Quantum computation and quantum simulation

Fan Heng

doi:10.7498/aps.67.20180710

Abstract

In past few years, quantum computation and quantum simulation have been developed rapidly. The research on quantum computation and quantum simulation involving medium scale number of qubits will have a development priority. In this paper, we review recent developments in those directions. The review will include quantum simulation of many-body system, quantum computation, digital quantum simulators and cloud quantum computation platforms, and quantum software. The quantum simulation of many-body system will include the simulation of quantum dynamics, time crystal and many-body localization, quantum statistical physics and quantum chemistry. The review of those results is based on our consideration to the current characteristics of quantum computation and quantum simulation. Specifically, the number of available qubits is on a medium scale from dozens to several hundreds, the fidelity of the quantum logic gate is not high enough for several thousand of operations. In this sense, the present research is at the stage from fundamental explorations to practical applications. With these in mind, we hope that this review can be helpful for the future study in quantum computation and quantum simulation.

Keywords:

Authors and contacts

Fan Heng^1,2

1.
Solid State Quantum Information and Computation Laboratory, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2.
Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Fan Heng, hfan@iphy.ac.cn

Funds: Project supported by the National Key RD Program of China (Grant Nos. 2016YFA0302104, 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 91536108, 11774406), and the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-3).

References

[1]	Feynman R P 1982 Int. J. Theor. Phys. 21 467
[2]	Bernie H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletić V, Lukin M D 2017 Nature 551 579
[3]	Zhang J, Pagano G, Hess P W, Kyprianidi A, Becker P, Kaplan H, Gorshkov A V, Gong Z X, Monroe C 2017 Nature 551 601
[4]	Heyl M, Polkovnikov A, Kehrein S 2013 Phys. Rev. Lett. 110 135704
[5]	Wilczek F 2013 Phys. Rev. Lett. 111 250402
[6]	Yao N Y, Potter A C, Potimiche I D, Vishwanath A 2017 Phys. Rev. Lett. 118 030401
[7]	Zhang J, Hess P W, Kyprianidis A, Becker P, Lee A, Smith J, Pagano G, Potirniche I D, Potter A C, Vishwanath A, Yao N Y, Monroe C 2017 Nature 543 217
[8]	Choi S, Choi J, Landig R, Kucsko G, Zhou H, Isoya J, Jelezko F, Onoda S, Sumiya H, Khemani V, Keyserlingk C, Yao N Y, Demler E, Lukin M D 2017 Nature 543 221
[9]	Schreiber M, Hodgman S S, Bordia P, Lschen H P, Fischer M H, Vosk R, Altman E, Schneider U, Bloch I 2015 Science 349 842
[10]	Alvarez G A, Suter D, Kaiser R M 2015 Science 349 846
[11]	Choi J Y, Hild S, Zeiher J, Schau P, Rubio-Abadal A, Yefsah T, Khemani V, Huse D A, Bloch I, Gross C 2016 Science 352 1547
[12]	Smith J, Richerme P, Neyenhuis B, Hess P W, Hauke P, Heyl M, Huse M A, Monroe C 2016 Nat. Phys. 12 907
[13]	Xu K, Chen J J, Zeng Y, Zhang Y R, Song C, Liu W, Guo Q, Zhang P, Xu D, Deng H, Huang K, Wang H, Zhu X, Zheng D, Fan H 2018 Phys. Rev. Lett. 120 050507
[14]	Roushan P, Neill C, Tangpanitanon J, Bastidas V M, Megrant A, Barends R, Chen Y, Chen Z, Chiaro B, Dunsworth A, Fowler A, Foxen B, Giustina M, Jeffrey E, Kelly J, Lucero E, Mutus J, Neeley M, Quintana C, Sank D, Vainsencher A, Wenner J, White T, Neven H, Angelakis D G, Martinis J 2017 Science 358 1175
[15]	An S, Zhang J N, Um M, L D, Lu Y, Zhan J, Yin Z Q, Quan H T, Kim K 2015 Nat. Phys. 11 193
[16]	Liu B H, Li L, Huang Y F, Li C F, Guo G C, Laine E M, Breuer H P, Piilo J 2011 Nat. Phys. 7 931
[17]	Guo X Y, Peng Y, Peng C N, Deng H, Jin Y R, Tang C, Zhu X B, Zheng D, Fan H 2017 arXiv:171010234[quant-ph]
