Approximate constructions of counterdiabatic driving with NMR quantum systems

doi:10.1088/1674-1056/ad58b2

中国物理B ›› 2024, Vol. 33 ›› Issue (9): 90301-090301.doi: 10.1088/1674-1056/ad58b2

Approximate constructions of counterdiabatic driving with NMR quantum systems

Hui Zhou(周辉)^1,†, Xiaoli Dai(代晓莉)¹, Jianpei Geng(耿建培)¹, Yunlan Ji(季云兰)¹, and Xinhua Peng(彭新华)^2,3,4,‡

1 School of Physics, Hefei University of Technology, Hefei 230009, China;
2 Chinese Academy of Sciences Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China;
3 Chinese Academy of Sciences Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China;
4 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

收稿日期:2024-04-30 修回日期:2024-06-13 接受日期:2024-06-15 出版日期:2024-08-15 发布日期:2024-08-15
通讯作者: Hui Zhou,Xinhua Peng E-mail:zhouhui9240@163.com;xhpeng@ustc.edu.cn
基金资助:
Acknowledgments Project supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0303205), the National Natural Science Foundation of China (Grant Nos. 12104282 and 12305014), the Initiative in Quantum Information Technologies of Anhui Province (Grant No. AHY050000), and the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2024HGTB0253 and JZ2023HGTA0172).

Approximate constructions of counterdiabatic driving with NMR quantum systems

Hui Zhou(周辉)^1,†, Xiaoli Dai(代晓莉)¹, Jianpei Geng(耿建培)¹, Yunlan Ji(季云兰)¹, and Xinhua Peng(彭新华)^2,3,4,‡

1 School of Physics, Hefei University of Technology, Hefei 230009, China;
2 Chinese Academy of Sciences Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China;
3 Chinese Academy of Sciences Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China;
4 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Received:2024-04-30 Revised:2024-06-13 Accepted:2024-06-15 Online:2024-08-15 Published:2024-08-15
Contact: Hui Zhou,Xinhua Peng E-mail:zhouhui9240@163.com;xhpeng@ustc.edu.cn
Supported by:
Acknowledgments Project supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0303205), the National Natural Science Foundation of China (Grant Nos. 12104282 and 12305014), the Initiative in Quantum Information Technologies of Anhui Province (Grant No. AHY050000), and the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2024HGTB0253 and JZ2023HGTA0172).

摘要/Abstract

摘要： Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespread applications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimental realization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. In this topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applications of approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.

关键词: nuclear magnetic resonance, quantum simulation, quantum state engineering

Abstract: Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespread applications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimental realization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. In this topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applications of approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.

Key words: nuclear magnetic resonance, quantum simulation, quantum state engineering

中图分类号: (Quantum information)

03.67.-a

42.50.Dv (Quantum state engineering and measurements) 82.56.-b (Nuclear magnetic resonance)

Hui Zhou(周辉), Xiaoli Dai(代晓莉), Jianpei Geng(耿建培), Yunlan Ji(季云兰), and Xinhua Peng(彭新华). Approximate constructions of counterdiabatic driving with NMR quantum systems[J]. 中国物理B, 2024, 33(9): 90301-090301.

