量子人工智能中的对抗学习

沈培鑫; 蒋文杰; 李炜康; 鲁智德; 邓东灵

doi:10.7498/aps.70.20210789

摘要

量子人工智能是一个探究人工智能与量子物理交叉的领域: 一方面人工智能的方法和技术可以用来解决量子科学中的问题; 另一方面, 量子计算的发展也可能为人工智能, 尤其是机器学习, 提供新的范式, 极大促进人工智能的发展. 然而, 量子机器学习和经典学习系统对于对抗样本同样具有脆弱性: 在原始数据样本上添加精心制作的微小扰动将很可能导致系统做出错误的预测. 本文介绍经典与量子对抗机器学习的基本概念、原理、以及最新进展. 首先从经典和量子两个方面介绍对抗学习, 通过二维经典伊辛模型和三维手征拓扑绝缘体的对抗样本揭示出经典机器学习在识别物质相时的脆弱性, 同时利用手写字体的对抗样本直观展示出量子分类器的脆弱性. 随后从理论层面上分别阐述经典与量子的“没有免费午餐”定理, 并探讨了量子分类器的普适对抗样本. 最后, 分析并讨论了相应的防御策略. 量子人工智能中对抗学习的研究揭示了量子智能系统潜在的风险以及可能的防御策略, 将对未来量子技术与人工智能的交叉产生深刻影响.

关键词:

Abstract

Quantum artificial intelligence exploits the interplay between artificial intelligence and quantum physics: on the one hand, a plethora of tools and ideas from artificial intelligence can be adopted to tackle intricate quantum problems; on the other hand, quantum computing could also bring unprecedented opportunities to enhance, speed up, or innovate artificial intelligence. Yet, quantum learning systems, similar to classical ones, may also suffer adversarial attacks: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we introduce the basic concepts and ideas of classical and quantum adversarial learning, as well as some recent advances along this line. First, we introduce the basics of both classical and quantum adversarial learning. Through concrete examples, involving classifications of phases of two-dimensional Ising model and three-dimensional chiral topological insulators, we reveal the vulnerability of classical machine learning phases of matter. In addition, we demonstrate the vulnerability of quantum classifiers with the example of classifying hand-written digit images. We theoretically elucidate the celebrated no free lunch theorem from the classical and quantum perspectives, and discuss the universality properties of adversarial attacks in quantum classifiers. Finally, we discuss the possible defense strategies. The study of adversarial learning in quantum artificial intelligence uncovers notable potential risks for quantum intelligence systems, which would have far-reaching consequences for the future interactions between the two areas.

Keywords:

作者及机构信息

1.
清华大学交叉信息研究院, 北京　100084

2.
上海期智研究院, 上海　200232

通信作者: 邓东灵, dldeng@mail.tsinghua.edu.cn

基金项目: 国家自然科学基金(批准号: 12075128)、清华大学启动经费(批准号: 53330300320) 和上海期智研究院资助的课题

Authors and contacts

1.
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China

2.
Shanghai Qi Zhi Institute, Shanghai 200232, China

Corresponding author: Deng Dong-Ling, dldeng@mail.tsinghua.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12075128), the Start-up Fund from Tsinghua University, China (Grant No. 53330300320), and the Shanghai Qi Zhi Institute, China

