Quantum generative models for data generation

Sun Tai-Ping; Wu Yu-Chun; Guo Guo-Ping

doi:10.7498/aps.70.20210930

Abstract

In recent years, many generation-based machine learning algorithms such as generative adversarial networks, Boltzmann machine, auto-encoder, etc. are widely used in data generation and probability distribution simulation. On the other hand, the combined algorithms of quantum computation and classical machine learning algorithms are proposed in various styles. Especially, there exist many relevant researches about quantum generative models, which are regarded as the branch of quantum machine learning. Quantum generative models are hybrid quantum-classical algorithms, in which parameterized quantum circuits are introduced to obtain the cost function of the task as well as its gradient, and then classical optimization algorithms are used to find the optima. Compared with its classical counterpart, quantum generative models map the data stream to high-dimensional Hilbert space with parameterized quantum circuits. In the mapping space, data features are easier to learn, which can surpass classical generative models in some tasks. Besides, quantum generative models are potential to realize the quantum advantage in noisy intermediate-scale quantum devices.

Keywords:

Authors and contacts

1.
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
2.
Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230088, China
3.
Origin Quantum Computing Company Limited, Hefei 230026, China

Corresponding author: Wu Yu-Chun, wuyuchun@ustc.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0301700), the National Natural Science Foundation of China (Grant No. 11625419), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB24030600), and the Anhui Initiative in Quantum Information Technologies, China (Grant No. AHY080000)

