Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Systematical study of effects of chip parameters and control waveforms on fidelity of CZ gate

WANG Shi ZHENG Yan HOU Jie YE Yongjin JI Yang WU Yongzheng

Citation:

Systematical study of effects of chip parameters and control waveforms on fidelity of CZ gate

WANG Shi, ZHENG Yan, HOU Jie, YE Yongjin, JI Yang, WU Yongzheng
Article Text (iFLYTEK Translation)
PDF
HTML
Get Citation
  • Efficient and high-fidelity two-qubit gates are crucial to achieving fault-tolerant quantum computing and have become one of the key research topics in the quantum computing field. The fidelity of quantum gates is affected by many factors, such as quantum chip parameters and control waveforms. In theory, the chip paramters and waveforms can be precisely designed. However, in practice, the actual chip parameters and waveforms may deviate from the theoretical values. It is necessary to systematically study the effects of chip parameters, control waveforms, and other factors on the fidelity of two-qubit gates, and determine the magnitude and direction of the each factor's effect. Here, we systematically study the effects of chip parameters, control waveforms, coupler start frequency, qubit frequency, etc. on the fidelity of CZ gates. On this basis, the response of gate fidelity to deviations in control parameters is further studied. At the chip design level, quantum chips based on CBQ parameters can achieve higher-fidelity CZ gates in shorter gate operation time. In terms of controlling waveforms, the three-level Fourier series wave is superior to the square wave and rounded trapezoidal wave in achieving lower gate error rate and shorter gate operation time, and can better meet the requirements for efficient implementation of high-fidelity quantum gates. Factors such as the coupler starting frequency and qubit frequency have relatively little effect on the fidelity of the CZ gate. In a wide frequency range, high-fidelity CZ gates can always be achieved by optimizing the control waveform parameters. It should be pointed out that slight deviations of control parameters will lead to a significant increase in the gating error. This study is of great significance for clarifying the effects of various factors on the fidelity of the CZ gate. It can provide theoretical and technical support for designing superconducting quantum chips and realizing high-fidelity CZ gate, thereby promoting the engineering development of quantum computing.
  • 图 1  三种不同$ \omega_{{\mathrm{c}}}(t) $波形示意图. 图(a)和(b)是方波, (c)和(d)是圆角梯形波, (e)和(f)是傅里叶级数波. 图(a)、(c)和(e)对应着$ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ < $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $的情形, 而图(b)、(d)和(f)对应着$ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ > $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $的情形. 图(e)和(f)中的三条细虚线对应着傅里叶级数波形的三个分量: $ \omega_{{\mathrm{c}}}^{{\rm{off}}} + \lambda_{m} \left( 1 - \cos \dfrac{2 \pi m t}{t_{{\mathrm{gate}}}} \right), m=1, 2, 3 $

    Figure 1.  Schematic diagram of square pulse ((a) and (b)), rounded-trapezoid-shaped pulse ((c) and (d)) and Fourier-series pulse ((e) and (f)). (a), (c), and (e) correspond to the case where $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ < $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $, and (b), (d), and (f) correspond to the case where $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ > $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $. The three thin dashed lines in (e) and (f) correspond to the three components of the Fourier series pulse: $ \omega_{{\mathrm{c}}}^{{\rm{off}}} + \lambda_{m} \left( 1 - \cos \dfrac{2 \pi m t}{t_{{\mathrm{gate}}}} \right), m=1, 2, 3 $.

    图 2  哈密顿量H和$ H_{0} $的能谱((a)和(c))以及ZZ相互作用$ \left\lvert \zeta \right\rvert /2 \pi $((b)和(d))与耦合器频率$ \omega_{{\mathrm{c}}}/2\pi $的关系. (a)和(b)对应CAQ模型参数; (c)和(d)对应CBQ模型参数; 图(a)和(c)中的黑色虚线对应着无相互作用哈密顿量$ H_{0} $的本征能量, 彩色实线对应着系统哈密顿量H的本征能量

    Figure 2.  Energy-level spectra ((a) and (c)) and ZZ interaction $ \left\lvert \zeta \right\rvert /2 \pi $ ((b) and (d)) of the system Hamiltonian H as a function of the coupler frequency $ \omega_{{\mathrm{c}}}/2\pi $. Figure (a) and (b) correspond to the CAQ model parameters, and figure (c) and (d) correspond to the CBQ model parameters. The black dashed lines in figure (a) and (c) corresponds to the eigen-energies of the non-interacting Hamiltonian $ H_{0} $, and the colored solid lines correspond to the eigen-energies of the system Hamiltonian H.