文章全文 : translate this paragraph

参考文献

[1]	Krizhevsky A, Sutskever I, Hinton G E 2012 Proceedings of the 25th International Conference on Neural Information Processing Systems (Volume 1) New York, USA, December 3−8, 2012 p1097
[2]	Hinton G, Deng L, Yu D, Dahl G E, Mohamed A, Jaitly N, Senior A, Vanhoucke V, Nguyen P, Sainath T N, Kingsbury B 2012 IEEE Signal Process. Mag. 29 82 Google Scholar
[3]	Kononenko I 2001 Artif. Intell. Med. 23 89 Google Scholar
[4]	Grigorescu S, Trasnea B, Cocias T, Macesanu G 2020 J. Field Robot 37 362 Google Scholar
[5]	LeCun Y, Bengio Y, Hinton G 2015 Nature 521 436 Google Scholar
[6]	Jordan M, Mitchell T 2015 Science 349 255 Google Scholar
[7]	Silver D, Huang A, Maddison C J, et al. 2016 Nature 529 484 Google Scholar
[8]	Silver D, Schrittwieser J, Simonyan K, et al. 2017 Nature 550 354 Google Scholar
[9]	Senior A W, Evans R, Jumper J, et al. 2020 Nature 577 706 Google Scholar
[10]	Russell S, Norvig P 2020 Artificial Intelligence: A Modern Approach (Hoboken: Pearson) pp1−61
[11]	Bishop C 2006 Pattern Recognition and Machine Learning (New York: Springer-Verlag) pp225−284
[12]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp171−352
[13]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[14]	Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460
[15]	Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S 2017 Nature 549 195 Google Scholar
[16]	Dunjko V, Briegel H J 2018 Rep. Prog. Phys. 81 074001 Google Scholar
[17]	Das Sarma S, Deng D L, Duan L M 2019 Phys. Today 72 48 Google Scholar
[18]	Carleo G, Troyer M 2017 Science 355 602 Google Scholar
[19]	Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melko R, Carleo G 2018 Nat. Phys. 14 447 Google Scholar
[20]	Zhang Y H, Zheng P L, Zhang Y, Deng D L 2020 Phys. Rev. Lett. 125 170501 Google Scholar
[21]	Deringer V L, Bernstein N, Csányi G, Ben Mahmoud C, Ceriotti M, Wilson M, Drabold D A, Elliott S R 2021 Nature 589 59 Google Scholar
[22]	Deng D L 2018 Phys. Rev. Lett. 120 240402 Google Scholar
[23]	Deng D L, Li X, Das Sarma S 2017 Phys. Rev. B 96 195145 Google Scholar
[24]	Zhang Y, Kim E A 2017 Phys. Rev. Lett. 118 216401 Google Scholar
[25]	Carrasquilla J, Melko R G 2017 Nat. Phys. 13 431 Google Scholar
[26]	van Nieuwenburg E P L, Liu Y H, Huber S D 2017 Nat. Phys. 13 435 Google Scholar
[27]	Wang L 2016 Phys. Rev. B 94 195105 Google Scholar
[28]	Broecker P, Carrasquilla J, Melko R G, Trebst S 2017 Sci. Rep. 7 8823 Google Scholar
[29]	Ch’ng K, Carrasquilla J, Melko R G, Khatami E 2017 Phys. Rev. X 7 031038 Google Scholar
[30]	Wetzel S J 2017 Phys. Rev. E 96 022140 Google Scholar
[31]	Hu W, Singh R R P, Scalettar R T 2017 Phys. Rev. E 95 062122 Google Scholar
[32]	Zhang Y, Mesaros A, Fujita K, Edkins S D, Hamidian M H, Ch’ng K, Eisaki H, Uchida S, Davis J C S, Khatami E, Kim E-A 2019 Nature 570 484 Google Scholar
[33]	Lian W, Wang S T, Lu S, Huang Y, Wang F, Yuan X, Zhang W, Ouyang X, Wang X, Huang X, He L, Chang X, Deng D L, Duan L 2019 Phys. Rev. Lett. 122 210503 Google Scholar
[34]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[35]	Lloyd S, Mohseni M, Rebentrost P 2014 Nat. Phys. 10 631 Google Scholar
[36]	Dunjko V, Taylor J M, Briegel H J 2016 Phys. Rev. Lett. 117 130501 Google Scholar
[37]	Amin M H, Andriyash E, Rolfe J, Kulchytskyy B, Melko R 2018 Phys. Rev. X 8 021050 Google Scholar
[38]	Gao X, Zhang Z Y, Duan L M 2018 Sci. Adv. 4 eaat9004 Google Scholar
[39]	Lloyd S, Weedbrook C 2018 Phys. Rev. Lett. 121 040502 Google Scholar
[40]	Hu L, Wu S H, Cai W, Ma Y, Mu X, Xu Y, Wang H, Song Y, Deng D L, Zou C L, Sun L 2019 Sci. Adv. 5 eaav2761 Google Scholar
[41]	Schuld M, Killoran N 2019 Phys. Rev. Lett. 122 040504 Google Scholar
[42]	Rebentrost P, Mohseni M, Lloyd S 2014 Phys. Rev. Lett. 113 130503 Google Scholar
[43]	Chakraborty A, Alam M, Dey V, Chattopadhyay A, Mukhopadhyay D 2018 arXiv: 1810.00069 [cs, stat]
[44]	Biggio B, Roli F 2018 Pattern Recognit. 84 317 Google Scholar
[45]	Miller D J, Xiang Z, Kesidis G 2019 arXiv: 1904.06292 [cs, stat]
[46]	Szegedy C, Zaremba W, Sutskever I, Bruna J, Erhan D, Goodfellow I, Fergus R 2014 arXiv: 1312.6199 [cs]
[47]	Goodfellow I J, Shlens J, Szegedy C 2015 arXiv: 1412.6572 [cs, stat]
[48]	Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y 2014 Adv. Neural Inf. Process. Syst. 27 2672
[49]	Preskill J 2018 Quantum 2 79 Google Scholar
[50]	Lu S, Duan L M, Deng D L 2020 Phys. Rev. Res. 2 033212 Google Scholar
[51]	Guan J, Fang W, Ying M 2020 arXiv: 2008.07230 [quant-ph]
[52]	Wiebe N, Kumar R S S 2018 New J. Phys. 20 123019 Google Scholar
[53]	Liu N, Wittek P 2020 Phys. Rev. A 101 062331 Google Scholar
[54]	Gong W, Deng D L 2021 arXiv: 2102.07788 [cond-mat, physics: quant-ph]