FullText HTML : translate this paragraph

References

[1]	Zhu J Y, Krähenbühl P, Shechtman E, Efros A A 2016 European Conference on Computer Vision, Berlin, September 16, 2016 p597
[2]	Oord A, Dieleman S, Zen H, Simonyan K, Vinyals O, Graves A, Kalchbrenner N, Senior A, Kavukcuoglu K 2016 arXiv: 1609.03499 [cs.SD]
[3]	Gómez-Bombarelli R, Wei J N, Duvenaud D, Hernández-Lobato J M, Sánchez-Lengeling B, Sheberla D, Aguilera-Iparraguirre J, Hirzel T D, Adams R P, Aspuru-Guzik A 2018 ACS Cent. Sci. 4 268 Google Scholar
[4]	Isola P, Zhu J Y, Zhou T, Efros A A 2016 arXiv: 1611.07004[cs.CV]
[5]	Dallaire-Demers P L, Killoran N 2018 Phys. Rev. A 98 012324 Google Scholar
[6]	Lloyd S, Weedbrook C 2018 Phys. Rev. Lett. 121 040502 Google Scholar
[7]	Benedetti M, Garcia-Pintos D, Perdomo O, Leyton-Ortega V, Nam Y, Perdomo-Ortiz A 2019 npj Quantum Inf. 5 1
[8]	Liu J G, Wang L 2018 Phys. Rev. A 98 062324 Google Scholar
[9]	Amin M H, Andriyash E, Rolfe J, Kulchytskyy B, Melko R 2018 Phys. Rev. X 8 021050
[10]	Khoshaman A, Vinci W, Denis B, Andriyash E, Amin M H 2019 Quantum Sci. Technol. 4 014001
[11]	Benedetti M, Realpe-Gómez J, Biswas R, PerdomoOrtiz A 2017 Phys. Rev. X 7 041052
[12]	Kieferová M, Wiebe N 2017 Phys. Rev. A 96 062327 Google Scholar
[13]	Romero J, Olson J P, Aspuru-Guzik A 2017 Quantum Sci. Technol. 2 045001 Google Scholar
[14]	Lamata L, Alvarez-Rodriguez U, Martn-Guerrero J, Sanz M, Solano E 2018 Quantum Sci. Technol. 4 014007 Google Scholar
[15]	Li R, Alvarez-Rodriguez U, Lamata L, Solano E 2017 Quantum Meas. Quantum Metrol. 4 1
[16]	Du Y, Liu T, Tao D 2018 arXiv: 1805.11089 [quant-ph]
[17]	Peruzzo A, McClean J, Shadbolt P, Yung M H, Zhou Z Q, Love P J, Aspuru-Guzik A, O'Brien J L 2014 Nat. Commun. 5 4213 Google Scholar
[18]	Nielsen M A, Chuang I L 2002 Quantum computation and quantum information (Cambridge: Cambridge University Press) pp221–225
[19]	Preskill J 2018 Quantum 2 79 Google Scholar
[20]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[21]	Huang H L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y, Yang R, Liu T, Hsieh M H, Deng H, Rong H, Peng C Z, Lu C Y, Chen Y A, Tao D, Zhu X, Pan J W 2020 arXiv: 2010.06201 [quant-ph]
[22]	Du Y, Hsieh M-H, Liu T, Tao D 2020 Phys. Rev. Research 2 033125 Google Scholar
[23]	Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, WardeFarley D, Ozair S, Courville A, Bengio Y 2014 Proceedings of the 27th International Conference on Neural Information Processing Systems 2 pp2672–2680
[24]	Gulrajani I, Ahmed F, Arjovsky M, Dumoulin V, Courville A C 2017 arXiv: 1704.00028 [cs.LG]
[25]	Zoufal C, Lucchi A, Woerner S 2019 npj Quantum Inf. 5 103 Google Scholar
[26]	Zeng J, Wu Y, Liu J G, Wang L, Hu J 2019 Phys. Rev. A 99 052306 Google Scholar
[27]	Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N 2019 Phys. Rev. A 99 032331 Google Scholar
[28]	MacKay D J C 2002 Information Theory, Inference & Learning Algorithms (Cambridge: Cambridge University)
[29]	Situ H, He Z, Wang Y, Li L, Zheng S 2020 Information Sciences 538 193 Google Scholar
[30]	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
[31]	Rudolph M S, Toussaint N B, Katabarwa A, Johri S, Peropadre B, Perdomo-Ortiz A 2020 arXiv: 2012.03924 v2 [quant-ph]
[32]	Cheng S, Chen J, Wang L 2018 Entropy 20 583 Google Scholar
[33]	Hinton G E, Sejnowski T J 1986 In Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1 282
[34]	Hinton G E 2012 In Neural Networks: Tricks of the Trade Berlin Heidelberg, Germany, 2012 p599
[35]	Coyle B, Mills D, Danos V, Kashefi E 2020 npj Quantum Inf. 6 60 Google Scholar
[36]	Hofmann T, Schölkopf B, Smola A J 2008 Ann. Statist. 36 1171
[37]	Hinton G E, Sejnowski T J 1983 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Washington D. C., USA, 1983 p448
[38]	Hinton G E, Osindero S, Teh Y-W 2006 Neural Comput. 18 1527 Google Scholar
[39]	Salakhutdinov R, Hinton G 2009 Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics Florida, USA 2009 p448
[40]	Smolensky P 1986 Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol.1) (Cambridge: MIT press) pp194–281
[41]	Dorband J E 2015 12th International Conference on Information Technology-New Generations Las Vegas, USA, April 13–15, 2015 p703
[42]	Buhrman H, Cleve R, Watrous J, Wolf R D 2001 Phys. Rev. Lett. 87 167902 Google Scholar
[43]	Ding Y, Lamata L, Sanz M, Chen X, Solano E 2019 Adv. Quantum Technol. 2 1800065 Google Scholar
[44]	Pepper A, Tischler N, Pryde G J 2019 Phys. Rev. Lett. 122 060501 Google Scholar
[45]	Bondarenko D, Feldmann P 2020 Phys. Rev. Lett. 124 130502 Google Scholar
[46]	Huang C J, Ma H, Yin Q, Tang J F, Dong D, Chen C, Xiang G Y, Li C F, Guo G C 2020 Phys. Rev. A 102 032412 Google Scholar
[47]	Cao C, Wang X 2021 Phys. Rev. Applied. 15 054012 Google Scholar
[48]	Cerezo M, Sone A, Volkoff T, Patrick L C, Coles J 2021 Nat. Commun. 12 1791 Google Scholar
[49]	Gao X, Zhang Z Y, Duan L-M 2018 Sci. Adv. 4 eaat9004 Google Scholar
[50]	Gao X, Anschuetz E R, Wang S T, Cirac J I, Lukin M D 2021 arXiv: 2101.08354 v1 [quant-ph]

Cited By

图 1 量子生成对抗网络结构^[5]

Figure 1. The general structure of QGAN^[5].

DownLoad: Full-Size Img PowerPoint

图 2 量子自编码器的训练示意图, 其中$ {{{p}}}$表示变量, 摘自^[13]

Figure 2. Schematic representation of the hybrid scheme for training a quantum autoencoder where $ {{{p}}}$ represents variables, image from^[13].