    图 3  不同模型参数下的CZ门错误率. 图(a)和图(b)分别对应CAQ和CBQ两组模型参数. 图中蓝色、绿色和红色实线分别对应$ m_{\max} = 1, 2, 3 $三种不同的傅里叶级数波形

    Figure 3.  CZ gate errors under different model parameters. Figure (a) and (b) correspond to the CAQ and CBQ model parameters, respectively. The blue, green, and red solid lines in the figures correspond to three different Fourier series pulses with $ m_{\max} $ = 1, 2, and 3, respectively.

    图 4  (a) 方波对应的CZ门错误率; (b) 圆角梯形波对应的CZ门错误率; 傅里叶级数波对应的CZ门错误率见图3(b). (a)、(b)和图3(b)均是采用CBQ模型参数计算所得

    Figure 4.  (a) CZ gate errors under square pulse; (b) CZ gate errors under rounded-trapezoid-shaped pulse; for CZ gate errors under Fourier-series pulse, see Fig. 3(b). Both (a), (b) and Fig. 3(b) are calculated using CBQ model parameters.

    图 5  不同$ \omega_{c}^{{\rm{off}}} $下的CZ门错误率. 每一行的五张子图((a1)—(e1)以及(a2)—(e2))对应的$ \omega_{{\mathrm{c}}}^{{\rm{off}}} $分别为3594、3636、3678、3800和4000 MHz, 其他参数同CBQ模型参数. (a1)—(e1)的门错误率是使用$ H_{0} $的本征态计算的, 见公式(11); (a2)—(e2)的门错误率是使用系统哈密顿量H的本征态计算的, 见公式(12). (f)和(g)是采用傅里叶级数波形时的门错误率, 分别对应$ \omega_{{\mathrm{c}}}^{{\rm{off}}} = 3594, $$ 3678 $ MHz

    Figure 5.  CZ gate errors rate under different $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $. The corresponding $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ of the five sub-figures ((a1)–(e1) and (a2)–(e2)) in each row are: 3594, 3636, 3678, 3800 and 4000 MHz respectively, other model paramters are the same as CBQ. The gate errors in (a1)–(e1) are calculated using the eigenstates of $ H_{0} $, see Eq(11); (a2)–(e2) are calculated using the eigenstates of H, see Eq(12). (f) and (g) are the gate error rates with Fourier series pulse, $ \omega_{{\mathrm{c}}}^{{\rm{off}}} = 3594, 3678 $ MHz, respectively.

    图 6  不同量子比特频率$ \omega_{2} $下的CZ门错误率, 横轴是门操作时间$ t_{{\mathrm{gate}}} $, 纵轴是量子比特$ Q_{2} $的比特频率$ \omega_{2} $, 一共选取了$ \omega_{2} / 2 \pi = 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, $$ 4.95 $ GHz共11个不同的$ \omega_{2} $值, 其他模型参数同CBQ模型参数. (a)—(c)分别对应傅里叶分量数目$ m_{\max} = 1, 2, 3 $的情形

    Figure 6.  CZ gate error under different qubit frequencies $ \omega_{2} $. The horizontal axis is the gate operation time $ t_{{\mathrm{gate}}} $, and the vertical axis is the qubit frequency $ \omega_{2} $ of the $ Q_{2} $. A total of 11 different $ \omega_{2} $ values were selected, including $ \omega_{2} / 2 \pi = $$ 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.95 $ GHz. Other model parameters are the same as the CBQ model parameters.

    图 7  控制波形参数偏移对CZ门保真度的影响

    Figure 7.  Effect of control waveform parameter deviation on CZ gate fidelity.

    表 1  本文选取的两组模型参数, 分别标记为CAQ和CBQ

    Table 1.  The two sets of model parameters used in this paper, marked as CAQ and CBQ respectively.