[55]	Dalvi N, Domingos P, Mausam, Sanghai S, Verma D 2004 Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining Seattle, USA, August 22−25, 2004 p99
[56]	Lowd D, Meek C 2005 Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining Chicago, USA, August 21−24, 2005 p641
[57]	Barreno M, Nelson B, Sears R, Joseph A D, Tygar J D 2006 Proceedings of the 2006 ACM Symposium on Information, Computer and Communications Security Taipei, China, March 21−24, 2006 p16
[58]	Huang L, Joseph A D, Nelson B, Rubinstein B I P, Tygar J D 2011 Proceedings of the 4th ACM Workshop on Security and Artificial Intelligence Chicago, USA, October 21, 2011 p43
[59]	Vorobeychik Y, Kantarcioglu M 2018 Synth. Lect. Artif. Intell. Mach. Learn. 12 1 Google Scholar
[60]	Kurakin A, Goodfellow I, Bengio S 2017 arXiv: 1611.01236 [cs, stat]
[61]	Ben-Tal A, Ghaoui L E, Nemirovski A 2009 Robust Optimization (Princeton: Princeton University Press) pp1−146
[62]	Madry A, Makelov A, Schmidt L, Tsipras D, Vladu A 2018 International Conference on Learning Representations Vancouver, Canada, April 30−May 3, 2018 p1
[63]	Kurakin A, Goodfellow I, Bengio S 2017 arXiv: 1607.02533 [cs, stat]
[64]	Dong Y, Liao F, Pang T, Su H, Zhu J, Hu X, Li J 2018 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Salt Lake City, USA, June 18−23, 2018 p9185
[65]	Hsu Y T, Li X, Deng D L, Das Sarma S 2018 Phys. Rev. Lett. 121 245701 Google Scholar
[66]	Rodriguez-Nieva J F, Scheurer M S 2019 Nat. Phys. 15 790 Google Scholar
[67]	Zhang P, Shen H, Zhai H 2018 Phys. Rev. Lett. 120 066401 Google Scholar
[68]	Huembeli P, Dauphin A, Wittek P 2018 Phys. Rev. B 97 134109 Google Scholar
[69]	Rem B S, Käming N, Tarnowski M, Asteria L, Fläschner N, Becker C, Sengstock K, Weitenberg C 2019 Nat. Phys. 15 917 Google Scholar
[70]	Bohrdt A, Chiu C S, Ji G, Xu M, Greif D, Greiner M, Demler E, Grusdt F, Knap M 2019 Nat. Phys. 15 921 Google Scholar
[71]	Jiang S, Lu S, Deng D L 2019 arXiv: 1910.13453 [cond-mat, physics: quant-ph]
[72]	Neupert T, Santos L, Ryu S, Chamon C, Mudry C 2012 Phys. Rev. B 86 035125 Google Scholar
[73]	Deng D L, Wang S T, Duan L M 2014 Phys. Rev. A 90 041601 Google Scholar
[74]	Finlayson S G, Bowers J D, Ito J, Zittrain J L, Beam A L, Kohane I S 2019 Science 363 1287 Google Scholar
[75]	Ren K, Zheng T, Qin Z, Liu X 2020 Engineering 6 346 Google Scholar
[76]	Goodfellow I, Bengio Y, Courville A 2016 Deep Learning (Cambridge: The MIT Press) pp98−165
[77]	Sutskever I, Vinyals O, Le Q V 2014 Proceedings of the 27th International Conference on Neural Information Processing Systems (Volume 2) Montréal, Canada, December 8−13, 2014 p3104
[78]	Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I 2017 arXiv: 1706.03762 [cs]
[79]	Wolpert D H, Macready W G 1997 IEEE Trans. Evol. Comput. 1 67 Google Scholar
[80]	Shalev-Shwartz S, Ben-David S 2014 Understanding Machine Learning: From Theory to Algorithms (New York: Cambridge University Press) pp36−41
[81]	Poland K, Beer K, Osborne T J 2020 arXiv: 2003.14103 [quant-ph]
[82]	Schroff F, Kalenichenko D, Philbin J 2015 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Boston, USA, June 7−12, 2015 p815
[83]	Walters M 2015 arXiv: 1508.05448 [math-ph]
[84]	Schwabl F 2006 Statistical Mechanics (Berlin Heidelberg: Springer-Verlag) pp1−20
[85]	Dohmatob E 2019 arXiv: 1810.04065 [cs, stat]
[86]	Sharif M, Bhagavatula S, Bauer L, Reiter M K 2016 Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security Vienna, Austria, October 24−28, 2016 p1528
[87]	Papernot N, McDaniel P, Goodfellow I, Jha S, Celik Z B, Swami A 2017 Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security Abu Dhabi, UAE, April 2−6 2017 p506
[88]	Ledoux M 2001 The Concentration of Measure Phenomenon (Providence: American Mathematical Society) pp1–21
[89]	Hoeffding W 1963 J. Am. Stat. Assoc. 58 13 Google Scholar
[90]	Sharma K, Cerezo M, Holmes Z, Cincio L, Sornborger A, Coles P J 2020 arXiv: 2007.04900 [quant-ph]
[91]	Du Y, Hsieh M H, Liu T, Tao D, Liu N 2020 arXiv: 2003.09416 [quant-ph]
[92]	Tramèr F, Kurakin A, Papernot N, Goodfellow I, Boneh D, McDaniel P 2017 arXiv: 1705.07204 [cs, stat]
[93]	Papernot N, McDaniel P, Wu X, Jha S, Swami A 2016 37th IEEE Symposium on Security and Privacy San Jose, USA, May 23−25, 2016 p582
[94]	Samangouei P, Kabkab M, Chellappa R 2018 arXiv: 1805.06605 [cs, stat]
[95]	Dallaire-Demers P L, Killoran N 2018 Phys. Rev. A 98 012324 Google Scholar
[96]	Huang K, Wang Z A, Song C, Xu K, Li H, Wang Z, Guo Q, Song Z, Liu Z-B, Zheng D, Deng D L, Wang H, Tian J G, Fan H 2020 arXiv: 2009.12827 [quant-ph]
[97]	Zeng J, Wu Y, Liu J G, Wang L, Hu J 2019 Phys. Rev. A 99 052306 Google Scholar
[98]	Anderson P W 1967 Phys. Rev. Lett. 18 1049 Google Scholar
[99]	Deng D L, Pixley J H, Li X, Das Sarma S 2015 Phys. Rev. B 92 220201 Google Scholar