[18]	Peng X H, Zhou H, Wei B B, Cui J, Du J, Liu R B 2015 Phys. Rev. Lett. 114 010601
[19]	Lu C Y, Gao W B, Ghne O, Zhou X Q, Chen Z B, Pan J W 2009 Phys. Rev. Lett. 102 030502
[20]	Zhong Y P, Xu D, Wang P, Song C, Guo Q J, Liu W X, Xu K, Xia B X, Lu C Y, Han S, Pan J W, Wang H 2016 Phys. Rev. Lett. 117 110501
[21]	Martinez E A, Muschik C A, Schindler P, Nigg D, Erhard A, Heyl M, Hauke P, Dalmonte M, Monz T, Zoller P, Blatt R 2016 Nature 534 516
[22]	Aspuru-Guzik A, Dutoi A D, Love P J, Head-Gordon M 2005 Science 309 1704
[23]	Lanyon B P, Whitfield J D, Gillett G G, Goggin M E, Almeida M P, Kassal I, Biamonte J D, Mohseni M, Powell B J, Barbieri M, Aspuru-Guzik A, White A G 2010 Nat. Chem. 2 106
[24]	McClean J R, Kivlichan I D, Sung K J, Steiger D S, Cao Y, Dai C, Fried E S, Gidney C, Gimby B, Hner T, Hardikar T, Havlček V, Huang C, Jiang Z, Neeley M, O'Brien T, Ozfidan I, Radin M D, Romero J, Rubin N, Sawaya N P D, Setia K, Sim S, Steudtner M, Sun W, Zhang F, Babbush R 2017 arXiv:171007629[quant-ph]
[25]	Georgescu I M, Ashhab S, Nori F 2014 Rev. Mod. Phys. 86 153
[26]	Shor P 1997 SIAM J. Comput. 26 1484
[27]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502
[28]	Grover L K 1997 Phys. Rev. Lett. 79 325
[29]	Cai X D, Weedbrook C, Su Z E, Chen M C, Gu M, Zhu M J, Li L, Liu N L, Lu C Y, Pan J W 2013 Phys. Rev. Lett. 110 230501
[30]	Pan J, Cao Y, Yao X, Li Z, Ju C, Chen H, Peng X, Kais S, Du J 2014 Phys. Rev. A 89 022313
[31]	Zheng Y R, Song C, Chen M C, Xia B, Liu W, Guo Q J, Zhang L, Xu D, Deng H, Huang K, Wu Y, Yan Z, Zheng D, Lu L, Pan J W, Wang H, Lu C Y, Zhu X 2017 Phys. Rev. Lett. 118 210504
[32]	Vandersypen L M K, Steffen M, Breyta G, Yannoni C S, Mark H, Sherwood M H, Chuang I L 2001 Nature 414 883
[33]	Lu C Y, Browne D E, Yang T, Pan J W 2007 Phys. Rev. Lett. 99 250504
[34]	Monz T, Nigg D, Martinez E A, Brandl M F, Schindler P, Rines R, Wang S X, Chuang I L, Blatt R 2016 Science 351 1068
[35]	Xu N Y, Zhu J, Lu D, Zhou X, Peng X, Du J 2012 Phys. Rev. Lett. 108 130501
[36]	Xu K B, Xie T, Li Z, Xu X, Wang M, Ye X, Kong F, Geng G, Duan C, Shi F, Du J 2017 Phys. Rev. Lett. 118 130504
[37]	Jones J L, Mosca M, Hansen R H 1998 Nature 393 344
[38]	Figgat C, Maslov D, Landsman K A, Linke N M, Debnath S, Monroe C 2017 Nat. Commun. 8 1918
[39]	Johnson M W, Amin M H, Gildert S, Lanting T, Hamze F, Dickson N, Harris R, Berkley A J, Johansson J, Bunyk P, Chapple E M, Enderud C, Hilton J P, Karimi K, Ladizinsky E, Ladizinsky N, Oh T, Perminov I, Rich C, Thom M C, Tolkacheva E, Truncik C J, Uchaikin S, Wang J, Wilson B, Rose G 2011 Nature 473 194
[40]	Boixo S, Rnnow T, Isakov S V, Wang Z, Wecker D, Lidar D A, Martinis J M, Troyer M 2014 Nat. Phys. 10 218
[41]	Mott A, Job J, Vlimant J R, Lidar D, Spiropulu M 2017 Nature 550 375
[42]	Ronnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A, Troyer M 2014 Science 345 420
[43]	Heim B, Ronnow T F, Isakov S V, Troyer M 2015 Science 348 215
[44]	Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794
[45]	Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R, Walmsley I A 2013 Science 339 798
[46]	Tillmann M, Dakić B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photon. 7 540
[47]	Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Hfling S, Lu C Y, Pan J W 2017 Nat. Photon. 11 361
[48]	OriginQC, www.qubitonline.cn
[49]	Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y, Sandvik A W 2017 Phys. Rev. X 7 041072
[50]	Liao H J, Xie Z Y, Chen J, Liu Z Y, Xie H D, Huang R Z, Normand B, Xiang T 2017 Phys. Rev. Lett. 118 137202
[51]	Chong F T, Franklin D, Martonosi M 2017 Nature 549 180
[52]	Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S 2017 Nature 549 195
[53]	Lloyd S 2000 Phys. Rev. A 62 022108