参考文献

[1] Bharti K, Cervera-Lierta A, Kyaw T H, Haug T, Alperin-Lea S, Anand A, Degroote M, Heimonen H, Kottmann J S, Menke T, Mok W K, Sim S, Kwek L C and Aspuru-Guzik A 2022 Rev. Mod. Phys. 94 015004
[2] Portmann C and Renner R 2022 Rev. Mod. Phys. 94 025008
[3] Degen C L, Reinhard F and Cappellaro P 2017 Rev. Mod. Phys. 89 035002
[4] Suter D and Alvarez G ′A 2016 Rev. Mod. Phys. 88 041001
[5] Koch C P, Boscain U, Calarco T, Dirr G, Filipp S, Glaser S J, Kosloff R, Montangero S, Schulte-Herbrüggen T, Sugny D and Wilhelm F K 2022 Eur. Phys. J. Quantum Technol. 9 19
[6] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A and Preda D 2001 Science 292 472
[7] Král P, Thanopulos I and Shapiro M 2007 Rev. Mod. Phys. 79 53
[8] Peng X, Liao Z, Xu N, Qin G, Zhou X, Suter D and Du J 2008 Phys. Rev. Lett. 101 220405
[9] Xu N, Zhu J, Lu D, Zhou X, Peng X and Du J 2012 Phys. Rev. Lett. 108 130501
[10] Cirac J I and Zoller P 2012 Nat. Phys. 8 264
[11] Albash T and Lidar D A 2018 Rev. Mod. Phys. 90 015002
[12] Born M and Fock V 1928 Z. Phys. 51 165
[13] Kato T 1950 J. Phys. Soc. Jpn. 5 435
[14] Demirplak M and Rice S A 2003 J. Phys. Chem. A 107 9937
[15] Demirplak M and Rice S A 2005 J. Phys. Chem. B 109 6838
[16] Berry M V 2009 J. Phys. A 42 365303
[17] Chen X, Ruschhaupt A, Schmidt S, del Campo A, Guéry-Odelin D and Muga J G 2010 Phys. Rev. Lett. 104 063002
[18] Masuda S and Nakamura K 2010 Proc. R. Soc. A 466 1135
[19] Zhang J, Shim J H, Niemeyer I, Taniguchi T, Teraji T, Abe H, Onoda S, Yamamoto T, Ohshima T, Isoya J and Suter D 2013 Phys. Rev. Lett. 110 240501
[20] Yan T, Liu B J, Xu K, Song C, Liu S, Zhang Z, Deng H, Yan Z, Rong H, Huang K, Yung M H, Chen Y and Yu D 2019 Phys. Rev. Lett. 122 080501
[21] Du Y X, Liang Z T, Li Y C, Yue X X, Lv Q X, Huang W, Chen X, Yan H and Zhu S L 2016 Nat. Commun. 7 12479
[22] An S, Lv D, del Campo A and Kim K 2016 Nat. Commun. 7 12999
[23] Okuyama M and Takahashi K 2016 Phys. Rev. Lett. 117 070401
[24] Baksic A, Ribeiro H and Clerk A A 2016 Phys. Rev. Lett. 116 230503
[25] Campbell S and Deffner S 2017 Phys. Rev. Lett. 118 100601
[26] Funo K, Zhang J N, Chatou C, Kim K, Ueda M and del Campo A 2017 Phys. Rev. Lett. 118 100602
[27] Kleissler F, Lazariev A and Arroyo-Camejo S 2018 npj Quantum. Inf. 4 49
[28] Vepsäläinen A, Danilin S and Paraoanu G S 2019 Sci. Adv. 5 eaau5999
[29] Zhou B B, Baksic A, Ribeiro H, Yale C G, Heremans F J, Jerger P C, Auer A, Burkard G, Clerk A A and Awschalom D D 2017 Nat. Phys. 13 330
[30] Guéry-Odelin D, Ruschhaupt A, Kiely A, Torrontegui E, MartínezGaraot S and Muga J G 2019 Rev. Mod. Phys. 91 045001
[31] del Campo A and Kim K 2019 New J. Phys. 21 050201
[32] Chen X, Lizuain I, Ruschhaupt A, Guéry-Odelin D and Muga J G 2010 Phys. Rev. Lett. 105 123003
[33] Smith A, Lu Y, An S, Zhang X, Zhang J N, Gong Z, Quan H T, Jarzynski C and Kim K 2018 New J. Phys. 20 013008
[34] del Campo A, Rams M M and Zurek W H 2012 Phys. Rev. Lett. 109 115703
[35] Takahashi K 2013 Phys. Rev. E 87 062117
