Experimental demonstration of quantum optimal control via the alternating control-evolution protocol

doi:10.1088/1674-1056/ae56e0

中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60302-060302.doi: 10.1088/1674-1056/ae56e0

Experimental demonstration of quantum optimal control via the alternating control-evolution protocol

Ruiqi Tang(汤睿琪)¹, Yanjun Hou(侯彦君)¹, Zhenyue Du(杜臻越)¹, Zhuoyue Xu(徐卓越)¹, Yuquan Chen(陈昱全)^1,†, Zhaokai Li(李兆凯)^1,2,3,‡, and Xinhua Peng(彭新华)^1,2,3

1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China;
2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

收稿日期:2026-01-08 修回日期:2026-03-15 接受日期:2026-03-25 发布日期:2026-06-05
通讯作者: Yuquan Chen, Zhaokai Li E-mail:yuquanchen@ustc.edu.cn;zkli@ustc.edu.cn
基金资助:
This work is supported by Quantum Science and Technology — National Science and Technology Major Project of China (Grant Nos. 2024ZD0302000 and 2021ZD0303205), the National Natural Science Foundation of China (Grant Nos. 92165108, 12261160569, 12150014, and 11927811), and the XPLORER Prize.

Experimental demonstration of quantum optimal control via the alternating control-evolution protocol

Ruiqi Tang(汤睿琪)¹, Yanjun Hou(侯彦君)¹, Zhenyue Du(杜臻越)¹, Zhuoyue Xu(徐卓越)¹, Yuquan Chen(陈昱全)^1,†, Zhaokai Li(李兆凯)^1,2,3,‡, and Xinhua Peng(彭新华)^1,2,3

1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China;
2 Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China;
3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Received:2026-01-08 Revised:2026-03-15 Accepted:2026-03-25 Published:2026-06-05
Contact: Yuquan Chen, Zhaokai Li E-mail:yuquanchen@ustc.edu.cn;zkli@ustc.edu.cn
Supported by:
This work is supported by Quantum Science and Technology — National Science and Technology Major Project of China (Grant Nos. 2024ZD0302000 and 2021ZD0303205), the National Natural Science Foundation of China (Grant Nos. 92165108, 12261160569, 12150014, and 11927811), and the XPLORER Prize.

摘要/Abstract

摘要： As a crucial component of quantum technologies, quantum optimal control enables the high-fidelity engineering of desired quantum states and operations. Conventional approaches, such as the widely used gradient ascent pulse engineering (GRAPE) algorithm, typically rely on dense pulse sequences with a large number of control parameters, leading to inefficient optimization and increased sensitivity to experimental imperfections. In this work, we propose the alternating control–evolution (ACE) protocol, a flexible framework that constructs quantum operations by interleaving elementary control operations with tunable free evolutions, thereby enabling the design of sparse pulse sequences that exploit intrinsic system dynamics. This design substantially reduces the number of control parameters while retaining high expressibility and control fidelity. Numerical simulations on nuclear magnetic resonance systems show that the ACE protocol achieves more than a 20-fold reduction in the number of control parameters compared to GRAPE, with comparable fidelity in state preparation tasks. We further experimentally validate the ACE protocol on a four-qubit NMR platform by preparing a Greenberger–Horne–Zeilinger (GHZ) state with a fidelity of 99.52%. These results demonstrate that the ACE protocol provides an efficient and experimentally robust strategy for quantum optimal control, particularly suitable for the noisy intermediate-scale quantum (NISQ) era.

关键词: quantum optimal control, nuclear magnetic resonance, quantum state preparation