DownLoad: Full-Size Img PowerPoint

图 3 经典和量子生成模型　(a) 因子图表示; (b)张量网络态表示; (c)量子生成模型定义^[49]

Figure 3. Classical and quantum generative models: (a) Illustration of a factor graph; (b) illustration of a tensor network state; (c) QGM definition^[49]

DownLoad: Full-Size Img PowerPoint

图 A1 参数量子线路示意图

Figure A1. Illustration of MPQCs.

DownLoad: Full-Size Img PowerPoint

[1]	Zhu J Y, Krähenbühl P, Shechtman E, Efros A A 2016 European Conference on Computer Vision, Berlin, September 16, 2016 p597
[2]	Oord A, Dieleman S, Zen H, Simonyan K, Vinyals O, Graves A, Kalchbrenner N, Senior A, Kavukcuoglu K 2016 arXiv: 1609.03499 [cs.SD]
[3]	Gómez-Bombarelli R, Wei J N, Duvenaud D, Hernández-Lobato J M, Sánchez-Lengeling B, Sheberla D, Aguilera-Iparraguirre J, Hirzel T D, Adams R P, Aspuru-Guzik A 2018 ACS Cent. Sci. 4 268 Google Scholar
[4]	Isola P, Zhu J Y, Zhou T, Efros A A 2016 arXiv: 1611.07004[cs.CV]
[5]	Dallaire-Demers P L, Killoran N 2018 Phys. Rev. A 98 012324 Google Scholar
[6]	Lloyd S, Weedbrook C 2018 Phys. Rev. Lett. 121 040502 Google Scholar
[7]	Benedetti M, Garcia-Pintos D, Perdomo O, Leyton-Ortega V, Nam Y, Perdomo-Ortiz A 2019 npj Quantum Inf. 5 1
[8]	Liu J G, Wang L 2018 Phys. Rev. A 98 062324 Google Scholar
[9]	Amin M H, Andriyash E, Rolfe J, Kulchytskyy B, Melko R 2018 Phys. Rev. X 8 021050
[10]	Khoshaman A, Vinci W, Denis B, Andriyash E, Amin M H 2019 Quantum Sci. Technol. 4 014001
[11]	Benedetti M, Realpe-Gómez J, Biswas R, PerdomoOrtiz A 2017 Phys. Rev. X 7 041052
[12]	Kieferová M, Wiebe N 2017 Phys. Rev. A 96 062327 Google Scholar
[13]	Romero J, Olson J P, Aspuru-Guzik A 2017 Quantum Sci. Technol. 2 045001 Google Scholar
[14]	Lamata L, Alvarez-Rodriguez U, Martn-Guerrero J, Sanz M, Solano E 2018 Quantum Sci. Technol. 4 014007 Google Scholar
[15]	Li R, Alvarez-Rodriguez U, Lamata L, Solano E 2017 Quantum Meas. Quantum Metrol. 4 1
[16]	Du Y, Liu T, Tao D 2018 arXiv: 1805.11089 [quant-ph]
[17]	Peruzzo A, McClean J, Shadbolt P, Yung M H, Zhou Z Q, Love P J, Aspuru-Guzik A, O'Brien J L 2014 Nat. Commun. 5 4213 Google Scholar
[18]	Nielsen M A, Chuang I L 2002 Quantum computation and quantum information (Cambridge: Cambridge University Press) pp221–225
[19]	Preskill J 2018 Quantum 2 79 Google Scholar
[20]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502 Google Scholar
[21]	Huang H L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y, Yang R, Liu T, Hsieh M H, Deng H, Rong H, Peng C Z, Lu C Y, Chen Y A, Tao D, Zhu X, Pan J W 2020 arXiv: 2010.06201 [quant-ph]
[22]	Du Y, Hsieh M-H, Liu T, Tao D 2020 Phys. Rev. Research 2 033125 Google Scholar
