Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

doi:10.1088/1674-1056/ac65ee

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 20202-020202.doi: 10.1088/1674-1056/ac65ee

Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Xin Cheng(程鑫)^1,†, Xiu-Juan Lu(鲁秀娟)^2,†, Ya-Nan Liu(刘亚楠)³, and Sen Kuang(匡森)^1,‡

1 Department of Automation, University of Science and Technology of China, Hefei 230027, China;
2 Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China;
3 Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan

收稿日期:2022-02-07 修回日期:2022-04-08 接受日期:2022-04-11 出版日期:2023-01-10 发布日期:2023-01-18
通讯作者: Sen Kuang E-mail:skuang@ustc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61873251).

Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Xin Cheng(程鑫)^1,†, Xiu-Juan Lu(鲁秀娟)^2,†, Ya-Nan Liu(刘亚楠)³, and Sen Kuang(匡森)^1,‡

1 Department of Automation, University of Science and Technology of China, Hefei 230027, China;
2 Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China;
3 Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan

Received:2022-02-07 Revised:2022-04-08 Accepted:2022-04-11 Online:2023-01-10 Published:2023-01-18
Contact: Sen Kuang E-mail:skuang@ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61873251).

摘要/Abstract

摘要： Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution (DE), particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), and quantum evolutionary algorithm (QEA). We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered. This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.

关键词: quantum control, state preparation, intelligent optimization algorithm

Abstract: Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution (DE), particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), and quantum evolutionary algorithm (QEA). We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered. This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.

Key words: quantum control, state preparation, intelligent optimization algorithm

中图分类号: (Numerical optimization)

02.60.Pn

03.65.Aa (Quantum systems with finite Hilbert space) 02.30.Yy (Control theory) 02.60.Cb (Numerical simulation; solution of equations)

Xin Cheng(程鑫), Xiu-Juan Lu(鲁秀娟), Ya-Nan Liu(刘亚楠), and Sen Kuang(匡森). Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states[J]. 中国物理B, 2023, 32(2): 20202-020202.

参考文献

[1] Dong D and Petersen I R 2010 IET Control Theory & Applications 4 2651
[2] Brif C, Chakrabarti R and Rabitz H 2010 New J. Phys. 12 075008
[3] Khaneja N, Reiss T, Kehlet C, Schulte-Herbrüggen T and Glaser S J 2005 Journal of Magnetic Resonance 172 296
[4] Lu D, Li K, Li J, Katiyar H, Park A J, Feng G, Xin T, Li H, Long G, Brodutch A, Baugh J, Zeng B and Laflamme R 2017 npj Quantum Information 3 1
[5] Assion A, Baumert T, Bergt M, Brixner T, Kiefer B, Seyfried V, Strehle M and Gerber G 1998 Science 282 919
[6] Zahedinejad E, Ghosh J and Sanders B C 2015 Phys. Rev. Lett. 114 200502
[7] Schulte-Herbrüggen T, Spörl A, Khaneja N and Glaser S 2005 Phys. Rev. A 72 042331
[8] Shapiro E, Milner V, Menzel-Jones C and Shapiro M 2007 Phys. Rev. Lett. 99 033002
[9] Yamamoto N, Tsumura K and Hara S 2007 Automatica 43 981
[10] Lu X J and Kuang S 2019 IET Control Theory & Applications 13 711
[11] Rabitz H, de Vivie-Riedle R, Motzkus M and Kompa K H 2000 Science 288 824
[12] Kuang S and Cong S 2008 Automatica 44 98
[13] Dong D, Xing X, Ma H, Chen C, Liu Z and Rabitz H 2019 IEEE Transactions on Cybernetics 50 3581
[14] Ma H, Dong D, Shu C C, Zhu Z and Chen C 2017 Control Theory and Technology 15 226
[15] Yang X, Li J and Peng X 2019 Science Bulletin 64 1402
[16] Eitan R, Mundt M and Tannor D J 2011 Phys. Rev. A 83 053426
[17] Kuang S, Qi P and Cong S 2018 Phys. Lett. A 382 1858-1863
[18] Rabitz H A, Hsieh M M and Rosenthal C M 2004 Science 303 1998
[19] Holland J H 1992 Scientific American 276 66
[20] Venter G and Sobieszczanski-Sobieski J 2003 AIAA Journal 41 1583
[21] Storn R and Price K 1997 Journal of Global Optimization 11 341
[22] Li N Q, Pan W, Yan L S, Luo B, Xu M F and Jiang N 2011 Chin. Phys. B 20 060502
[23] Guan X, Kuang S, Lu X and Yan J 2020 IEEE Access 8 49765
[24] Vesterstrom J and Thomsen R 2004 Proceedings of the 2004 Congress on Evolutionary Computation, June 19-23, 2004, Portland, USA 2 1980-1987
[25] Han K H and Kim J H 2002 IEEE Transactions on Evolutionary Computation 6 580
[26] Sun J, Fang W, Wu X, Palade V and Xu W 2012 Evolutionary Computation 20 349
[27] Meng K, Wang H G, Dong Z and Wong K P 2009 IEEE Transactions on Power Systems 25 215
[28] Zhang G 2011 Journal of Heuristics 17 303
[29] Zahedinejad E, Schirmer S and Sanders B C 2014 Phys. Rev. A 90 032310
[30] Breuer H P and Petruccione F 2022 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
[31] Kimura G 2003 Phys. Lett. A 314 339
[32] Yang F, Cong S, Long R, Ho T S, Wu R and Rabitz H 2013 Phys. Rev. A 88 033420
[33] Lindblad G 1976 Communications in Mathematical Physics 48 119

Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Comparison of differential evolution, particle swarm optimization, quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

RichHTML

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]	Wenjing Cheng(程文静), Yuan Li(李媛), Hongzhen Qiao(乔红贞), Meng Wang(王蒙), Shaoshuo Ma(马绍朔), Fangjie Shu(舒方杰), Chuanqi Xie(解传奇), and Guo Liang(梁果). Simulating the resonance-mediated (1+2)-three-photon absorption enhancement in Pr³⁺ ions by a rectangle phase modulation[J]. 中国物理B, 2022, 31(6): 63201-063201.
[2]	Zhihang Xu(许智航), Yuzhen Wei(魏玉震), Cong Jiang(江聪), and Min Jiang(姜敏). Deterministic remote state preparation of arbitrary three-qubit state through noisy cluster-GHZ channel[J]. 中国物理B, 2022, 31(4): 40304-040304.
[3]	Yan Yu(于妍), Nan Zhao(赵楠), Chang-Xing Pei(裴昌幸), and Wei Li(李玮). Quantum multicast schemes of different quantum states via non-maximally entangled channels with multiparty involvement[J]. 中国物理B, 2021, 30(9): 90302-090302.
[4]	查新未, 王敏锐, 姜若虚. Efficient scheme for remote preparation of arbitrary n-qubit equatorial states[J]. 中国物理B, 2020, 29(4): 40304-040304.
[5]	陈娜, 颜斌, 陈赓, 张曼君, 裴昌幸. Deterministic hierarchical joint remote state preparation with six-particle partially entangled state[J]. 中国物理B, 2018, 27(9): 90304-090304.
[6]	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.
[7]	齐大龙, 郑烨, 程文静, 姚云华, 邓联忠, 冯东海, 贾天卿, 孙真荣, 张诗按. Simulating resonance-mediated two-photon absorption enhancement in rare-earth ions by a rectangle phase modulation[J]. 中国物理B, 2018, 27(1): 13202-013202.
[8]	陈维林, 马松雅, 瞿治国. Controlled remote preparation of an arbitrary four-qubit cluster-type state[J]. 中国物理B, 2016, 25(10): 100304-100304.
[9]	陈娜, 权东晓, 徐馥芳, 杨宏, 裴昌幸. Deterministic joint remote state preparation of arbitrary single- and two-qubit states[J]. 中国物理B, 2015, 24(10): 100307-100307.
[10]	常利伟, 郑世慧, 谷利泽, 肖达, 杨义先. Joint remote preparation of an arbitrary five-qubit Brown state via non-maximally entangled channels[J]. , 2014, 23(9): 90307-090307.
[11]	马松雅, 罗明星. Efficient remote preparation of arbitrary two-and three-qubit states via the χ state[J]. , 2014, 23(9): 90308-090308.
[12]	陈忠芳, 刘金明, 马雷. Deterministic joint remote preparation of an arbitrary two-qubit state in the presence of noise[J]. 中国物理B, 2014, 23(2): 20312-020312.
[13]	赵瑞通, 郭奇, 程留永, 孙立莉, 王洪福, 张寿. Two-qubit and three-qubit controlled gates with cross-Kerr nonlinearity[J]. 中国物理B, 2013, 22(3): 30313-030313.
[14]	王媛, 计新. Deterministic joint remote state preparation of arbitrary two- and three-qubit states[J]. 中国物理B, 2013, 22(2): 20306-020306.
[15]	戴宏毅, 张明, 陈菊梅, 李承祖. Probabilistic remote preparation of a high-dimensional equatorial multiqubit with four-party and classical communication cost[J]. 中国物理B, 2011, 20(5): 50310-050310.