    模型参数 CAQ CBQ
    $ \rho_{1 {\mathrm{c}}} $ 0.0180 0.0220
    $ \rho_{2 {\mathrm{c}}} $ 0.0180 –0.0220
    $ \rho_{12} $ 0.0015 0.0013
    $ \omega_{1} / 2 \pi \quad ({\rm{GHz}}) $ 6.0 5.0
    $ \omega_{2} / 2 \pi \quad ({\rm{GHz}}) $ 5.4 4.8
    $ \alpha_{1} / 2 \pi \quad ({\rm{MHz}}) $ –250.0 –220.0
    $ \alpha_{2} / 2 \pi \quad ({\rm{MHz}}) $ –250.0 –220.0
    $ \alpha_{c} / 2 \pi \quad ({\rm{MHz}}) $ –300.0 –170.0
    DownLoad: CSV

    表 2  不同$ \omega_{{\mathrm{c}}}^{{\rm{off}}} $下的CZ门错误率

    Table 2.  CZ gate errors rate under different $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $.

    $ \omega_{{\mathrm{c}}}^{{\rm{off}}} $ (MHz) Bare Dressed
    $ t_{{\mathrm{gate}}} (ns) $ $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $ (MHz) $ E_{{\mathrm{g}}} $ $ t_{{\mathrm{gate}}} (ns) $ $ \omega_{{\mathrm{c}}}^{{\rm{on}}} $ (MHz) $ E_{{\mathrm{g}}} $
    359453/2.44514.07.2431e–343/2.44615.55.9816e–4
    104/2.44582.59.1781e–393/2.44623.51.6110e–3
    220/2.44144.05.5215e–3212/2.44159.02.4819e–4
    272/2.44327.55.1956e–3273/2.44326.08.4726e–5
    363654/2.44505.07.4825e–343/2.44614.55.0617e–4
    114/2.44548.59.7407e–393/2.44623.51.4097e–4
    220/2.44141.56.0894e–3212/2.44158.52.3052e–4
    272/2.44325.56.0173e–3273/2.44326.07.3497e–5
    367843/2.44612.57.3516e–343/2.44613.54.4968e–4
    102/2.44587.56.6712e–393/2.44623.51.2503e–3
    209/2.44163.06.3633e–3213/2.44156.52.1617e–4
    273/2.44325.56.2150e–3273/2.44326.08.0159e–5
    380041/2.44624.08.2440e–343/2.44610.54.9159e–4
    101/2.44590.08.6945e–393/2.44622.01.0150e–3
    209/2.44154.07.6224e–3213/2.44155.51.7852e–4
    271/2.44323.57.8218e–3273/2.44325.51.0117e–5
    400040/2.44610.01.0993e–253/2.44508.05.3763e–4
    100/2.44584.56.1489e–3105/2.44576.09.3363e–4
    208/2.44148.01.1798e–2218/2.44144.52.4616e–5
    273/2.44318.01.1304e–2274/2.44322.53.1172e–4
    DownLoad: CSV
  • [1]

    Easttom C 2022 Modern Cryptography: Applied Mathematics for Encryption and Information Security (Cham: Springer International Publishing) pp397–407

    [2]

    Hossain Faruk M J, Tahora S, Tasnim M, Shahriar H, Sakib N 2022 2022 1 st International Conference on AI in Cybersecurity Victoria, TX, USA, May 24-26, 2022 p1

    [3]

    Cavaliere F, Mattsson J, Smeets B 2020 Network Security 2020 9

    [4]

    Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S 2017 Nature 549 195Google Scholar

    [5]

    Wang Y, Liu J 2024 Rep. Prog. Phys. 87 116402Google Scholar

    [6]

    Lanyon B P, Whitfield J D, Gillett G G, Goggin M E, Almeida M P, Kassal I, Biamonte J D, Mohseni M, Powell B J, Barbieri M, Aspuru-Guzik A, White A G 2010 Nat. Chem. 2 106Google Scholar

    [7]