[23]	Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, WardeFarley D, Ozair S, Courville A, Bengio Y 2014 Proceedings of the 27th International Conference on Neural Information Processing Systems 2 pp2672–2680
[24]	Gulrajani I, Ahmed F, Arjovsky M, Dumoulin V, Courville A C 2017 arXiv: 1704.00028 [cs.LG]
[25]	Zoufal C, Lucchi A, Woerner S 2019 npj Quantum Inf. 5 103 Google Scholar
[26]	Zeng J, Wu Y, Liu J G, Wang L, Hu J 2019 Phys. Rev. A 99 052306 Google Scholar
[27]	Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N 2019 Phys. Rev. A 99 032331 Google Scholar
[28]	MacKay D J C 2002 Information Theory, Inference & Learning Algorithms (Cambridge: Cambridge University)
[29]	Situ H, He Z, Wang Y, Li L, Zheng S 2020 Information Sciences 538 193 Google Scholar
[30]	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
[31]	Rudolph M S, Toussaint N B, Katabarwa A, Johri S, Peropadre B, Perdomo-Ortiz A 2020 arXiv: 2012.03924 v2 [quant-ph]
[32]	Cheng S, Chen J, Wang L 2018 Entropy 20 583 Google Scholar
[33]	Hinton G E, Sejnowski T J 1986 In Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1 282
[34]	Hinton G E 2012 In Neural Networks: Tricks of the Trade Berlin Heidelberg, Germany, 2012 p599
[35]	Coyle B, Mills D, Danos V, Kashefi E 2020 npj Quantum Inf. 6 60 Google Scholar
[36]	Hofmann T, Schölkopf B, Smola A J 2008 Ann. Statist. 36 1171
[37]	Hinton G E, Sejnowski T J 1983 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Washington D. C., USA, 1983 p448
[38]	Hinton G E, Osindero S, Teh Y-W 2006 Neural Comput. 18 1527 Google Scholar
[39]	Salakhutdinov R, Hinton G 2009 Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics Florida, USA 2009 p448
[40]	Smolensky P 1986 Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol.1) (Cambridge: MIT press) pp194–281
[41]	Dorband J E 2015 12th International Conference on Information Technology-New Generations Las Vegas, USA, April 13–15, 2015 p703
[42]	Buhrman H, Cleve R, Watrous J, Wolf R D 2001 Phys. Rev. Lett. 87 167902 Google Scholar
[43]	Ding Y, Lamata L, Sanz M, Chen X, Solano E 2019 Adv. Quantum Technol. 2 1800065 Google Scholar
[44]	Pepper A, Tischler N, Pryde G J 2019 Phys. Rev. Lett. 122 060501 Google Scholar
[45]	Bondarenko D, Feldmann P 2020 Phys. Rev. Lett. 124 130502 Google Scholar
[46]	Huang C J, Ma H, Yin Q, Tang J F, Dong D, Chen C, Xiang G Y, Li C F, Guo G C 2020 Phys. Rev. A 102 032412 Google Scholar
[47]	Cao C, Wang X 2021 Phys. Rev. Applied. 15 054012 Google Scholar
[48]	Cerezo M, Sone A, Volkoff T, Patrick L C, Coles J 2021 Nat. Commun. 12 1791 Google Scholar
[49]	Gao X, Zhang Z Y, Duan L-M 2018 Sci. Adv. 4 eaat9004 Google Scholar
[50]	Gao X, Anschuetz E R, Wang S T, Cirac J I, Lukin M D 2021 arXiv: 2101.08354 v1 [quant-ph]

