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Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution |
| Jianwen Xu1,2†, Yujia Zhang1,2†, Wen Zheng1,2†*, Haoyang Cai1,2, Haoyu Zhou1,2, Xianke Li1,2, Xudong Liao1,2, Yu Zhang1,2,3, Shaoxiong Li1,2,3, Dong Lan1,2,3, Xinsheng Tan1,2,3*, and Yang Yu1,2,3* |
1National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
2Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou 215163, China
3Hefei National Laboratory, Hefei 230088, China
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| Cite this article: |
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Jianwen Xu, Yujia Zhang, Wen Zheng et al 2024 Chin. Phys. Lett. 41 040202 |
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Abstract Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times. However, practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian. Here, we experimentally show that using a transmon qubit that, even in the presence of vanishing energy gaps, it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process. This validates the recently derived general solution of the quantum Zermelo navigation problem, paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes, including the well-known counter-diabatic driving. By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture, we reveal the relationship between the quantum speed limit and instantaneous energy cost. Consequently, we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths, indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.
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Received: 28 February 2024
Editors' Suggestion
Published: 11 April 2024
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| PACS: |
02.40.-k
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(Geometry, differential geometry, and topology)
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03.67.-a
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(Quantum information)
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42.50.Dv
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(Quantum state engineering and measurements)
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| [1] | Albash T and Lidar D A 2018 Rev. Mod. Phys. 90 015002 |
| [2] | Brooke J, Bitko D, Rosenbaum F T, and Aeppli G 1999 Science 284 779 |
| [3] | Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, and Preda D 2001 Science 292 472 |
| [4] | Degen C L, Reinhard F, and Cappellaro P 2017 Rev. Mod. Phys. 89 035002 |
| [5] | Georgescu I M, Ashhab S, and Nori F 2014 Rev. Mod. Phys. 86 153 |
| [6] | Shi A, Guan H, Zhang J, and Zhang W 2020 Chin. Phys. Lett. 37 120301 |
| [7] | Altman E, Brown K R, Carleo G et al. 2021 PRX Quantum 2 017003 |
| [8] | Devoret M H and Schoelkopf R J 2013 Science 339 1169 |
| [9] | You J Q and Nori F 2011 Nature 474 589 |
| [10] | Ehrenfest P 1916 Ann. Phys. (Berlin) 356 327 |
| [11] | Born M and Fock V 1928 Z. Phys. 51 165 |
| [12] | Schwinger J 1937 Phys. Rev. 51 648 |
| [13] | Kato T 1950 J. Phys. Soc. Jpn. 5 435 |
| [14] | Wei Z H and Ying M S 2007 Phys. Rev. A 76 024304 |
| [15] | Comparat D 2009 Phys. Rev. A 80 012106 |
| [16] | Tong D M, Singh K, Kwek L C, and Oh C H 2007 Phys. Rev. Lett. 98 150402 |
| [17] | Wang Z Y and Plenio M B 2016 Phys. Rev. A 93 052107 |
| [18] | Xu K B, Xie T Y, Shi F Z, Wang Z Y, Xu X K, Wang P F, Wang Y, Plenio M B, and Du J F 2019 Sci. Adv. 5 eaax3800 |
| [19] | Zheng W, Xu J W, Wang Z M, Dong Y Q, Lan D, Tan X S, and Yu Y 2022 Phys. Rev. Appl. 18 044014 |
| [20] | Dodin A and Brumer P 2021 PRX Quantum 2 030302 |
| [21] | Pontryagin L S 1987 Mathematical Theory of Optimal Processes 1st edn (New York: CRC Press) |
| [22] | Boscain U, Sigalotti M, and Sugny D 2021 PRX Quantum 2 030203 |
| [23] | Martinis J M and Geller M R 2014 Phys. Rev. A 90 022307 |
| [24] | Zheng W, Zhang Y, Dong Y Q et al. 2022 npj Quantum Inf. 8 9 |
| [25] | Torrontegui E, Ibáñez S, Martínez-Garaot S, Modugno M, del Campo A, Guéry-Odelin D, Ruschhaupt A, Chen X, and Muga J G 2013 Shortcuts to adiabaticity, in Adv. At. Mol. Opt. Phys. vol 62 p 117, edited by Arimondo E, Berman P R, and Lin C C (Academic Press) |