    Cao Y, Romero J, Olson J P, Degroote M, Johnson P D, Kieferová M, Kivlichan I D, Menke T, Peropadre B, Sawaya N P D, Sim S, Veis L, Aspuru-Guzik A 2019 Chem. Rev. 119 10856Google Scholar

    [8]

    Orús R, Mugel S, Lizaso E 2019 Rev. Phys. 4 100028Google Scholar

    [9]

    Herman D, Googin C, Liu X, Sun Y, Galda A, Safro I, Pistoia M, Alexeev Y 2023 Nat. Rev. Phys. 5 450Google Scholar

    [10]

    Egger D J, Gambella C, Marecek J, McFaddin S, Mevissen M, Raymond R, Simonetto A, Woerner S, Yndurain E 2020 IEEE Transactions on Quantum Engineering 1 1

    [11]

    Preskill J 2018 Quantum 2 79Google Scholar

    [12]

    Aharonov D, Ben-Or M 2008 Siam J Comput. 38 1207Google Scholar

    [13]

    Knill E, Laflamme R, Zurek W H 1998 Science 279 342Google Scholar

    [14]

    Krinner S, Lacroix N, Remm A, Di Paolo A, Genois E, Leroux C, Hellings C, Lazar S, Swiadek F, Herrmann J, Norris G J, Andersen C K, Müller M, Blais A, Eichler C, Wallraff A 2022 Nature 605 669Google Scholar

    [15]

    Zhao Y, Ye Y, Huang H L, Zhang Y, Wu D, Guan H, Zhu Q, Wei Z, He T, Cao S, Chen F, Chung T H, Deng H, Fan D, Gong M, Guo C, Guo S, Han L, Li N, Li S, Li Y, Liang F, Lin J, Qian H, Rong H, Su H, Sun L, Wang S, Wu Y, Xu Y, Ying C, Yu J, Zha C, Zhang K, Huo Y H, Lu C Y, Peng C Z, Zhu X, Pan J W 2022 Phys. Rev. Lett. 129 030501Google Scholar

    [16]

    Google Quantum AI 2023 Nature 614 676Google Scholar

    [17]

    Gupta R S, Sundaresan N, Alexander T, Wood C J, Merkel S T, Healy M B, Hillenbrand M, Jochym-O'Connor T, Wootton J R, Yoder T J, Cross A W, Takita M, Brown B J 2024 Nature 625 259Google Scholar

    [18]

    Brock B L, Singh S, Eickbusch A, Sivak V V, Ding A Z, Frunzio L, Girvin S M, Devoret M H 2025 Nature 641 612Google Scholar

    [19]

    Babbush R, McClean J R, Newman M, Gidney C, Boixo S, Neven H 2021 PRX Quantum 2 010103Google Scholar

    [20]

    Litinski D 2019 Quantum 3 128Google Scholar

    [21]

    Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324Google Scholar

    [22]

    Tomita Y, Svore K M 2014 Phys. Rev. A 90 062320Google Scholar

    [23]

    O’Brien T E, Tarasinski B, DiCarlo L 2017 npj Quantum Inf. 3 39Google Scholar

    [24]

    Raussendorf R, Harrington J 2007 Phys. Rev. Lett. 98 190504Google Scholar

    [25]