[36] Sels D and Polkovnikov A 2017 Proc. Natl. Acad. Sci. USA 114 E3909
[37] del Campo A 2013 Phys. Rev. Lett. 111 100502
[38] Ibáñez S, Chen X and Muga J G 2013 Phys. Rev. A 87 043402
[39] Opatrný T and Mølmer K 2014 New J. Phys. 16 015025
[40] Chen Y H, Xia Y, Wu Q C, Huang B H and Song J 2016 Phys. Rev. A 93 052109
[41] Saberi H, Opatrný T c v, Mølmer K and del Campo A 2014 Phys. Rev. A 90 060301
[42] Ji Y, Bian J, Chen X, Li J, Nie X, Zhou H and Peng X 2019 Phys. Rev. A 99 032323
[43] Campbell S, De Chiara G, Paternostro M, Palma G M and Fazio R 2015 Phys. Rev. Lett. 114 177206
[44] Kyaw T H and Kwek L C 2018 New J. Phys. 20 045007
[45] Zhou H, Dai X, Geng J, Jin F and Ji Y 2024 Phys. Lett. B 852 138632
[46] Boyers E, Pandey M, Campbell D K, Polkovnikov A, Sels D and Sushkov A O 2019 Phys. Rev. A 100 012341
[47] Zhou H, Ji Y, Nie X, Yang X, Chen X, Bian J and Peng X 2020 Phys. Rev. Appl. 13 044059
[48] Petiziol F, Dive B, Mintert F and Wimberger S 2018 Phys. Rev. A 98 043436
[49] Claeys P W, Pandey M, Sels D and Polkovnikov A 2019 Phys. Rev. Lett. 123 090602
[50] Hatomura T and Takahashi K 2021 Phys. Rev. A 103 012220
[51] Zhou H, Chen X, Nie X, Bian J, Ji Y, Li Z and Peng X 2019 Sci. Bull. 64 888
[52] Mbeng G B and Lechner W 2022 arXiv:2207.03553
[quant-ph]
[53] Ji Y, Zhou F, Chen X, Liu R, Li Z, Zhou H and Peng X 2022 Phys. Rev. A 105 052422
[54] Ji Y, Wu Z, Liu R, Li Y, Jin F, Zhou H and Peng X 2024 New J. Phys. 26 013041
[55] Peng X, Zhang J, Du J and Suter D 2009 Phys. Rev. Lett. 103 140501
[56] Du J, Xu N, Peng X, Wang P, Wu S and Lu D 2010 Phys. Rev. Lett. 104 030502
[57] Feng G, Xu G and Long G 2013 Phys. Rev. Lett. 110 190501
[58] Li Z, Zhou H, Ju C, Chen H, Zheng W, Lu D, Rong X, Duan C, Peng X and Du J 2014 Phys. Rev. Lett. 112 220501
[59] Chen X, Wu Z, Jiang M, Lü X Y, Peng X and Du J 2021 Nat. Commun. 12 6281
[60] Nie X, Wei B B, Chen X, Zhang Z, Zhao X, Qiu C, Tian Y, Ji Y, Xin T, Lu D and Li J 2020 Phys. Rev. Lett. 124 250601
[61] Xin T, Che L, Xi C, Singh A, Nie X, Li J, Dong Y and Lu D 2021 Phys. Rev. Lett. 126 110502
[62] Long X, He W T, Zhang N N, Tang K, Lin Z, Liu H, Nie X, Feng G, Li J, Xin T, Ai Q and Lu D 2022 Phys. Rev. Lett. 129 070502
[63] Li J, Luo Z, Xin T, Wang H, Kribs D, Lu D, Zeng B and Laflamme R 2019 Phys. Rev. Lett. 123 030502
[64] Li K, Wan Y, Hung L Y, Lan T, Long G, Lu D, Zeng B and Laflamme R 2017 Phys. Rev. Lett. 118 080502
[65] Peng X, Zhou H, Wei B B, Cui J, Du J and Liu R B 2015 Phys. Rev. Lett. 114 010601
[66] Luo Z, Li J, Li Z, Hung L Y, Wan Y, Peng X and Du J 2018 Nat. Phys. 14 160
[67] Liu R, Chen Y, Jiang M, Yang X, Wu Z, Li Y, Yuan H, Peng X and Du J 2021 npj Quantum Information 7 170
[68] Wu Z, Wang P, Wang T, Li Y, Liu R, Chen Y, Peng X and Liu R B 2024 Phys. Rev. Lett. 132 200802
[69] Torrontegui E, Martínez-Garaot S, Ruschhaupt A and Muga J G 2012 Phys. Rev. A 86 013601
[70] Passarelli G, Cataudella V, Fazio R and Lucignano P 2020 Phys. Rev. Res. 2 013283