施引文献

图 1 量子与经典对抗学习示意图　输入的原始熊猫图像样本可以编码为经典或量子数据, 分类器(包含变分量子线路或人工神经网络)能够以非常高的准确率识别出熊猫; 但添加少量精心制作的噪声后, 同一分类器将以非常高的置信度把轻微修改过的熊猫图像错误分类为长臂猿

Fig. 1. A schematic illustration of quantum and classical adversarial learning. The image of a panda can be encoded as classical or quantum data. A classifier, which uses either variational quantum circuits or classical artificial neural networks, can successfully identify the image as a panda with the state-of-the-art accuracy. However, adding a small amount of carefully crafted noise will cause the same classifier to misclassify the slightly modified image into a gibbon with a notably high confidence.

下载: 全尺寸图片幻灯片

图 2 机器学习物质相中的对抗样本　(a)一个原始的经典二维伊辛模型铁磁相的自旋构型; (b)被分类器错误识别成顺磁相的对抗样本, 其相对于(a)只改变了一个自旋; (c)一个原始的三维手征拓扑绝缘体的拓扑相样本; (d)被分类器错误识别成其他相的对抗样本, 其相对于(c)只有肉眼难以识别的细微差别

Fig. 2. Adversarial examples in machine learning phases of matter: (a) A legitimate sample of the spin configuration in the ferromagnetic phase of the two-dimensional (2D) classical Ising model; (b) an adversarial example misclassified as the paramagnetic phase, which only differs from the original legitimate one shown in (a) by a single pixel; (c) a legitimate sample of the topological phase of three-dimensional (3D) chiral topological insulators; (d) an adversarial example misclassified as the other phase, which only differs from the original legitimate one shown in (c) by a tiny amount of noises that are imperceptible to human eyes.

