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强驱动单态-三重态量子比特的高保真单比特门

刘启沛 张程贤 薛正远

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强驱动单态-三重态量子比特的高保真单比特门

刘启沛, 张程贤, 薛正远

High-fidelity single-qubit gates of a strong driven singlet-triplet qubit

Liu Qi-Pei, Zhang Cheng-Xian, Xue Zheng-Yuan
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  • 半导体量子点量子比特是最有希望实现量子计算的候选者之一. 其中自旋单态-三重态量子比特因具有全电控制和读取准确的优良性质而备受关注. 为增强对电荷噪声的免疫, 通常引进强脉冲驱动以尽可能加快门操作速度. 但是, 强驱动脉冲引起的复杂动力学导致旋波近似不再适用, 反而会阻碍高保真度比特操作的实现. 本文提出了一种增加简单的正交脉冲的方法, 可以很好地抑制强驱动引起的高频振荡项的操作错误. 数值计算结果表明, NOT门的保真度在无噪声时可达99.99%且操作时间只需2 ns. 特别地, 即便电荷噪声强度到了$ 2\ \mu{\rm{eV}} $的水平, NOT门的平均保真度也可高于99.9%. 值得注意的是, 该方案同时也适用于任意单比特量子门的优化. 因此, 本文的脉冲优化方案将有助于获得快速高保真度的自旋单态-三重态量子比特.
    Semiconductor quantum dot qubits are one of the most promising candidates for quantum computing. Among them, singlet-triplet qubits have attracted much attention due to their excellent properties of all-electric control and accurate readout. To improve qubit immunity to charge noise, strong driving pulses are usually introduced to make operation as fast as possible. However, the complex dynamics induced by strong driving pulses make the rotating wave approximation inapplicable and hinder the implementation of high-fidelity qubit operation. In this work, we present a method of utilizing simple quadrature pulses to correct errors of high-frequency oscillatory terms induced by strong driving. A scheme to obtain these pulses is proposed based on a full quantization of the system and derivative removal by adiabatic gate (DRAG) theory, as the former clarifies the elementary processes of strong driving effects and enables the latter to find correction pulse shapes. The numerical simulation results show that, a NOT gate with 99.99% fidelity and gate time as short as 2 ns can be achieved with the help of the control pulses of this method, which indicates that the control error brought by strong driving is no longer a limiting factor. In particular, NOT gate fidelity higher than 99.9% is achievable even when the charge noise is at a level of $ 2\ \mu{\rm{eV}} $. Notice that this method can be applied to any resonant-driving single-qubit rotation but not just NOT gates. Therefore, our approach will facilitate qubits to realize fast, high-fidelity single-qubit gates under charge noise.
      通信作者: 张程贤, cxzhang@gxu.edu.cn ; 薛正远, zyxue83@163.com
    • 基金项目: 国家自然科学基金(批准号: 11905065, 12275090)、广西科技基地和人才专项(批准号: 桂科AD22035186)、广东省重点实验室(批准号: 2020B1212060066)和科技创新2030——“量子通信与量子计算机”重大项目(批准号: 2021ZD0302303)资助的课题.
      Corresponding author: Zhang Cheng-Xian, cxzhang@gxu.edu.cn ; Xue Zheng-Yuan, zyxue83@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11905065, 12275090), the Guangxi Science Foundation, China (Grant No. AD22035186), the Key Laboratory of Guangdong Province, China (Grant No. 2020B1212060066), and the Innovation Program for Quantum Science and Technology, China (Grant No. 2021ZD0302303).
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    Friesen M, Ghosh J, Eriksson M A, Coppersmith S N 2017 Nat. Commun. 8 15923Google Scholar

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    Barthel C, Medford J, Bluhm H, Yacoby A, Marcus C M, Hanson M P, Gossard A C 2012 Phys. Rev. B 85 035306Google Scholar

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    Borjans F, Mi X, Petta J R 2021 Phys. Rev. Appl. 15 044052Google Scholar

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    Eng K, Ladd T D, Smith A, et al. 2015 Sci. Adv. 1 e1500214Google Scholar

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    Andrews R W, Jones C, Reed M D, et al. 2019 Nat. Nanotech. 14 747Google Scholar

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    Chan K W, Huang W, Yang C H, et al. 2018 Phys. Rev. Appl. 10 044017Google Scholar

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    Martins F, Malinowski F K, Nissen P D, et al. 2016 Phys. Rev. Lett. 116 116801Google Scholar

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    Reed M D, Maune B M, Andrews R W, et al. 2016 Phys. Rev. Lett. 116 110402Google Scholar

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    Abadillo-Uriel J C, Eriksson M A, Coppersmith S N, Friesen M 2019 Nat. Commun. 10 5641Google Scholar