Cited By

[1]	Feynman R P 1982 Int. J. Theor. Phys. 21 467
[2]	Bernie H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletić V, Lukin M D 2017 Nature 551 579
[3]	Zhang J, Pagano G, Hess P W, Kyprianidi A, Becker P, Kaplan H, Gorshkov A V, Gong Z X, Monroe C 2017 Nature 551 601
[4]	Heyl M, Polkovnikov A, Kehrein S 2013 Phys. Rev. Lett. 110 135704
[5]	Wilczek F 2013 Phys. Rev. Lett. 111 250402
[6]	Yao N Y, Potter A C, Potimiche I D, Vishwanath A 2017 Phys. Rev. Lett. 118 030401
[7]	Zhang J, Hess P W, Kyprianidis A, Becker P, Lee A, Smith J, Pagano G, Potirniche I D, Potter A C, Vishwanath A, Yao N Y, Monroe C 2017 Nature 543 217
[8]	Choi S, Choi J, Landig R, Kucsko G, Zhou H, Isoya J, Jelezko F, Onoda S, Sumiya H, Khemani V, Keyserlingk C, Yao N Y, Demler E, Lukin M D 2017 Nature 543 221
[9]	Schreiber M, Hodgman S S, Bordia P, Lschen H P, Fischer M H, Vosk R, Altman E, Schneider U, Bloch I 2015 Science 349 842
[10]	Alvarez G A, Suter D, Kaiser R M 2015 Science 349 846
[11]	Choi J Y, Hild S, Zeiher J, Schau P, Rubio-Abadal A, Yefsah T, Khemani V, Huse D A, Bloch I, Gross C 2016 Science 352 1547
[12]	Smith J, Richerme P, Neyenhuis B, Hess P W, Hauke P, Heyl M, Huse M A, Monroe C 2016 Nat. Phys. 12 907
[13]	Xu K, Chen J J, Zeng Y, Zhang Y R, Song C, Liu W, Guo Q, Zhang P, Xu D, Deng H, Huang K, Wang H, Zhu X, Zheng D, Fan H 2018 Phys. Rev. Lett. 120 050507
[14]	Roushan P, Neill C, Tangpanitanon J, Bastidas V M, Megrant A, Barends R, Chen Y, Chen Z, Chiaro B, Dunsworth A, Fowler A, Foxen B, Giustina M, Jeffrey E, Kelly J, Lucero E, Mutus J, Neeley M, Quintana C, Sank D, Vainsencher A, Wenner J, White T, Neven H, Angelakis D G, Martinis J 2017 Science 358 1175
[15]	An S, Zhang J N, Um M, L D, Lu Y, Zhan J, Yin Z Q, Quan H T, Kim K 2015 Nat. Phys. 11 193
[16]	Liu B H, Li L, Huang Y F, Li C F, Guo G C, Laine E M, Breuer H P, Piilo J 2011 Nat. Phys. 7 931
[17]	Guo X Y, Peng Y, Peng C N, Deng H, Jin Y R, Tang C, Zhu X B, Zheng D, Fan H 2017 arXiv:171010234[quant-ph]
[18]	Peng X H, Zhou H, Wei B B, Cui J, Du J, Liu R B 2015 Phys. Rev. Lett. 114 010601
[19]	Lu C Y, Gao W B, Ghne O, Zhou X Q, Chen Z B, Pan J W 2009 Phys. Rev. Lett. 102 030502
[20]	Zhong Y P, Xu D, Wang P, Song C, Guo Q J, Liu W X, Xu K, Xia B X, Lu C Y, Han S, Pan J W, Wang H 2016 Phys. Rev. Lett. 117 110501
[21]	Martinez E A, Muschik C A, Schindler P, Nigg D, Erhard A, Heyl M, Hauke P, Dalmonte M, Monz T, Zoller P, Blatt R 2016 Nature 534 516