下载: 全尺寸图片幻灯片

图 3 量子分类器在识别MNIST中手写字体图片时的对抗样本　(a)经过无差别攻击, 量子分类器以极高置信度将数字7, 9分别识别成9, 7, 即使对抗样本和初始样本的差别非常微小; (b)通过针对性攻击, 量子分类器将把对抗样本预测为给定错误标签, 尽管对抗样本和初始样本相差无几

Fig. 3. Adversarial examples in quantum learning of MNIST hand-written images: (a) After untargeted attacks, the quantum classifier will misclassify the images of digit 7 (9) as digit 9 (7) with notably high confidence, although the differences between the adversarial and legitimate images are tiny; (b) after targeted attack, the quantum classifier will misclassify the adversarial examples into the category with the targeted label, even though the adversarial and legitimate images only differ slightly from each other.

下载: 全尺寸图片幻灯片

[1]	Krizhevsky A, Sutskever I, Hinton G E 2012 Proceedings of the 25th International Conference on Neural Information Processing Systems (Volume 1) New York, USA, December 3−8, 2012 p1097
[2]	Hinton G, Deng L, Yu D, Dahl G E, Mohamed A, Jaitly N, Senior A, Vanhoucke V, Nguyen P, Sainath T N, Kingsbury B 2012 IEEE Signal Process. Mag. 29 82 Google Scholar
[3]	Kononenko I 2001 Artif. Intell. Med. 23 89 Google Scholar
[4]	Grigorescu S, Trasnea B, Cocias T, Macesanu G 2020 J. Field Robot 37 362 Google Scholar
[5]	LeCun Y, Bengio Y, Hinton G 2015 Nature 521 436 Google Scholar
[6]	Jordan M, Mitchell T 2015 Science 349 255 Google Scholar
[7]	Silver D, Huang A, Maddison C J, et al. 2016 Nature 529 484 Google Scholar
[8]	Silver D, Schrittwieser J, Simonyan K, et al. 2017 Nature 550 354 Google Scholar
[9]	Senior A W, Evans R, Jumper J, et al. 2020 Nature 577 706 Google Scholar
[10]	Russell S, Norvig P 2020 Artificial Intelligence: A Modern Approach (Hoboken: Pearson) pp1−61
[11]	Bishop C 2006 Pattern Recognition and Machine Learning (New York: Springer-Verlag) pp225−284
[12]	Nielsen M A, Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp171−352
[13]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[14]	Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460
[15]	Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S 2017 Nature 549 195 Google Scholar
[16]	Dunjko V, Briegel H J 2018 Rep. Prog. Phys. 81 074001 Google Scholar
[17]	Das Sarma S, Deng D L, Duan L M 2019 Phys. Today 72 48 Google Scholar
[18]	Carleo G, Troyer M 2017 Science 355 602 Google Scholar
[19]	Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melko R, Carleo G 2018 Nat. Phys. 14 447 Google Scholar
[20]	Zhang Y H, Zheng P L, Zhang Y, Deng D L 2020 Phys. Rev. Lett. 125 170501 Google Scholar
[21]	Deringer V L, Bernstein N, Csányi G, Ben Mahmoud C, Ceriotti M, Wilson M, Drabold D A, Elliott S R 2021 Nature 589 59 Google Scholar
[22]	Deng D L 2018 Phys. Rev. Lett. 120 240402 Google Scholar
[23]	Deng D L, Li X, Das Sarma S 2017 Phys. Rev. B 96 195145 Google Scholar
[24]	Zhang Y, Kim E A 2017 Phys. Rev. Lett. 118 216401 Google Scholar
[25]	Carrasquilla J, Melko R G 2017 Nat. Phys. 13 431 Google Scholar
[26]	van Nieuwenburg E P L, Liu Y H, Huber S D 2017 Nat. Phys. 13 435 Google Scholar
[27]	Wang L 2016 Phys. Rev. B 94 195105 Google Scholar
[28]	Broecker P, Carrasquilla J, Melko R G, Trebst S 2017 Sci. Rep. 7 8823 Google Scholar
[29]	Ch’ng K, Carrasquilla J, Melko R G, Khatami E 2017 Phys. Rev. X 7 031038 Google Scholar
[30]	Wetzel S J 2017 Phys. Rev. E 96 022140 Google Scholar
[31]	Hu W, Singh R R P, Scalettar R T 2017 Phys. Rev. E 95 062122 Google Scholar