[71] Prielinger L, Hartmann A, Yamashiro Y, Nishimura K, Lechner W and Nishimori H 2021 Phys. Rev. Res. 3 013227
[72] Hartmann A and Lechner W 2019 New. J. Phys. 21 043025
[73] Xie Q, Seki K and Yunoki S 2022 Phys. Rev. B 106 155153
[74] Schindler P M and Bukov M 2024 arXiv:2310.02728
[quant-ph]
[75] Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V and Kurlov D V 2023 Phys. Rev. B 107 184312
[76] Bhattacharjee B 2023 arXiv:2302.07228
[quant-ph]
[77] Takahashi K and del Campo A 2024 Phys. Rev. X 14 011032
[78] Petiziol F, Dive B, Carretta S, Mannella R, Mintert F and Wimberger S 2019 Phys. Rev. A 99 042315
[79] Hatomura T 2024 J. Phys. B: At. Mol. Opt. Phys. 57 102001
[80] Vandersypen L M K and Chuang I L 2005 Rev. Mod. Phys. 76 1037
[81] Peng X H and Suter D 2010 Front. Phys. China 5 1
[82] Jones J A 2024 Prog. Nucl. Magn. Reson. Spectrosc. 140 49
[83] Gershenfeld N A and Chuang I L 1997 Science 275 350
[84] Knill E, Chuang I and Laflamme R 1998 Phys. Rev. A 57 3348
[85] Vandersypen L M K, Steffen M, Breyta G, Yannoni C S, Cleve R and Chuang I L 2000 Phys. Rev. Lett. 85 5452
[86] Peng X, Zhu X, Fang X, Feng M, Gao K, Yang X and Liu M 2001 Chem. Phys. Lett. 340 509
[87] Suzuki M 1993 Proc. Jpn. Acad. Ser. B 69 161
[88] Khaneja N, Reiss T, Kehlet C, Schulte-Herbruggen T and Glaser S 2005 J. Magn. Reson. 172 296
[89] Lee J S 2002 Phys. Lett. A 305 349
[90] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[91] Čepaitė I, Polkovnikov A, Daley A J and Duncan C W · 2023 PRX Quantum 4 010312
[92] Kolodrubetz M, Sels D, Mehta P and Polkovnikov A 2017 Phys. Rep. 697 1
[93] Ibáñez S, Chen X, Torrontegui E, Muga J G and Ruschhaupt A 2012 Phys. Rev. Lett. 109 100403
[94] Kang Y H, Chen Y H, Shi Z C, Huang B H, Song J and Xia Y 2018 Phys. Rev. A 97 033407
[95] Huang B H, Kang Y H, Chen Y H, Shi Z C, Song J and Xia Y 2018 Phys. Rev. A 97 012333
[96] Chandarana P, Hegade N N, Paul K, Albarrán-Arriagada F, Solano E, del Campo A and Chen X 2022 Phys. Rev. Res. 4 013141
[97] Wurtz J and Love P J 2022 Quantum 6 635
[98] Chandarana P, Hegade N N, Montalban I, Solano E and Chen X 2023 Phys. Rev. Appl. 20 014024
[99] Guan H, Zhou F, Albarrán-Arriagada F, Chen X, Solano E, Hegade N N and Huang H L 2023 arXiv:2311.06682
[quant-ph]
[100] Chandarana P, Paul K, de Andoin M G, Ban Y, Sanz M and Chen X 2023 arXiv:2307.14853
[quant-ph]
[101] Vizzuso M, Passarelli G, Cantele G and Lucignano P 2024 New J. Phys. 26 013002
[102] del Campo A, Goold J and Paternostro M 2014 Sci. Rep. 4 6208
[103] Beau M, Jaramillo J and del Campo A 2016 Entropy 18 168
[104] Cakmak B and Mustecaplioglu O E 2019 Phys. Rev. E 99 032108
[105] Deng S, Chenu A, Diao P, Li F, Yu S, Coulamy I, del Campo A and Wu H 2018 Sci. Adv. 4 eaar5909
[106] Funo K, Lambert N, Karimi B, Pekola J P, Masuyama Y and Nori F 2019 Phys. Rev. B 100 035407
[107] Hartmann A, Mukherjee V, Niedenzu W and Lechner W 2020 Phys. Rev. Res. 2 023145
[108] Williamson L A and Davis M J 2024 Phys. Rev. B 109 024310