Abstract: As a crucial component of quantum technologies, quantum optimal control enables the high-fidelity engineering of desired quantum states and operations. Conventional approaches, such as the widely used gradient ascent pulse engineering (GRAPE) algorithm, typically rely on dense pulse sequences with a large number of control parameters, leading to inefficient optimization and increased sensitivity to experimental imperfections. In this work, we propose the alternating control–evolution (ACE) protocol, a flexible framework that constructs quantum operations by interleaving elementary control operations with tunable free evolutions, thereby enabling the design of sparse pulse sequences that exploit intrinsic system dynamics. This design substantially reduces the number of control parameters while retaining high expressibility and control fidelity. Numerical simulations on nuclear magnetic resonance systems show that the ACE protocol achieves more than a 20-fold reduction in the number of control parameters compared to GRAPE, with comparable fidelity in state preparation tasks. We further experimentally validate the ACE protocol on a four-qubit NMR platform by preparing a Greenberger–Horne–Zeilinger (GHZ) state with a fidelity of 99.52%. These results demonstrate that the ACE protocol provides an efficient and experimentally robust strategy for quantum optimal control, particularly suitable for the noisy intermediate-scale quantum (NISQ) era.

Key words: quantum optimal control, nuclear magnetic resonance, quantum state preparation

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

76.60.-k (Nuclear magnetic resonance and relaxation)

Ruiqi Tang(汤睿琪), Yanjun Hou(侯彦君), Zhenyue Du(杜臻越), Zhuoyue Xu(徐卓越), Yuquan Chen(陈昱全), Zhaokai Li(李兆凯), and Xinhua Peng(彭新华). Experimental demonstration of quantum optimal control via the alternating control-evolution protocol[J]. 中国物理B, 2026, 35(6): 60302-060302.