[32]	Zhang Y, Mesaros A, Fujita K, Edkins S D, Hamidian M H, Ch’ng K, Eisaki H, Uchida S, Davis J C S, Khatami E, Kim E-A 2019 Nature 570 484 Google Scholar
[33]	Lian W, Wang S T, Lu S, Huang Y, Wang F, Yuan X, Zhang W, Ouyang X, Wang X, Huang X, He L, Chang X, Deng D L, Duan L 2019 Phys. Rev. Lett. 122 210503 Google Scholar
[34]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[35]	Lloyd S, Mohseni M, Rebentrost P 2014 Nat. Phys. 10 631 Google Scholar
[36]	Dunjko V, Taylor J M, Briegel H J 2016 Phys. Rev. Lett. 117 130501 Google Scholar
[37]	Amin M H, Andriyash E, Rolfe J, Kulchytskyy B, Melko R 2018 Phys. Rev. X 8 021050 Google Scholar
[38]	Gao X, Zhang Z Y, Duan L M 2018 Sci. Adv. 4 eaat9004 Google Scholar
[39]	Lloyd S, Weedbrook C 2018 Phys. Rev. Lett. 121 040502 Google Scholar
[40]	Hu L, Wu S H, Cai W, Ma Y, Mu X, Xu Y, Wang H, Song Y, Deng D L, Zou C L, Sun L 2019 Sci. Adv. 5 eaav2761 Google Scholar
[41]	Schuld M, Killoran N 2019 Phys. Rev. Lett. 122 040504 Google Scholar
[42]	Rebentrost P, Mohseni M, Lloyd S 2014 Phys. Rev. Lett. 113 130503 Google Scholar
[43]	Chakraborty A, Alam M, Dey V, Chattopadhyay A, Mukhopadhyay D 2018 arXiv: 1810.00069 [cs, stat]
[44]	Biggio B, Roli F 2018 Pattern Recognit. 84 317 Google Scholar
[45]	Miller D J, Xiang Z, Kesidis G 2019 arXiv: 1904.06292 [cs, stat]
[46]	Szegedy C, Zaremba W, Sutskever I, Bruna J, Erhan D, Goodfellow I, Fergus R 2014 arXiv: 1312.6199 [cs]
[47]	Goodfellow I J, Shlens J, Szegedy C 2015 arXiv: 1412.6572 [cs, stat]
[48]	Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y 2014 Adv. Neural Inf. Process. Syst. 27 2672
[49]	Preskill J 2018 Quantum 2 79 Google Scholar
[50]	Lu S, Duan L M, Deng D L 2020 Phys. Rev. Res. 2 033212 Google Scholar
[51]	Guan J, Fang W, Ying M 2020 arXiv: 2008.07230 [quant-ph]
[52]	Wiebe N, Kumar R S S 2018 New J. Phys. 20 123019 Google Scholar
[53]	Liu N, Wittek P 2020 Phys. Rev. A 101 062331 Google Scholar
[54]	Gong W, Deng D L 2021 arXiv: 2102.07788 [cond-mat, physics: quant-ph]
[55]	Dalvi N, Domingos P, Mausam, Sanghai S, Verma D 2004 Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining Seattle, USA, August 22−25, 2004 p99
[56]	Lowd D, Meek C 2005 Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining Chicago, USA, August 21−24, 2005 p641
[57]	Barreno M, Nelson B, Sears R, Joseph A D, Tygar J D 2006 Proceedings of the 2006 ACM Symposium on Information, Computer and Communications Security Taipei, China, March 21−24, 2006 p16
[58]	Huang L, Joseph A D, Nelson B, Rubinstein B I P, Tygar J D 2011 Proceedings of the 4th ACM Workshop on Security and Artificial Intelligence Chicago, USA, October 21, 2011 p43
[59]	Vorobeychik Y, Kantarcioglu M 2018 Synth. Lect. Artif. Intell. Mach. Learn. 12 1 Google Scholar
[60]	Kurakin A, Goodfellow I, Bengio S 2017 arXiv: 1611.01236 [cs, stat]
[61]	Ben-Tal A, Ghaoui L E, Nemirovski A 2009 Robust Optimization (Princeton: Princeton University Press) pp1−146
[62]	Madry A, Makelov A, Schmidt L, Tsipras D, Vladu A 2018 International Conference on Learning Representations Vancouver, Canada, April 30−May 3, 2018 p1
[63]	Kurakin A, Goodfellow I, Bengio S 2017 arXiv: 1607.02533 [cs, stat]
[64]	Dong Y, Liao F, Pang T, Su H, Zhu J, Hu X, Li J 2018 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Salt Lake City, USA, June 18−23, 2018 p9185
[65]	Hsu Y T, Li X, Deng D L, Das Sarma S 2018 Phys. Rev. Lett. 121 245701 Google Scholar