    Gao D, Fan D, Zha C, Bei J, Cai G, Cai J, Cao S, Chen F, Chen J, Chen K, Chen X, Chen X, Chen Z, Chen Z, Chen Z, Chu W, Deng H, Deng Z, Ding P, Ding X, Ding Z, Dong S, Dong Y, Fan B, Fu Y, Gao S, Ge L, Gong M, Gui J, Guo C, Guo S, Guo X, Han L, He T, Hong L, Hu Y, Huang H L, Huo Y H, Jiang T, Jiang Z, Jin H, Leng Y, Li D, Li D, Li F, Li J, Li J, Li J, Li J, Li N, Li S, Li W, Li Y, Li Y, Liang F, Liang X, Liao N, Lin J, Lin W, Liu D, Liu H, Liu M, Liu X, Liu X, Liu Y, Lou H, Ma Y, Meng L, Mou H, Nan K, Nie B, Nie M, Ning J, Niu L, Peng W, Qian H, Rong H, Rong T, Shen H, Shen Q, Su H, Su F, Sun C, Sun L, Sun T, Sun Y, Tan Y, Tan J, Tang L, Tu W, Wan C, Wang J, Wang B, Wang C, Wang C, Wang C, Wang J, Wang L, Wang R, Wang S, Wang X, Wang X, Wang X, Wang Y, Wei Z, Wei J, Wu D, Wu G, Wu J, Wu S, Wu Y, Xie S, Xin L, Xu Y, Xue C, Yan K, Yang W, Yang X, Yang Y, Ye Y, Ye Z, Ying C, Yu J, Yu Q, Yu W, Zeng X, Zhan S, Zhang F, Zhang H, Zhang K, Zhang P, Zhang W, Zhang Y, Zhang Y, Zhang L, Zhao G, Zhao P, Zhao X, Zhao X, Zhao Y, Zhao Z, Zheng L, Zhou F, Zhou L, Zhou N, Zhou N, Zhou S, Zhou S, Zhou Z, Zhu C, Zhu Q, Zou G, Zou H, Zhang Q, Lu C Y, Peng C Z, Zhu X, Pan J W 2025 Phys. Rev. Lett. 134 090601Google Scholar

    [26]

    Krantz P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S, Oliver W D 2019 Appl. Phys. Rev. 6 021318Google Scholar

    [27]

    DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240Google Scholar

    [28]

    Dewes A, Ong F R, Schmitt V, Lauro R, Boulant N, Bertet P, Vion D, Esteve D 2012 Phys. Rev. Lett. 108 057002Google Scholar

    [29]

    Zhao P, Xu P, Lan D, Chu J, Tan X, Yu H, Yu Y 2020 Phys. Rev. Lett. 125 200503Google Scholar

    [30]

    Barends R, Quintana C M, Petukhov A G, Chen Y, Kafri D, Kechedzhi K, Collins R, Naaman O, Boixo S, Arute F, Arya K, Buell D, Burkett B, Chen Z, Chiaro B, Dunsworth A, Foxen B, Fowler A, Gidney C, Giustina M, Graff R, Huang T, Jeffrey E, Kelly J, Klimov P V, Kostritsa F, Landhuis D, Lucero E, McEwen M, Megrant A, Mi X, Mutus J, Neeley M, Neill C, Ostby E, Roushan P, Sank D, Satzinger K J, Vainsencher A, White T, Yao J, Yeh P, Zalcman A, Neven H, Smelyanskiy V N, Martinis J M 2019 Phys. Rev. Lett. 123 210501Google Scholar

    [31]

    Chen Y, Neill C, Roushan P, Leung N, Fang M, Barends R, Kelly J, Campbell B, Chen Z, Chiaro B, Dunsworth A, Jeffrey E, Megrant A, Mutus J Y, O'Malley P J J, Quintana C M, Sank D, Vainsencher A, Wenner J, White T C, Geller M R, Cleland A N, Martinis J M 2014 Phys. Rev. Lett. 113 220502Google Scholar

    [32]

    Foxen B, Neill C, Dunsworth A, Roushan P, Chiaro B, Megrant A, Kelly J, Chen Z, Satzinger K, Barends R, Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Boixo S, Buell D, Burkett B, Chen Y, Collins R, Farhi E, Fowler A, Gidney C, Giustina M, Graff R, Harrigan M, Huang T, Isakov S V, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Klimov P, Korotkov A, Kostritsa F, Landhuis D, Lucero E, McClean J, McEwen M, Mi X, Mohseni M, Mutus J Y, Naaman O, Neeley M, Niu M, Petukhov A, Quintana C, Rubin N, Sank D, Smelyanskiy V, Vainsencher A, White T C, Yao Z, Yeh P, Zalcman A, Neven H, Martinis J M 2020 Phys. Rev. Lett. 125 120504Google Scholar

    [33]

    Yan F, Krantz P, Sung Y, Kjaergaard M, Campbell D L, Orlando T P, Gustavsson S, Oliver W D 2018 Phys. Rev. Appl. 10 054062Google Scholar

    [34]