参考文献

[1] Glaser S J, Boscain U, Calarco T, Koch C P, Kockenberger W, Kosloff R, Kuprov I, Luy B, Schirmer S, Schulte-Herbruggen T, Sugny D and Wilhelm F K 2015 Eur. Phys. J. D 69 279
[2] Waldherr G, Wang Y, Zaiser S, Jamali M, Schulte-Herbruggen T, Abe H, Ohshima T, Isoya J, Du J F, Neumann P and Wrachtrup J 2014 Nature 506 204
[3] Dolde F, Bergholm V, Wang Y, Jakobi I, Naydenov B, Pezzagna S, Meijer J, Jelezko F, Neumann P, Schulte-Herbruggen T, Biamonte J and Wrachtrup J 2014 Nat. Commun. 5 3371
[4] Krotov V F 1993 Advances in Nonlinear Dynamics and Control: A Report from Russia (Boston, MA: Birkhauser Boston) pp. 74–121 ¨
[5] Bryson A E 1975 Applied Optimal Control: Optimization, Estimation and Control (1st edn.) (New York: Routledge)
[6] D’Alessandro D 2021 Introduction to Quantum Control and Dynamics (2nd edn.) (New York: Chapman and Hall/CRC)
[7] Machnes S, Assemat E, Tannor D and Wilhelm F K 2018 Phys. Rev. Lett. 120 150401
[8] Liebermann P J and Wilhelm F K 2016 Phys. Rev. Appl. 6 024022
[9] Egger D J and Wilhelm F K 2014 Phys. Rev. Lett. 112 240503
[10] Khaneja N, Reiss T, Kehlet C, Schulte-Herbruggen T and Glaser S J 2005 J. Magn. Reson. 172 296
[11] August M and Hernandez-Lobato J M 2018 High Performance Computing (Cham: Springer International Publishing) pp. 591–613
[12] Ge X, Ding H, Rabitz H and Wu R B 2020 Phys. Rev. A 101 052317
[13] Ge X and Wu R B 2021 Phys. Rev. A 104 012422
[14] Turinici G 2019 Phys. Rev. A 100 053403
[15] Morzhin O V and Pechen A N 2019 Russ. Math. Surv. 74 851
[16] Fernandes M E F, Fanchini F F, de Lima E F and Castelano L K 2023 J. Phys. A: Math. Theor. 56 495303
[17] Caneva T, Calarco T and Montangero S 2011 Phys. Rev. A 84 022326
[18] Rach N, Muller M M, Calarco T and Montangero S 2015 Phys. Rev. A 92 062343
[19] Zhiyenbayev Y, Akulin V M and Mandilara A 2018 Phys. Rev. A 98 012325
[20] Kwon S, Tomonaga A, Bhai G L, Devitt S J and Tsai J S 2021 J. Appl. Phys. 129 041102
[21] Boutin S, Andersen C K, Venkatraman J, Ferris A J and Blais A 2017 Phys. Rev. A 96 042315
[22] Dalgaard M, Motzoi F, Jensen J H M and Sherson J 2020 Phys. Rev. A 102 042612
[23] Saywell J, Carey M, Belal M, Kuprov I and Freegarde T 2020 J. Phys. B: At. Mol. Opt. Phys. 53 085006
[24] Katz O, Cetina M and Monroe C 2023 PRX Quantum 4 030311
[25] Yang X D, Arenz C, Pelczer I, Chen Q M, Wu R B, Peng X H and Rabitz H 2020 Phys. Rev. A 102 062605
[26] Li S Y, Fan Y D, Li X, Ruan X H, Zhao Q C, Peng Z H, Wu R B, Zhang J and Song P T 2025 npj Quantum Inf. 11 124
[27] Kim L, Lloyd S and Marvian M 2024 Phys. Rev. Res. 6 033019
[28] Guo L L, Duan P, Zhang S, Yang X X, Zhang C, Du L, Zhang H F, Tao H R, Wang T L, Jia Z L, Chen Z Y and Guo G P 2024 Phys. Rev. Appl. 21 064060
[29] Undseth B, Pietx-Casas O, Raymenants E, Mehmandoost M, Madzik M T, Philips S G J, de Snoo S L, Michalak D J, Amitonov S V, Tryputen L, Wuetz B P, Fezzi V, Esposti D D, Sammak A, Scappucci G and Vandersypen L M K 2023 Phys. Rev. X 13 041015
[30] Liu R, Yang X, Lin Y, Lu Y, Li J 2025 Chin. Phys. Lett. 42 080601
[31] Bruzewicz C D, Chiaverini J, McConnell R and Sage J M 2019 Appl. Phys. Rev. 6 021314
[32] Levine H, Keesling A, Omran A, Bernien H, Schwartz S, Zibrov A S, Endres M, Greiner M, Vuletic V and Lukin M D 2018 Phys. Rev. Lett. 121 123603
[33] Krantz P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S and Oliver W D 2019 Appl. Phys. Rev. 6 021318
[34] Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y and Du J F 2015 Nat. Commun. 6 8748
[35] Dobrovitski V V, Fuchs G D, Falk A L, Santori C and Awschalom D D 2013 Annu. Rev. Condens. Matter Phys. 4 23
[36] Pan J, Yu Q and Peng X H 2017 Acta Phys. Sin. 66 150302 (in Chinese)
[37] Correr G I, Medina I, Azado P C, Drinko A and Soares-Pinto D O 2024 Quantum Sci. Technol. 10 015008
[38] Chen C C, Watabe M, Shiba K, Sogabe M, Sakamoto K and Sogabe T 2021 ACM Trans. Quantum Comput. 2 8
[39] Liu Y, Kaneko K, Baba K, Koyama J, Kimura K and Takeda N 2025 IEEE Trans. Quantum Eng. 6 1
[40] Nakata Y, Koashi M and Murao M 2014 New J. Phys. 16 053043
[41] Sim S, Johnson P D and Aspuru-Guzik A 2019 Adv. Quantum Technol. 2 1900070
[42] Zyczkowski K and Sommers H J · 2005 Phys. Rev. A 71 032313
[43] Møllersen K, Dhar S and Godtliebsen F 2016 Appl. Math. 7 1674
[44] Mele A A 2024 Quantum 8 1340
[45] Byrd R H, Lu P, Nocedal J and Zhu C 1995 SIAM J. Sci. Comput. 16 1190
[46] Li J, Fan R H, Wang H Y, Ye B T, Zeng B, Zhai H, Peng X H and Du J F 2017 Phys. Rev. X 7 031011
[47] Chen X, Wu Z, Jiang M, Lu X Y, Peng X H and Du J F 2021 Nat. Commun. 12 6281
[48] Peng X H, Zhu X W, Fang X M, Feng M, Gao K L, Yang X D and Liu M L 2001 Chem. Phys. Lett. 340 509
[49] Cerezo M, Sone A, Volkoff T, Cincio L and Coles P J 2021 Nat. Commun. 12 1791
[50] Arenz C and Rabitz H 2020 Phys. Rev. A 102 042207
[51] Wang X M, Yang C R and Gu M 2024 Phys. Rev. Lett. 133 130602
[52] Li W K, Lu Z D and Deng D L 2022 SciPost Phys. Lect. Notes 61
[53] Bondarenko D and Feldmann P 2020 Phys. Rev. Lett. 124 130502
[54] Shen H Z, Wang Q, Wang J and Yi X X 2020 Phys. Rev. A 101 013826
[55] Shen H Z, Shang C, Zhou Y H, and Yi X X 2018 Phys. Rev. A 98 023856
[56] Shen H Z, Yang J F and Yi X X 2024 Phys. Rev. A 109 043714
[57] Breuer H P, Laine E M and Piilo J 2009 Phys. Rev. Lett. 103 210401
[58] Vacchini B and Breuer H P 2010 Phys. Rev. A 81 042103