[66]	Rodriguez-Nieva J F, Scheurer M S 2019 Nat. Phys. 15 790 Google Scholar
[67]	Zhang P, Shen H, Zhai H 2018 Phys. Rev. Lett. 120 066401 Google Scholar
[68]	Huembeli P, Dauphin A, Wittek P 2018 Phys. Rev. B 97 134109 Google Scholar
[69]	Rem B S, Käming N, Tarnowski M, Asteria L, Fläschner N, Becker C, Sengstock K, Weitenberg C 2019 Nat. Phys. 15 917 Google Scholar
[70]	Bohrdt A, Chiu C S, Ji G, Xu M, Greif D, Greiner M, Demler E, Grusdt F, Knap M 2019 Nat. Phys. 15 921 Google Scholar
[71]	Jiang S, Lu S, Deng D L 2019 arXiv: 1910.13453 [cond-mat, physics: quant-ph]
[72]	Neupert T, Santos L, Ryu S, Chamon C, Mudry C 2012 Phys. Rev. B 86 035125 Google Scholar
[73]	Deng D L, Wang S T, Duan L M 2014 Phys. Rev. A 90 041601 Google Scholar
[74]	Finlayson S G, Bowers J D, Ito J, Zittrain J L, Beam A L, Kohane I S 2019 Science 363 1287 Google Scholar
[75]	Ren K, Zheng T, Qin Z, Liu X 2020 Engineering 6 346 Google Scholar
[76]	Goodfellow I, Bengio Y, Courville A 2016 Deep Learning (Cambridge: The MIT Press) pp98−165
[77]	Sutskever I, Vinyals O, Le Q V 2014 Proceedings of the 27th International Conference on Neural Information Processing Systems (Volume 2) Montréal, Canada, December 8−13, 2014 p3104
[78]	Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I 2017 arXiv: 1706.03762 [cs]
[79]	Wolpert D H, Macready W G 1997 IEEE Trans. Evol. Comput. 1 67 Google Scholar
[80]	Shalev-Shwartz S, Ben-David S 2014 Understanding Machine Learning: From Theory to Algorithms (New York: Cambridge University Press) pp36−41
[81]	Poland K, Beer K, Osborne T J 2020 arXiv: 2003.14103 [quant-ph]
[82]	Schroff F, Kalenichenko D, Philbin J 2015 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Boston, USA, June 7−12, 2015 p815
[83]	Walters M 2015 arXiv: 1508.05448 [math-ph]
[84]	Schwabl F 2006 Statistical Mechanics (Berlin Heidelberg: Springer-Verlag) pp1−20
[85]	Dohmatob E 2019 arXiv: 1810.04065 [cs, stat]
[86]	Sharif M, Bhagavatula S, Bauer L, Reiter M K 2016 Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security Vienna, Austria, October 24−28, 2016 p1528
[87]	Papernot N, McDaniel P, Goodfellow I, Jha S, Celik Z B, Swami A 2017 Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security Abu Dhabi, UAE, April 2−6 2017 p506
[88]	Ledoux M 2001 The Concentration of Measure Phenomenon (Providence: American Mathematical Society) pp1–21
[89]	Hoeffding W 1963 J. Am. Stat. Assoc. 58 13 Google Scholar
[90]	Sharma K, Cerezo M, Holmes Z, Cincio L, Sornborger A, Coles P J 2020 arXiv: 2007.04900 [quant-ph]
[91]	Du Y, Hsieh M H, Liu T, Tao D, Liu N 2020 arXiv: 2003.09416 [quant-ph]
[92]	Tramèr F, Kurakin A, Papernot N, Goodfellow I, Boneh D, McDaniel P 2017 arXiv: 1705.07204 [cs, stat]
[93]	Papernot N, McDaniel P, Wu X, Jha S, Swami A 2016 37th IEEE Symposium on Security and Privacy San Jose, USA, May 23−25, 2016 p582
[94]	Samangouei P, Kabkab M, Chellappa R 2018 arXiv: 1805.06605 [cs, stat]
[95]	Dallaire-Demers P L, Killoran N 2018 Phys. Rev. A 98 012324 Google Scholar
[96]	Huang K, Wang Z A, Song C, Xu K, Li H, Wang Z, Guo Q, Song Z, Liu Z-B, Zheng D, Deng D L, Wang H, Tian J G, Fan H 2020 arXiv: 2009.12827 [quant-ph]
[97]	Zeng J, Wu Y, Liu J G, Wang L, Hu J 2019 Phys. Rev. A 99 052306 Google Scholar
[98]	Anderson P W 1967 Phys. Rev. Lett. 18 1049 Google Scholar
[99]	Deng D L, Pixley J H, Li X, Das Sarma S 2015 Phys. Rev. B 92 220201 Google Scholar