| [26] | Guéry-Odelin D, Ruschhaupt A, Kiely A, Torrontegui E, Martínez-Garaot S, and Muga J G 2019 Rev. Mod. Phys. 91 045001 |
| [27] | Berry M V 2009 J. Phys. A 42 365303 |
| [28] | Zheng Y J, Campbell S, De Chiara G, and Poletti D 2016 Phys. Rev. A 94 042132 |
| [29] | Campbell S and Deffner S 2017 Phys. Rev. Lett. 118 100601 |
| [30] | Mandelstam L and Tamm I 1991 The uncertainty relation between energy and time in non-relativistic quantum mechanics, in Selected Papers, edited by Bolotovskii B M, Frenkel V Y, and Peierls R (Berlin: Springer) p 115 |
| [31] | Margolus N and Levitin L B 1998 Physica D 120 188 |
| [32] | Levitin L B and Toffoli T 2009 Phys. Rev. Lett. 103 160502 |
| [33] | Marvian I and Lidar D A 2015 Phys. Rev. Lett. 115 210402 |
| [34] | Sun S N and Zheng Y J 2019 Phys. Rev. Lett. 123 180403 |
| [35] | Ness G, Alberti A, and Sagi Y 2022 Phys. Rev. Lett. 129 140403 |
| [36] | Pires D P, Cianciaruso M, Céleri L C, Adesso G, and Soares-Pinto D O 2016 Phys. Rev. X 6 021031 |
| [37] | Sun S N, Peng Y G, Hu X H, and Zheng Y J 2021 Phys. Rev. Lett. 127 100404 |
| [38] | Wu W and An J H 2022 Phys. Rev. A 106 062438 |
| [39] | García-Pintos L P, Nicholson S B, Green J R, del Campo A, and Gorshkov A V 2022 Phys. Rev. X 12 011038 |
| [40] | Dou F Q, Han M P, and Shu C C 2023 Phys. Rev. Appl. 20 014031 |
| [41] | Bukov M, Sels D, and Polkovnikov A 2019 Phys. Rev. X 9 011034 |
| [42] | Suzuki K and Takahashi K 2020 Phys. Rev. Res. 2 032016 |
| [43] | Xu T N, Li J, Busch T, Chen X, and Fogarty T 2020 Phys. Rev. Res. 2 023125 |
| [44] | Russell B and Stepney S 2014 Phys. Rev. A 90 012303 |
| [45] | Brody D C and Meier D M 2015 Phys. Rev. Lett. 114 100502 |
| [46] | Bofill J M, Sanz A S, Albareda G, Moreira d P R I, and Quapp W 2020 Phys. Rev. Res. 2 033492 |
| [47] | Garcia L, Bofill J M, Moreira I d P R, and Albareda G 2022 Phys. Rev. Lett. 129 180402; erratum in: 2023 Phys. Rev. Lett. 130 089901 |
| [48] | Koch J, Yu T M, Gambetta J, Houck A A, Schuster D I, Majer J, Blais A, Devoret M H, Girvin S M, and Schoelkopf R J 2007 Phys. Rev. A 76 042319 |
| [49] | Barends R, Kelly J, Megrant A et al. 2013 Phys. Rev. Lett. 111 080502 |
| [50] | Zhao P, Xu P, Lan D, Chu J, Tan X S, Yu H F, and Yu Y 2020 Phys. Rev. Lett. 125 200503 |
| [51] | Ye Y S, Cao S R, Wu Y L, Chen X W, Zhu Q L, Li S W, Chen F S, Gong M, Zha C, Huang H L, Zhao Y W, Wang S Y, Guo S J, Qian H R, Liang F T, Lin J, Xu Y, Guo C, Sun L H, Li N, Deng H, Zhu X B, and Pan J W 2021 Chin. Phys. Lett. 38 100301 |
| [52] | Krinner S, Storz S, Kurpiers P, Magnard P, Heinsoo J, Keller R, Lütolf J, Eichler C, and Wallraff A 2019 EPJ Quantum Technol. 6 2 |
| [53] | Wenner J, Neeley M, Bialczak R C, Lenander M, Lucero E, O'Connell A D, Sank D, Wang H, Weides M, Cleland A N, and Martinis J M 2011 Supercond. Sci. Technol. 24 065001 |
| [54] | Nuerbolati W, Han Z, Chu J, Zhou Y, Tan X, Yu Y, Liu S, and Yan F 2022 Appl. Phys. Lett. 120 174001 |
| [55] | Wang R X, Zhao P, Jin Y R, and Yu H F 2022 Appl. Phys. Lett. 121 152602 |
| [56] | Zhao P 2023 Phys. Rev. Appl. 20 054033 |
| [57] | Müller C, Cole J H, and Lisenfeld J 2019 Rep. Prog. Phys. 82 124501 |
| [58] | Sarovar M, Proctor T, Rudinger K, Young K, Nielsen E, and Blume-Kohout R 2020 Quantum 4 321 |
| [59] | Zhao P, Linghu K, Li Z Y, Xu P, Wang R X, Xue G M, Jin Y R, and Yu H F 2022 PRX Quantum 3 020301 |
| [60] | Zheng W, Xu J W, Ma Z, Li Y, Dong Y Q, Zhang Y, Wang X H, Sun G Z, Wu P H, Zhao J, Li S X, Lan D, Tan X S, and Yu Y 2022 Chin. Phys. Lett. 39 100202 |
| [61] | Zhao P, Wang R X, Hu M J, Ma T, Xu P, Jin Y R, and Yu H F 2023 Phys. Rev. Appl. 19 054050 |
| [62] | Zhou Z Y, Sitler R, Oda Y, Schultz K, and Quiroz G 2023 Phys. Rev. Lett. 131 210802 |
| [63] | Xu S B, Sun Z Z, Wang K, Xiang L, Bao Z H, Zhu Z, Shen F, Song Z, Zhang P, Ren W, Zhang X, Dong H, Deng J, Chen J, Wu Y, Tan Z, Gao Y, Jin F, Zhu X, Zhang C, Wang N, Zou Y, Zhong J, Zhang A, Li W, Jiang W, Yu L W, Yao Y, Wang Z, Li H, Guo Q, Song C, Wang H, and Deng D L 2023 Chin. Phys. Lett. 40 060301 |
| [64] | Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697 |
| [65] | Landau L D 1932 Phys. Z. Sowjetunion 2 46 |
| [66] | Zener C 1932 Proc. R. Soc. A 137 696 |
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