    [24]

    Yang Y C, Coppersmith S N, Friesen M 2017 Phys. Rev. A 95 062321Google Scholar

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    Takeda K, Noiri A, Yoneda J, Nakajima T, Tarucha S 2020 Phys. Rev. Lett. 124 117701Google Scholar

    [26]

    Xie W X, Zhang C X, Xue Z Y 2021 Ann. Phys. 533 2100054Google Scholar

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    Abadillo-Uriel, J C, King C, Coppersmith S N, Friesen M 2021 Phys. Rev. A 104 032612Google Scholar

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    Zajac D M, Sigillito A J, Russ M, Borjans F, Taylor J M, Burkard G, Petta J R 2018 Science 359 439Google Scholar

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    Shirley J H 1965 Phys. Rev. 138 B979Google Scholar

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    Cohen-Tannoudji C, Dupont-Roc J, Fabre C 1973 J. Phys. B 6 L214Google Scholar

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    Gambetta J M, Motzoi F, Merkel S T, Wilhelm F K 2011 Phys. Rev. A 83 012308Google Scholar

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    Motzoi F, Wilhelm F K 2013 Phys. Rev. A 88 062318Google Scholar

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    Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (10th Anniversary Ed.) (Cambridge: Cambridge University Press) pp174–177

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    Yoneda J, Otsuka T, Takakura T, et al. 2015 Appl. Phys. Exp. 8 084401Google Scholar

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    Nielsen M A 2002 Phys. Lett. A 303 249Google Scholar

    [37]

    Elman S J, Bartlett S D, Doherty A C 2017 Phys. Rev. B 96 115407Google Scholar

    [38]

    Mi X, Kohler S, Petta J R 2018 Phys. Rev. B 98 161404(RGoogle Scholar

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    Petersson K D, Petta J R, Lu H, Gossard A C 2010 Phys. Rev. Lett. 105 246804Google Scholar

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    Nichol J M, Orona L A, Harvey S P, Fallahi S, Gardner G C, Manfra M J, Yacoby A 2017 npj Quantum Inf. 3 3Google Scholar

  • 图 1  全量子化哈密顿量的裸态能级图

    Fig. 1.  Energy levels of the full quantized Hamiltonian for the bare states.

    图 2  (a)无噪声时和(b)电荷噪声下的NOT门表现. 频率修正和脉冲修正分别指文献[24]和本文所用的修正方案. 实线和虚线分别对应$\varOmega_x$脉冲的包络为高斯型和三角函数型. 图(a)右下角的插入图为高斯型$\varOmega_x$及其对应的$\varOmega_y$的示意图. 所用参数为$V_{01}=0.6402$, $V_{0 {\rm{f}}}=0.5309$, V1f = 0.0014

    Fig. 2.  NOT gate performance under (a) noise-free and (b) charge noise. The frequency correction and the pulse correction refers to the correction scheme used in Ref. [24] and this work, respectively. The Gaussian and trigonometric $\varOmega_x$ pulse envelopes are represented by the solid and dashed lines, respectively. The bottem right insert in panel (a) is a diagram of Gaussian $\varOmega_x$ and its corresponding $\varOmega_y$. Parameters: $ V_ {01} = 0.6402 $, $ V_ {0 {\rm{f}}} = 0.5309 $, $ V_ {1 {\rm{f}}} = 0.0014 $.

  • [1]

    Chatterjee A, Stevenson P, De Franceschi S, Morello A, de Leon N, Kuemmeth F 2021 Nat. Rev. Phys. 3 157Google Scholar

    [2]

    王保传, 陈明博, 曹刚, 郭国平 2018 物理 47 725Google Scholar

    Wang B C, Chen M B, Cao G, Guo G P 2018 PHYSICS.47 725Google Scholar

    [3]

    王宁, 王保传, 郭国平 2022 物理学报 71 230301Google Scholar

    Wang N, Wang B C, Guo G P 2022 Acta Phys. Sin. 71 230301Google Scholar

    [4]

    Yoneda J, Takeda K, Otsuka T, et al. 2018 Nat. Nanotech. 13 102Google Scholar

    [5]

    Takeda K, Kamioka J, Otsuka T, et al. 2016 Sci. Adv. 2 e1600694Google Scholar

    [6]

    Veldhorst M, Hwang J C C, Yang C H, et al. 2014 Nat. Nanotech. 9 981Google Scholar

    [7]

    Mills A R, Guinn C R, Gullans M J, Sigillito A J, Feldman M M, Nielsen E, Petta J R 2022 Sci. Adv. 8 eabn5130Google Scholar

    [8]

