亚洲精品成人久久久久久| 日本爱情动作片www.在线观看 | 高清午夜精品一区二区三区 | 久久久久久国产a免费观看| 国产麻豆成人av免费视频| 18+在线观看网站| 人人妻人人澡欧美一区二区| 我要搜黄色片| 欧美成人免费av一区二区三区| 小蜜桃在线观看免费完整版高清| 欧美最新免费一区二区三区| 菩萨蛮人人尽说江南好唐韦庄 | 亚洲国产色片| 亚洲精华国产精华液的使用体验 | 久久精品国产清高在天天线| 亚洲欧美日韩高清专用| 国产av麻豆久久久久久久| 日韩人妻高清精品专区| 18禁在线播放成人免费| 久久精品国产99精品国产亚洲性色| 又黄又爽又免费观看的视频| 12—13女人毛片做爰片一| 少妇的逼水好多| 亚洲成人久久性| 长腿黑丝高跟| 久久九九热精品免费| 黄色欧美视频在线观看| av在线蜜桃| 亚洲国产欧美人成| 国产亚洲欧美98| 伦理电影大哥的女人| 五月玫瑰六月丁香| 在线看三级毛片| 欧美日本视频| 一a级毛片在线观看| 色播亚洲综合网| 男人和女人高潮做爰伦理| 亚洲精品乱码久久久v下载方式| 免费观看在线日韩| 久久99热这里只有精品18| 精品一区二区三区人妻视频| 久久亚洲精品不卡| 免费人成视频x8x8入口观看| aaaaa片日本免费| a级一级毛片免费在线观看| 老熟妇仑乱视频hdxx| 黄色视频,在线免费观看| 极品教师在线视频| 成人亚洲欧美一区二区av| 长腿黑丝高跟| 日本撒尿小便嘘嘘汇集6| 又黄又爽又免费观看的视频| 亚洲av免费在线观看| 能在线免费观看的黄片| 91狼人影院| 国产高清激情床上av| 男人和女人高潮做爰伦理| 午夜日韩欧美国产| 搡老岳熟女国产| 日韩高清综合在线| 麻豆一二三区av精品| 国产精品无大码| 天天躁日日操中文字幕| 日韩大尺度精品在线看网址| 色在线成人网| av在线播放精品| 中文字幕人妻熟人妻熟丝袜美| 色哟哟哟哟哟哟| 国产黄色小视频在线观看| 欧美国产日韩亚洲一区| 在线观看一区二区三区| 欧美极品一区二区三区四区| 亚洲美女黄片视频| 成人鲁丝片一二三区免费| 日韩一本色道免费dvd| 男插女下体视频免费在线播放| 黄色配什么色好看| 岛国在线免费视频观看| 久久精品国产亚洲av涩爱 | 丝袜美腿在线中文| 免费看光身美女| 国产精品爽爽va在线观看网站| 亚洲av成人精品一区久久| 亚洲美女视频黄频| 99热这里只有精品一区| 久久精品国产自在天天线| 欧美3d第一页| 日韩欧美精品v在线| 国产麻豆成人av免费视频| 国产女主播在线喷水免费视频网站 | 小蜜桃在线观看免费完整版高清| 美女黄网站色视频| 亚洲国产精品国产精品| 亚洲综合色惰| 老师上课跳d突然被开到最大视频| 3wmmmm亚洲av在线观看| 一卡2卡三卡四卡精品乱码亚洲| 日本五十路高清| 午夜激情福利司机影院| 中文字幕av成人在线电影| 久久久国产成人免费| 熟女电影av网| 国产亚洲精品久久久com| 99视频精品全部免费 在线| av卡一久久| 黄色配什么色好看| 男女视频在线观看网站免费| 国产午夜精品论理片| 嫩草影院精品99| 国产伦精品一区二区三区四那| 国产av不卡久久| 欧美一级a爱片免费观看看| 国产精品国产三级国产av玫瑰| 亚洲国产精品国产精品| 国产精品,欧美在线| 国产av一区在线观看免费| 婷婷六月久久综合丁香| 午夜久久久久精精品| 亚洲欧美成人综合另类久久久 | 韩国av在线不卡| 亚洲精品亚洲一区二区| 亚洲成a人片在线一区二区| 久久精品人妻少妇| 热99re8久久精品国产| 日韩欧美 国产精品| 日本一二三区视频观看| 日本-黄色视频高清免费观看| 亚洲精品国产av成人精品 | 狂野欧美白嫩少妇大欣赏| 国产精品综合久久久久久久免费| 