Experimental demonstration of quantum optimal control via the alternating control-evolution protocol

Experimental demonstration of quantum optimal control via the alternating control-evolution protocol

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 0

[1]	Shuo Wang(王硕), Zhengjie Kang(康正杰), Hao Li(李浩), Jiaojiao Li(李姣姣), Yuanjie Zhang(张元杰), and Zhihuang Luo(罗智煌). Observation of topology of non-Hermitian systems without chiral symmetry[J]. 中国物理B, 2025, 34(11): 110304-110304.
[2]	Yi Zhang(张燚), Qiyuan Jiang(江奇渊), Bingfeng Sun(孙兵锋), Jiahu Wei(魏加湖), Lin Yang(杨麟), Yongyuan Li(李永远), Zhiguo Wang(汪之国), Kaiyong Yang(杨开勇), and Hui Luo(罗晖). Response analysis of NMRG system considering Rb-Xe coupling[J]. 中国物理B, 2024, 33(9): 94203-094203.
[3]	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.
[4]	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.
[5]	Yu Guo(郭裕), Songshan Ma(马松山), and Chuan-Cun Shu(束传存). Optimal and robust control of population transfer in asymmetric quantum-dot molecules[J]. 中国物理B, 2024, 33(2): 24203-024203.
[6]	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.
[7]	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.
[8]	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.
[9]	郭胜利, 宁凡龙. Progress of novel diluted ferromagnetic semiconductors with decoupled spin and charge doping: Counterparts of Fe-based superconductors[J]. 中国物理B, 2018, 27(9): 97502-097502.
[10]	李政, 郑国庆. Nuclear magnetic resonance measurement station in SECUF using hybrid superconducting magnets[J]. 中国物理B, 2018, 27(7): 77404-077404.
[11]	罗军, 杨杰, S Maeda, 李政, 郑国庆. Structural phase transition, precursory electronic anomaly, and strong-coupling superconductivity in quasi-skutterudite (Sr_1-xCa_x)₃Ir₄Sn₁₃ and Ca₃Rh₄Sn₁₃[J]. 中国物理B, 2018, 27(7): 77401-077401.
[12]	王瑞琦, 郑家成, 陈涛, 王朋帅, 张金珊, 崔祎, 王冲, 李源, 徐胜, 袁峰, 于伟强. NMR evidence of charge fluctuations in multiferroic CuBr₂[J]. 中国物理B, 2018, 27(3): 37502-037502.
[13]	辛涛, 王碧雪, 李可仁, 孔祥宇, 魏世杰, 王涛, 阮东, 龙桂鲁. Nuclear magnetic resonance for quantum computing: Techniques and recent achievements[J]. 中国物理B, 2018, 27(2): 20308-020308.
[14]	丁志超, 袁杰, 罗晖, 龙兴武. Optical pumping nuclear magnetic resonance system rotating in a plane parallel to the quantization axis[J]. 中国物理B, 2017, 26(9): 93301-093301.
[15]	张大伟, 徐正一, 周敏, 徐信业. Parameter analysis for a nuclear magnetic resonance gyroscope based on ^bf133Cs-¹²⁹Xe/¹³¹Xe[J]. 中国物理B, 2017, 26(2): 23201-023201.