    Li X, Cai T, Yan H, Wang Z, Pan X, Ma Y, Cai W, Han J, Hua Z, Han X, Wu Y, Zhang H, Wang H, Song Y, Duan L, Sun L 2020 Phys. Rev. Appl. 14 024070Google Scholar

    [35]

    Sete E A, Chen A Q, Manenti R, Kulshreshtha S, Poletto S 2021 Phys. Rev. Appl. 15 064063Google Scholar

    [36]

    Setiawan F, Groszkowski P, Clerk A A 2023 Phys. Rev. Appl. 19 034071Google Scholar

    [37]

    M?ller D, Madsen L B, M?lmer K 2008 Phys. Rev. Lett. 100 170504Google Scholar

    [38]

    Majer J, Chow J M, Gambetta J M, Koch J, Johnson B R, Schreier J A, Frunzio L, Schuster D I, Houck A A, Wallraff A, Blais A, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 449 443Google Scholar

    [39]

    Chow J M, Gambetta J M, Cross A W, Merkel S T, Rigetti C, Steffen M 2013 New J. Phys. 15 115012Google Scholar

    [40]

    Rigetti C, Devoret M 2010 Phys. Rev. B 81 134507Google Scholar

    [41]

    Poletto S, Gambetta J M, Merkel S T, Smolin J A, Chow J M, Córcoles A D, Keefe G A, Rothwell M B, Rozen J R, Abraham D W, Rigetti C, Steffen M 2012 Phys. Rev. Lett. 109 240505Google Scholar

    [42]

    Caldwell S A, Didier N, Ryan C A, Sete E A, Hudson A, Karalekas P, Manenti R, da Silva M P, Sinclair R, Acala E, Alidoust N, Angeles J, Bestwick A, Block M, Bloom B, Bradley A, Bui C, Capelluto L, Chilcott R, Cordova J, Crossman G, Curtis M, Deshpande S, Bouayadi T E, Girshovich D, Hong S, Kuang K, Lenihan M, Manning T, Marchenkov A, Marshall J, Maydra R, Mohan Y, O'Brien W, Osborn C, Otterbach J, Papageorge A, Paquette J P, Pelstring M, Polloreno A, Prawiroatmodjo G, Rawat V, Reagor M, Renzas R, Rubin N, Russell D, Rust M, Scarabelli D, Scheer M, Selvanayagam M, Smith R, Staley A, Suska M, Tezak N, Thompson D C, To T W, Vahidpour M, Vodrahalli N, Whyland T, Yadav K, Zeng W, Rigetti C 2018 Phys. Rev. Appl. 10 034050Google Scholar

    [43]

    Paik H, Mezzacapo A, Sandberg M, McClure D T, Abdo B, Córcoles A D, Dial O, Bogorin D F, Plourde B L T, Steffen M, Cross A W, Gambetta J M, Chow J M 2016 Phys. Rev. Lett. 117 250502Google Scholar

    [44]

    Pedersen L H, Møller N M, Mølmer K 2007 Phys. Lett. A 367 47Google Scholar

    [45]

    Wales D J, Doye J P K 1997 J. Phys. Chem. A 101 5111Google Scholar

    [46]