[1]	Zhang Yi-Fan, Ren Wei, Wang Wei-Li, Ding Shu-Jian, Li Nan, Chang Liang, Zhou Qian. Machine learning combined with solid solution strengthening model for predicting hardness of high entropy alloys. Acta Physica Sinica, 2023, 72(18): 180701. doi: 10.7498/aps.72.20230646
[2]	Qin Jian. Investigation of Gaussian boson sampling under phase noise of the light source. Acta Physica Sinica, 2023, 72(5): 050302. doi: 10.7498/aps.72.20221766
[3]	Chen Yi-Peng, Liu Jing-Yang, Zhu Jia-Li, Fang Wei, Wang Qin. Application of machine learning in optimal allocation of quantum communication resources. Acta Physica Sinica, 2022, 71(22): 220301. doi: 10.7498/aps.71.20220871
[4]	Shen Pei-Xin, Jiang Wen-Jie, Li Wei-Kang, Lu Zhi-De, Deng Dong-Ling. Adversarial learning in quantum artificial intelligence. Acta Physica Sinica, 2021, 70(14): 140302. doi: 10.7498/aps.70.20210789
[5]	Lin Jian, Ye Meng, Zhu Jia-Wei, Li Xiao-Peng. Machine learning assisted quantum adiabatic algorithm design. Acta Physica Sinica, 2021, 70(14): 140306. doi: 10.7498/aps.70.20210831
[6]	Zhao Jian, Chen Zhao-Yun, Zhuang Xi-Ning, Xue Cheng, Wu Yu-Chun, Guo Guo-Ping. Quantum state preparation and its prospects in quantum machine learning. Acta Physica Sinica, 2021, 70(14): 140307. doi: 10.7498/aps.70.20210958
[7]	Tian Yu, Lin Zi-Dong, Wang Xiang-Yu, Che Liang-Yu, Lu Da-Wei. Experimental progress of quantum machine learning based on spin systems. Acta Physica Sinica, 2021, 70(14): 140305. doi: 10.7498/aps.70.20210684
[8]	Li Bao-Min, Hu Ming-Liang, Fan Heng. Quantum coherence. Acta Physica Sinica, 2019, 68(3): 030304. doi: 10.7498/aps.68.20181779
[9]	Li Xiang, Wu De-Wei, Wang Xi, Miao Qiang, Chen Kun, Yang Chun-Yan. A method of evaluating the quality of dual-path entangled quantum microwave signal generated based on von Neumann entropy. Acta Physica Sinica, 2016, 65(11): 114204. doi: 10.7498/aps.65.114204
[10]	Fan Hong-Yi, Wu Ze. Statistical properties of binomial and negative-binomial combinational optical field state and its generation in quantum diffusion channel. Acta Physica Sinica, 2015, 64(8): 080303. doi: 10.7498/aps.64.080303
[11]	Liang Yan-Xia, Nie Min. A generation algorithm of unitary transformation applied in quantum data compression. Acta Physica Sinica, 2013, 62(20): 200305. doi: 10.7498/aps.62.200305
[12]	Chen Ji-Gen, Zeng Si-Liang, Yang Yu-Jun, Cheng Chao. Isolated intense sub-30-as pulse generation by quantum path control in the three-color laser pulse. Acta Physica Sinica, 2012, 61(12): 123201. doi: 10.7498/aps.61.123201
[13]	Wang Yu-Bo, Song Li-Jun, Yan Dong, Gai Yong-Jie. Relations of classical-quantum correspondencein Dicke model. Acta Physica Sinica, 2011, 60(2): 020302. doi: 10.7498/aps.60.020302
[14]	Chen Ji-Gen, Chen Gao, Chi Fang-Ping, Yang Yu-Jun. Generation of a broadband soft X-ray supercontinuum by quantum path control. Acta Physica Sinica, 2010, 59(5): 3162-3167. doi: 10.7498/aps.59.3162
[15]	Zhang Sheng, Wang Jian, Zhang Quan, Tang Chao-Jing. An analysis of the model of the error bits of quantum cryptography protocol. Acta Physica Sinica, 2009, 58(1): 73-77. doi: 10.7498/aps.58.73
[16]	Ye Bin, Xu Wen-Bo, Gu Bin-Jie. Robust quantum computation of the quantum kicked Harper model and dissipative decoherence. Acta Physica Sinica, 2008, 57(2): 689-695. doi: 10.7498/aps.57.689
[17]	Ye Bin, Gu Rui-Jun, Xu Wen-Bo. Robust quantum computation of the kicked Harper model and quantum chaos. Acta Physica Sinica, 2007, 56(7): 3709-3718. doi: 10.7498/aps.56.3709
[18]	MA YU-QIANG, LI ZHEN-YA. STUDY OF A QUANTUM TRANSVERSE ISING MODEL WITH RANDOM FIELDS. Acta Physica Sinica, 1990, 39(9): 1480-1487. doi: 10.7498/aps.39.1480
[19]	GU QIAO. THE QUANTUM STATISTICAL PROPERTIES OF THE JAYNES-CUMMINGS MODEL. Acta Physica Sinica, 1989, 38(5): 735-744. doi: 10.7498/aps.38.735
[20]	ZHENG WEI-MOU, LIU JI-XIN. EXACTLY SOLVABLE MODELS FOR QUANTUM DOUBLE-WELL POTENTIALS. Acta Physica Sinica, 1985, 34(12): 1658-1664. doi: 10.7498/aps.34.1658

Catalog

Vol. 70, Issue 14 - 2021-07-20

Metrics

Abstract views: 7140
PDF Downloads: 361
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板