Approximate constructions of counterdiabatic driving with NMR quantum systems

Approximate constructions of counterdiabatic driving with NMR quantum systems

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Xinyu Shi(史昕雨), Yi Cui(崔祎), Yanyan Shangguan(上官艳艳), Xiaoyu Xu(徐霄宇), Zhanlong Wu(吴占龙), Ze Hu(胡泽), Shuo Li(李硕), Kefan Du(杜柯帆), Ying Chen(陈颖), Long Ma(马龙), Zhengxin Liu(刘正鑫), Jinsheng Wen(温锦生), Jinshan Zhang(张金珊), and Weiqiang Yu(于伟强). Low-energy spin dynamics in a Kitaev material Na₃Ni₂BiO₆ investigated by nuclear magnetic resonance[J]. 中国物理B, 2024, 33(6): 67601-067601.
[2]	Zhi-Quan Shi(石志全), Xu-Dan Xie(谢旭丹), and Dan-Bo Zhang(张旦波). Variational quantum simulation of the quantum critical regime[J]. 中国物理B, 2023, 32(8): 80305-080305.
[3]	Zhi-Cheng Shi(施志成), Zhen Chen(陈阵), Jian-Hui Wang(王建辉), Yan Xia(夏岩), and X X Yi(衣学喜). Effective dynamics and quantum state engineering by periodic kicks[J]. 中国物理B, 2023, 32(4): 44210-044210.
[4]	Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁). Variational quantum simulation of thermal statistical states on a superconducting quantum processer[J]. 中国物理B, 2023, 32(1): 10307-010307.
[5]	Heng-Mei Li(李恒梅), Bao-Hua Yang(杨保华), Hong-Chun Yuan(袁洪春), and Ye-Jun Xu(许业军). Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors[J]. 中国物理B, 2023, 32(1): 14202-014202.
[6]	Shou-Kuan Zhao(赵寿宽), Zi-Yong Ge(葛自勇), Zhong-Cheng Xiang(相忠诚), Guang-Ming Xue(薛光明), Hai-Sheng Yan(严海生), Zi-Ting Wang(王子婷), Zhan Wang(王战), Hui-Kai Xu(徐晖凯), Fei-Fan Su(宿非凡), Zhao-Hua Yang(杨钊华), He Zhang(张贺), Yu-Ran Zhang(张煜然), Xue-Yi Guo(郭学仪), Kai Xu(许凯), Ye Tian(田野), Hai-Feng Yu(于海峰), Dong-Ning Zheng(郑东宁), Heng Fan(范桁), and Shi-Ping Zhao(赵士平). Measuring Loschmidt echo via Floquet engineering in superconducting circuits[J]. 中国物理B, 2022, 31(3): 30307-030307.
[7]	Zi-Yong Ge(葛自勇), Rui-Zhen Huang(黄瑞珍), Zi-Yang Meng(孟子杨), and Heng Fan(范桁). Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics[J]. 中国物理B, 2022, 31(2): 20304-020304.
[8]	Kai Xu(许凯), and Heng Fan(范桁). Quantum simulation and quantum computation of noisy-intermediate scale[J]. 中国物理B, 2022, 31(10): 100304-100304.
[9]	Chao Zheng(郑超). Quantum simulation of τ-anti-pseudo-Hermitian two-level systems[J]. 中国物理B, 2022, 31(10): 100301-100301.
[10]	Chao Mu(牟超), Qiangwei Yin(殷蔷薇), Zhijun Tu(涂志俊), Chunsheng Gong(龚春生), Ping Zheng(郑萍), Hechang Lei(雷和畅), Zheng Li(李政), and Jianlin Luo(雒建林). Tri-hexagonal charge order in kagome metal CsV₃Sb₅ revealed by ¹²¹Sb nuclear quadrupole resonance[J]. 中国物理B, 2022, 31(1): 17105-017105.
[11]	Kaiyong He(何楷泳), Xiao Geng(耿霄), Rutian Huang(黄汝田), Jianshe Liu(刘建设), and Wei Chen(陈炜). Quantum computation and simulation with superconducting qubits[J]. 中国物理B, 2021, 30(8): 80304-080304.
[12]	Wentao Chen(陈文涛), Jaren Gan, Jing-Ning Zhang(张静宁), Dzmitry Matuskevich, and Kihwan Kim(金奇奂). Quantum computation and simulation with vibrational modes of trapped ions[J]. 中国物理B, 2021, 30(6): 60311-060311.
[13]	罗军, 王春光, 王志成, 郭琦, 杨杰, 周睿, K Matano, T Oguchi, 任治安, 曹光旱, 郑国庆. NMR and NQR studies on transition-metal arsenide superconductors LaRu₂As₂, KCa₂Fe₄As₄F₂, and A₂Cr₃As₃[J]. 中国物理B, 2020, 29(6): 67402-067402.
[14]	詹颙涛, 许小冶, 王琴琴, 潘维韦, Munsif Jan, 常弗鸣, 孙凯, 许金时, 韩永建, 李传锋, 郭光灿. Linear optical approach to supersymmetric dynamics[J]. 中国物理B, 2020, 29(1): 14209-014209.
[15]	郑立玄, 李建, 吴涛. High-magnetic-field induced charge order in high-T_c cuprate superconductors[J]. 中国物理B, 2019, 28(11): 117402-117402.