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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.-
Keywords:
- singlet-triplet qubit /
- single-qubit quantum gate /
- strong driving
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图 1 全量子化哈密顿量的裸态能级图
Figure 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 = 0.0014Figure 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. 3 157
Google Scholar
[2] 王保传, 陈明博, 曹刚, 郭国平 2018 物理 47 725
Google Scholar
Wang B C, Chen M B, Cao G, Guo G P 2018 PHYSICS.47 725
Google Scholar
[3] 王宁, 王保传, 郭国平 2022 物理学报 71 230301
Google Scholar
Wang N, Wang B C, Guo G P 2022 Acta Phys. Sin. 71 230301
Google Scholar
[4] Yoneda J, Takeda K, Otsuka T, et al. 2018 Nat. Nanotech. 13 102
Google Scholar
[5] Takeda K, Kamioka J, Otsuka T, et al. 2016 Sci. Adv. 2 e1600694
Google Scholar
[6] Veldhorst M, Hwang J C C, Yang C H, et al. 2014 Nat. Nanotech. 9 981
Google 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 eabn5130
Google Scholar
[8] Xue X, Russ M, Samkharadze N, Undseth B, Sammak A, Scappucci G, Vandersypen L M K 2022 Nature 601 343
Google Scholar
[9] Noiri A, Takeda K, Nakajima T, Kobayashi T, Sammak A, Scappucci G, Tarucha S 2022 Nature 601 338
Google Scholar
[10] Loss D, DiVincenzo D P 1998 Phys. Rev. A 57 120
Google Scholar
[11] Petta J R, Johnson A C, Taylor J M, et al. 2005 Science 309 2180
Google Scholar
[12] DiVincenzo D P, Bacon D, Kempe J, Burkard G, Whaley K B 2000 Nature 408 339
Google Scholar
[13] Friesen M, Ghosh J, Eriksson M A, Coppersmith S N 2017 Nat. Commun. 8 15923
Google Scholar
[14] Wu X, Ward D R, Prance J R, et al. 2014 Proc. Natl. Acad. Sci. USA 111 11938
Google Scholar
[15] Barthel C, Medford J, Bluhm H, Yacoby A, Marcus C M, Hanson M P, Gossard A C 2012 Phys. Rev. B 85 035306
Google Scholar
[16] Borjans F, Mi X, Petta J R 2021 Phys. Rev. Appl. 15 044052
Google Scholar
[17] Eng K, Ladd T D, Smith A, et al. 2015 Sci. Adv. 1 e1500214
Google Scholar
[18] Andrews R W, Jones C, Reed M D, et al. 2019 Nat. Nanotech. 14 747
Google Scholar
[19] Bermeister A, Keith D, Culcer D 2014 Appl. Phys. Lett. 105 192102
Google Scholar
[20] Chan K W, Huang W, Yang C H, et al. 2018 Phys. Rev. Appl. 10 044017
Google Scholar
[21] Martins F, Malinowski F K, Nissen P D, et al. 2016 Phys. Rev. Lett. 116 116801
Google Scholar
[22] Reed M D, Maune B M, Andrews R W, et al. 2016 Phys. Rev. Lett. 116 110402
Google Scholar
[23] Abadillo-Uriel J C, Eriksson M A, Coppersmith S N, Friesen M 2019 Nat. Commun. 10 5641
Google Scholar
[24] Yang Y C, Coppersmith S N, Friesen M 2017 Phys. Rev. A 95 062321
Google Scholar
[25] Takeda K, Noiri A, Yoneda J, Nakajima T, Tarucha S 2020 Phys. Rev. Lett. 124 117701
Google Scholar
[26] Xie W X, Zhang C X, Xue Z Y 2021 Ann. Phys. 533 2100054
Google Scholar
[27] Abadillo-Uriel, J C, King C, Coppersmith S N, Friesen M 2021 Phys. Rev. A 104 032612
Google Scholar
[28] Zajac D M, Sigillito A J, Russ M, Borjans F, Taylor J M, Burkard G, Petta J R 2018 Science 359 439
Google Scholar
[29] Bloch F, Siegert A 1940 Phys. Rev. 57 522
Google Scholar
[30] Shirley J H 1965 Phys. Rev. 138 B979
Google Scholar
[31] Cohen-Tannoudji C, Dupont-Roc J, Fabre C 1973 J. Phys. B 6 L214
Google Scholar
[32] Gambetta J M, Motzoi F, Merkel S T, Wilhelm F K 2011 Phys. Rev. A 83 012308
Google Scholar
[33] Motzoi F, Wilhelm F K 2013 Phys. Rev. A 88 062318
Google 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 084401
Google Scholar
[36] Nielsen M A 2002 Phys. Lett. A 303 249
Google Scholar
[37] Elman S J, Bartlett S D, Doherty A C 2017 Phys. Rev. B 96 115407
Google Scholar
[38] Mi X, Kohler S, Petta J R 2018 Phys. Rev. B 98 161404(R
Google Scholar
[39] Petersson K D, Petta J R, Lu H, Gossard A C 2010 Phys. Rev. Lett. 105 246804
Google 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 3
Google Scholar
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