[1]	高吉明, 狄国文, 鱼自发, 唐荣安, 徐红萍, 薛具奎. 人工磁场下各向异性偶极玻色气体的量子相变. 物理学报, 2024, 73(13): 130503. doi: 10.7498/aps.73.20240376
[2]	刘钊. 莫尔超晶格中的分数化拓扑量子态. 物理学报, 2024, 73(20): 207303. doi: 10.7498/aps.73.20241029
[3]	刘畅, 王亚愚. 磁性拓扑绝缘体中的量子输运现象. 物理学报, 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
[4]	关欣, 陈刚. 双链超导量子电路中的拓扑非平庸节点. 物理学报, 2023, 72(14): 140301. doi: 10.7498/aps.72.20230152
[5]	王振宇, 李志雄, 袁怀洋, 张知之, 曹云姗, 严鹏. 磁子学中的拓扑物态与量子效应. 物理学报, 2023, 72(5): 057503. doi: 10.7498/aps.72.20221997
[6]	侯晨阳, 孟凡超, 赵一鸣, 丁进敏, 赵小艇, 刘鸿维, 王鑫, 娄淑琴, 盛新志, 梁生. “机器微纳光学科学家”: 人工智能在微纳光学设计的应用与发展. 物理学报, 2023, 72(11): 114204. doi: 10.7498/aps.72.20230208
[7]	杨光, 钞苏亚, 聂敏, 刘原华, 张美玲. 面向图像分类的混合量子长短期记忆神经网络构建方法. 物理学报, 2023, 72(5): 058901. doi: 10.7498/aps.72.20221924
[8]	陈以鹏, 刘靖阳, 朱佳莉, 方伟, 王琴. 机器学习在量子通信资源优化配置中的应用. 物理学报, 2022, 71(22): 220301. doi: 10.7498/aps.71.20220871
[9]	强晓斌, 卢海舟. 磁场中拓扑物态的量子输运. 物理学报, 2021, 70(2): 027201. doi: 10.7498/aps.70.20200914
[10]	李宇昂, 吴迪, 王栋立, 胡昊, 潘毅. 基于原子操纵技术的人工量子结构研究. 物理学报, 2021, 70(2): 020701. doi: 10.7498/aps.70.20201501
[11]	赵健, 陈昭昀, 庄希宁, 薛程, 吴玉椿, 郭国平. 量子态制备及其在量子机器学习中的前景. 物理学报, 2021, 70(14): 140307. doi: 10.7498/aps.70.20210958
[12]	田宇, 林子栋, 王翔宇, 车良宇, 鲁大为. 基于自旋体系的量子机器学习实验进展. 物理学报, 2021, 70(14): 140305. doi: 10.7498/aps.70.20210684
[13]	林键, 叶梦, 朱家纬, 李晓鹏. 机器学习辅助绝热量子算法设计. 物理学报, 2021, 70(14): 140306. doi: 10.7498/aps.70.20210831
[14]	刘彪, 周晓凡, 陈刚, 贾锁堂. 交错跃迁Hofstadter梯子的量子流相. 物理学报, 2020, 69(8): 080501. doi: 10.7498/aps.69.20191964
[15]	强晓斌, 卢海舟. 磁场中拓扑物态的量子输运. 物理学报, 2020, (): . doi: 10.7498/aps.69.20200914
[16]	陈西浩, 王秀娟. 一维扩展量子罗盘模型的拓扑序和量子相变. 物理学报, 2018, 67(19): 190301. doi: 10.7498/aps.67.20180855
[17]	喻祥敏, 谭新生, 于海峰, 于扬. 利用超导量子电路模拟拓扑量子材料. 物理学报, 2018, 67(22): 220302. doi: 10.7498/aps.67.20181857
[18]	刘辽, 裴寿镛. 量子史瓦茨黑洞和暗物质. 物理学报, 2006, 55(9): 4980-4982. doi: 10.7498/aps.55.4980
[19]	汪志诚. 双光子激光器的量子理论. 物理学报, 1991, 40(8): 1259-1279. doi: 10.7498/aps.40.1259-2
[20]	陈成明, 张全. 量子Hall效应与Berry相因数. 物理学报, 1991, 40(3): 345-352. doi: 10.7498/aps.40.345

计量

文章访问数: 10016
PDF下载量: 593
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

量子人工智能中的对抗学习