热99re8久久精品国产| 91午夜精品亚洲一区二区三区| 熟女人妻精品中文字幕| 日日啪夜夜撸| 久久精品国产99精品国产亚洲性色| 村上凉子中文字幕在线| 在线免费观看不下载黄p国产| 欧美+亚洲+日韩+国产| 国产麻豆成人av免费视频| 日韩av不卡免费在线播放| 最近的中文字幕免费完整| 欧美绝顶高潮抽搐喷水| 亚洲国产精品sss在线观看| 久久九九热精品免费| 欧美另类亚洲清纯唯美| 亚洲,欧美,日韩| 久久亚洲精品不卡| 一本一本综合久久| 看黄色毛片网站| 国产高清激情床上av| 中文字幕精品亚洲无线码一区| 国产精品亚洲美女久久久| 免费不卡的大黄色大毛片视频在线观看 | 国产视频内射| 两个人的视频大全免费| 丝袜美腿在线中文| 国产在线男女| 精品一区二区免费观看| 成人鲁丝片一二三区免费| 两个人的视频大全免费| 女人十人毛片免费观看3o分钟| 哪里可以看免费的av片| 欧洲精品卡2卡3卡4卡5卡区| 国产三级中文精品| 99riav亚洲国产免费| 亚洲,欧美,日韩| 亚洲精品粉嫩美女一区| 国产乱人偷精品视频| 美女免费视频网站| 一进一出抽搐动态| av.在线天堂| 男女视频在线观看网站免费| 成人永久免费在线观看视频| 亚洲熟妇熟女久久| 老师上课跳d突然被开到最大视频| 国产 一区精品| 精品无人区乱码1区二区| 免费观看在线日韩| 美女内射精品一级片tv| 亚洲,欧美,日韩| 狂野欧美激情性xxxx在线观看| 最近最新中文字幕大全电影3| 亚洲自拍偷在线| 久久午夜亚洲精品久久| 黄色一级大片看看| 99九九线精品视频在线观看视频| a级一级毛片免费在线观看| 免费不卡的大黄色大毛片视频在线观看 | 精品久久久久久久久久久久久| av国产免费在线观看| 麻豆精品久久久久久蜜桃| 亚洲激情五月婷婷啪啪| 亚洲成人久久爱视频| 成人毛片a级毛片在线播放| 亚洲va在线va天堂va国产| h日本视频在线播放| 亚洲av第一区精品v没综合| 97超碰精品成人国产| 九九热线精品视视频播放| 国产探花在线观看一区二区| 色吧在线观看| 久久久久精品国产欧美久久久| 男女下面进入的视频免费午夜| 一级av片app| 色在线成人网| 国产视频内射| 日韩一本色道免费dvd| 国产片特级美女逼逼视频| 你懂的网址亚洲精品在线观看 | 久久精品91蜜桃| 免费人成视频x8x8入口观看| 搡老熟女国产l中国老女人| 国产一区二区激情短视频| 精品久久久噜噜| 91麻豆精品激情在线观看国产| 99热这里只有精品一区| 97人妻精品一区二区三区麻豆| 久久精品夜色国产| 日韩欧美 国产精品| 午夜精品在线福利| 99视频精品全部免费 在线| 欧美成人a在线观看| 欧美不卡视频在线免费观看| 精品免费久久久久久久清纯| av在线亚洲专区| 亚洲性夜色夜夜综合| 在线播放无遮挡| 麻豆国产97在线/欧美| 精品一区二区三区av网在线观看| 欧美潮喷喷水| 99精品在免费线老司机午夜| 国产精品免费一区二区三区在线| 亚洲图色成人| 日韩中字成人| 欧美成人精品欧美一级黄| 无遮挡黄片免费观看| 美女 人体艺术 gogo| 欧美一区二区精品小视频在线| 久久国内精品自在自线图片| 免费av不卡在线播放| 91在线精品国自产拍蜜月| 欧美日韩国产亚洲二区| 91久久精品国产一区二区三区| 青春草视频在线免费观看| 国产一区亚洲一区在线观看| 精品人妻一区二区三区麻豆 | 亚洲性夜色夜夜综合| 久久久欧美国产精品| 成人特级av手机在线观看| 大又大粗又爽又黄少妇毛片口| av免费在线看不卡| 精品人妻一区二区三区麻豆 | 乱系列少妇在线播放| 成年女人看的毛片在线观看| 俺也久久电影网| 亚洲欧美精品自产自拍| 久久久久国内视频| 波野结衣二区三区在线| 