    Chu J, Yan F 2021 Phys. Rev. Appl. 16 054020Google Scholar

  • [1] Guo Mu-Cheng, Wang Fu-Dong, Hu Zhao-Gao, Ren Miao-Miao, Sun Wei-Ye, Xiao Wan-Ting, Liu Shu-Ping, Zhong Man-Jin. Research progress of quantum coherence performance and applications of micro/nano scale rare-earth doped crystals. Acta Physica Sinica, doi: 10.7498/aps.72.20222166
    [2] Wang Chen-Xu, He Ran, Li Rui-Rui, Chen Yan, Fang Ding, Cui Jin-Ming, Huang Yun-Feng, Li Chuan-Feng, Guo Guang-Can. Advances in the study of ion trap structures in quantum computation and simulation. Acta Physica Sinica, doi: 10.7498/aps.71.20220224
    [3] Zhou Zong-Quan. “Quantum memory” quantum computers and noiseless phton echoes. Acta Physica Sinica, doi: 10.7498/aps.71.20212245
    [4] Wang Ning, Wang Bao-Chuan, Guo Guo-Ping. New progress of silicon-based semiconductor quantum computation. Acta Physica Sinica, doi: 10.7498/aps.71.20221900
    [5] Zhang Jie-Yin, Gao Fei, Zhang Jian-Jun. Research progress of silicon and germanium quantum computing materials. Acta Physica Sinica, doi: 10.7498/aps.70.20211492
    [6] Zhang Shi-Hao, Zhang Xiang-Dong, Li Lü-Zhou. Research progress of measurement-based quantum computation. Acta Physica Sinica, doi: 10.7498/aps.70.20210923
    [7] Yao Hong-Bin, Jiang Xiang-Zhan, Cao Chang-Hong, Li Wen-Liang. Theoretical study of dissociation dynamics of HD+ and its quantum control with an intense laser field. Acta Physica Sinica, doi: 10.7498/aps.68.20190400
    [8] Fan Heng. Quantum computation and quantum simulation. Acta Physica Sinica, doi: 10.7498/aps.67.20180710
    [9] Wang Wen-Bin, Zhu Yin-Yan, Yin Li-Feng, Shen Jian. Quantum manipulation of electronic phase separation in complex oxides. Acta Physica Sinica, doi: 10.7498/aps.67.20182007
    [10] Jia Fang, Liu Cun-Jin, Hu Yin-Quan, Fan Hong-Yi. New formula for calculating the fidelity of teleportation and its applications. Acta Physica Sinica, doi: 10.7498/aps.65.220302
    [11] Yang Zeng-Qiang, Zhang Li-Da. Quantum control of the XUV photoabsorption spectrum of helium atoms via the carrier-envelope-phase of an infrared laser pulse. Acta Physica Sinica, doi: 10.7498/aps.64.133203
    [12] Yang Guang, Lian Bao-Wang, Nie Min. Fidelity recovery scheme for quantum teleportation in amplitude damping channel. Acta Physica Sinica, doi: 10.7498/aps.64.010303
    [13] Yao Hong-Bin, Li Wen-Liang, Zhang Ji, Peng Min. Quantum control of K2 molecule in an intense laser field:Selective population of dressed states. Acta Physica Sinica, doi: 10.7498/aps.63.178201
    [14] Nie Min, Zhang Lin, Liu Xiao-Hui. Poisson survival model of quantum entanglement signaling network and fidelity analysis. Acta Physica Sinica, doi: 10.7498/aps.62.230303
    [15] Zhao Jian-Hui. Ground state phase diagram of the quantum spin 1 Blume-Capel model: reduced density fidelity study. Acta Physica Sinica, doi: 10.7498/aps.61.220501
    [16] Fang Mao-Fa, Peng Xiao-Fang, Liao Xiang-Ping, Pan Chang-Ning, Fang Jian-Shu. Fidelity of quantum teleportation of atomic-state in dissipative environment. Acta Physica Sinica, doi: 10.7498/aps.60.090303
    [17] Ye Bin, Xu Wen-Bo, Gu Bin-Jie. Robust quantum computation of the quantum kicked Harper model and dissipative decoherence. Acta Physica Sinica, doi: 10.7498/aps.57.689
    [18] Xia Yun-Jie, Wang Guang-Hui, Du Shao-Jiang. Fidelity of the scheme of continunous variables quantum teleportation via minimum-correlation mixed quantum states. Acta Physica Sinica, doi: 10.7498/aps.56.4331
    [19] Zhang Deng-Yu, Guo Ping, Gao Feng. Fidelity of two-level atoms’ quantum states in a strong thermal radiation field. Acta Physica Sinica, doi: 10.7498/aps.56.1906
    [20] Ye Bin, Gu Rui-Jun, Xu Wen-Bo. Robust quantum computation of the kicked Harper model and quantum chaos. Acta Physica Sinica, doi: 10.7498/aps.56.3709
Metrics
  • Abstract views:  266
  • PDF Downloads:  5
  • Cited By: 0
Publishing process
  • Received Date:  23 January 2025
  • Accepted Date:  17 May 2025
  • Available Online:  11 June 2025
  • /

    返回文章
    返回