    Xue X, Russ M, Samkharadze N, Undseth B, Sammak A, Scappucci G, Vandersypen L M K 2022 Nature 601 343Google Scholar

    [9]

    Noiri A, Takeda K, Nakajima T, Kobayashi T, Sammak A, Scappucci G, Tarucha S 2022 Nature 601 338Google Scholar

    [10]

    Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120Google Scholar

    [11]

    Petta J R, Johnson A C, Taylor J M, et al. 2005 Science 309 2180Google Scholar

    [12]

    DiVincenzo D P, Bacon D, Kempe J, Burkard G, Whaley K B 2000 Nature 408 339Google Scholar

    [13]

    Friesen M, Ghosh J, Eriksson M A, Coppersmith S N 2017 Nat. Commun. 8 15923Google Scholar

    [14]

    Wu X, Ward D R, Prance J R, et al. 2014 Proc. Natl. Acad. Sci. USA 111 11938Google Scholar

    [15]

    Barthel C, Medford J, Bluhm H, Yacoby A, Marcus C M, Hanson M P, Gossard A C 2012 Phys. Rev. B 85 035306Google Scholar

    [16]

    Borjans F, Mi X, Petta J R 2021 Phys. Rev. Appl. 15 044052Google Scholar

    [17]

    Eng K, Ladd T D, Smith A, et al. 2015 Sci. Adv. 1 e1500214Google Scholar

    [18]

    Andrews R W, Jones C, Reed M D, et al. 2019 Nat. Nanotech. 14 747Google Scholar

    [19]

    Bermeister A, Keith D, Culcer D 2014 Appl. Phys. Lett. 105 192102Google Scholar

    [20]

    Chan K W, Huang W, Yang C H, et al. 2018 Phys. Rev. Appl. 10 044017Google Scholar

    [21]

    Martins F, Malinowski F K, Nissen P D, et al. 2016 Phys. Rev. Lett. 116 116801Google Scholar

    [22]

    Reed M D, Maune B M, Andrews R W, et al. 2016 Phys. Rev. Lett. 116 110402Google Scholar

    [23]

    Abadillo-Uriel J C, Eriksson M A, Coppersmith S N, Friesen M 2019 Nat. Commun. 10 5641Google Scholar

    [24]

    Yang Y C, Coppersmith S N, Friesen M 2017 Phys. Rev. A 95 062321Google Scholar

    [25]

    Takeda K, Noiri A, Yoneda J, Nakajima T, Tarucha S 2020 Phys. Rev. Lett. 124 117701Google Scholar

    [26]

    Xie W X, Zhang C X, Xue Z Y 2021 Ann. Phys. 533 2100054Google Scholar

    [27]

    Abadillo-Uriel, J C, King C, Coppersmith S N, Friesen M 2021 Phys. Rev. A 104 032612Google Scholar

    [28]

    Zajac D M, Sigillito A J, Russ M, Borjans F, Taylor J M, Burkard G, Petta J R 2018 Science 359 439Google Scholar

    [29]

    Bloch F, Siegert A 1940 Phys. Rev. 57 522Google Scholar

    [30]

    Shirley J H 1965 Phys. Rev. 138 B979Google Scholar

    [31]

    Cohen-Tannoudji C, Dupont-Roc J, Fabre C 1973 J. Phys. B 6 L214Google Scholar

    [32]

    Gambetta J M, Motzoi F, Merkel S T, Wilhelm F K 2011 Phys. Rev. A 83 012308Google Scholar

    [33]

    Motzoi F, Wilhelm F K 2013 Phys. Rev. A 88 062318Google Scholar

    [34]

    Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (10th Anniversary Ed.) (Cambridge: Cambridge University Press) pp174–177

    [35]

    Yoneda J, Otsuka T, Takakura T, et al. 2015 Appl. Phys. Exp. 8 084401Google Scholar

    [36]

    Nielsen M A 2002 Phys. Lett. A 303 249Google Scholar

    [37]

    Elman S J, Bartlett S D, Doherty A C 2017 Phys. Rev. B 96 115407Google Scholar

    [38]

    Mi X, Kohler S, Petta J R 2018 Phys. Rev. B 98 161404(RGoogle Scholar

    [39]

    Petersson K D, Petta J R, Lu H, Gossard A C 2010 Phys. Rev. Lett. 105 246804Google Scholar

    [40]

    Nichol J M, Orona L A, Harvey S P, Fallahi S, Gardner G C, Manfra M J, Yacoby A 2017 npj Quantum Inf. 3 3Google Scholar

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出版历程
  • 收稿日期:  2023-05-31
  • 修回日期:  2023-07-06
  • 上网日期:  2023-07-18
  • 刊出日期:  2023-10-20

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