夜夜爽天天搞| 亚洲色图av天堂| 少妇猛男粗大的猛烈进出视频 | 日韩欧美在线乱码| 中国国产av一级| 国产精品人妻久久久久久| 一级毛片电影观看 | 露出奶头的视频| 日日摸夜夜添夜夜添小说| 欧美精品国产亚洲| 亚洲国产精品久久男人天堂| 国产一区二区在线观看日韩| 人妻久久中文字幕网| 国产不卡一卡二| 晚上一个人看的免费电影| 精品久久久久久久久亚洲| 久久久国产成人精品二区| 少妇人妻一区二区三区视频| 少妇人妻精品综合一区二区 | 亚洲欧美精品自产自拍| 午夜精品在线福利| 亚洲成人久久性| 国产美女午夜福利| 神马国产精品三级电影在线观看| 久久精品国产亚洲网站| 2021天堂中文幕一二区在线观| 韩国av在线不卡| 村上凉子中文字幕在线| 男人狂女人下面高潮的视频| 深夜a级毛片| 老司机福利观看| 国产高清激情床上av| 国产乱人偷精品视频| 亚洲一级一片aⅴ在线观看| 亚洲av成人精品一区久久| 亚洲av成人av| 亚洲av中文字字幕乱码综合| 中文字幕熟女人妻在线| 亚洲无线观看免费| 亚洲av一区综合| 一个人看视频在线观看www免费| 99九九线精品视频在线观看视频| 免费看光身美女| 精品久久久久久久末码| 国产高清不卡午夜福利| 麻豆乱淫一区二区| 亚洲乱码一区二区免费版| 中出人妻视频一区二区| 亚洲精品成人久久久久久| 蜜桃久久精品国产亚洲av| 日韩制服骚丝袜av| 级片在线观看| 国产精品一区二区三区四区久久| 国产精品电影一区二区三区| a级毛片免费高清观看在线播放| 小蜜桃在线观看免费完整版高清| 舔av片在线| 日韩,欧美,国产一区二区三区 | 亚洲成人中文字幕在线播放| 欧美成人免费av一区二区三区| 一a级毛片在线观看| 国内久久婷婷六月综合欲色啪| 国产成年人精品一区二区| 午夜视频国产福利| 舔av片在线| 看免费成人av毛片| 一区二区三区免费毛片| 夜夜看夜夜爽夜夜摸| 久久久国产成人免费| 亚洲精品日韩在线中文字幕 | 日韩 亚洲 欧美在线| 高清毛片免费看| 最新中文字幕久久久久| 国产v大片淫在线免费观看| 国产真实伦视频高清在线观看| 免费看av在线观看网站| 日韩国内少妇激情av| 国内揄拍国产精品人妻在线| 老女人水多毛片| 国产高清视频在线观看网站| 国产激情偷乱视频一区二区| 成年女人永久免费观看视频| 伦精品一区二区三区| 性插视频无遮挡在线免费观看| 99久久精品一区二区三区| 国产大屁股一区二区在线视频| 亚洲精品日韩av片在线观看| 精品午夜福利视频在线观看一区| 亚洲自拍偷在线| 久久久久国内视频| 国产探花在线观看一区二区| 久久精品综合一区二区三区| 内射极品少妇av片p| 午夜福利在线观看吧| 麻豆久久精品国产亚洲av| 秋霞在线观看毛片| 五月伊人婷婷丁香| 尤物成人国产欧美一区二区三区| 天堂√8在线中文| 亚洲成av人片在线播放无| 91在线精品国自产拍蜜月| 亚洲人成网站在线播放欧美日韩| 成人av在线播放网站| 日本与韩国留学比较| 欧美极品一区二区三区四区| 国产精品,欧美在线| 日日摸夜夜添夜夜添小说| 欧美日韩乱码在线| 成人亚洲欧美一区二区av| 国产美女午夜福利| 国产 一区精品| 国产大屁股一区二区在线视频| 男女边吃奶边做爰视频| 亚洲欧美日韩东京热| av视频在线观看入口| 亚洲电影在线观看av| 国产成人aa在线观看| 亚洲精品成人久久久久久| 99久久成人亚洲精品观看| 亚洲熟妇熟女久久| 欧美人与善性xxx| 午夜老司机福利剧场| 中文字幕av成人在线电影| 91精品国产九色| 色吧在线观看| 午夜免费男女啪啪视频观看 | 啦啦啦观看免费观看视频高清| 超碰av人人做人人爽久久| 九九在线视频观看精品| 精品无人区乱码1区二区|