[22]	Aspuru-Guzik A, Dutoi A D, Love P J, Head-Gordon M 2005 Science 309 1704
[23]	Lanyon B P, Whitfield J D, Gillett G G, Goggin M E, Almeida M P, Kassal I, Biamonte J D, Mohseni M, Powell B J, Barbieri M, Aspuru-Guzik A, White A G 2010 Nat. Chem. 2 106
[24]	McClean J R, Kivlichan I D, Sung K J, Steiger D S, Cao Y, Dai C, Fried E S, Gidney C, Gimby B, Hner T, Hardikar T, Havlček V, Huang C, Jiang Z, Neeley M, O'Brien T, Ozfidan I, Radin M D, Romero J, Rubin N, Sawaya N P D, Setia K, Sim S, Steudtner M, Sun W, Zhang F, Babbush R 2017 arXiv:171007629[quant-ph]
[25]	Georgescu I M, Ashhab S, Nori F 2014 Rev. Mod. Phys. 86 153
[26]	Shor P 1997 SIAM J. Comput. 26 1484
[27]	Harrow A W, Hassidim A, Lloyd S 2009 Phys. Rev. Lett. 103 150502
[28]	Grover L K 1997 Phys. Rev. Lett. 79 325
[29]	Cai X D, Weedbrook C, Su Z E, Chen M C, Gu M, Zhu M J, Li L, Liu N L, Lu C Y, Pan J W 2013 Phys. Rev. Lett. 110 230501
[30]	Pan J, Cao Y, Yao X, Li Z, Ju C, Chen H, Peng X, Kais S, Du J 2014 Phys. Rev. A 89 022313
[31]	Zheng Y R, Song C, Chen M C, Xia B, Liu W, Guo Q J, Zhang L, Xu D, Deng H, Huang K, Wu Y, Yan Z, Zheng D, Lu L, Pan J W, Wang H, Lu C Y, Zhu X 2017 Phys. Rev. Lett. 118 210504
[32]	Vandersypen L M K, Steffen M, Breyta G, Yannoni C S, Mark H, Sherwood M H, Chuang I L 2001 Nature 414 883
[33]	Lu C Y, Browne D E, Yang T, Pan J W 2007 Phys. Rev. Lett. 99 250504
[34]	Monz T, Nigg D, Martinez E A, Brandl M F, Schindler P, Rines R, Wang S X, Chuang I L, Blatt R 2016 Science 351 1068
[35]	Xu N Y, Zhu J, Lu D, Zhou X, Peng X, Du J 2012 Phys. Rev. Lett. 108 130501
[36]	Xu K B, Xie T, Li Z, Xu X, Wang M, Ye X, Kong F, Geng G, Duan C, Shi F, Du J 2017 Phys. Rev. Lett. 118 130504
[37]	Jones J L, Mosca M, Hansen R H 1998 Nature 393 344
[38]	Figgat C, Maslov D, Landsman K A, Linke N M, Debnath S, Monroe C 2017 Nat. Commun. 8 1918
[39]	Johnson M W, Amin M H, Gildert S, Lanting T, Hamze F, Dickson N, Harris R, Berkley A J, Johansson J, Bunyk P, Chapple E M, Enderud C, Hilton J P, Karimi K, Ladizinsky E, Ladizinsky N, Oh T, Perminov I, Rich C, Thom M C, Tolkacheva E, Truncik C J, Uchaikin S, Wang J, Wilson B, Rose G 2011 Nature 473 194
[40]	Boixo S, Rnnow T, Isakov S V, Wang Z, Wecker D, Lidar D A, Martinis J M, Troyer M 2014 Nat. Phys. 10 218
[41]	Mott A, Job J, Vlimant J R, Lidar D, Spiropulu M 2017 Nature 550 375
[42]	Ronnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A, Troyer M 2014 Science 345 420
[43]	Heim B, Ronnow T F, Isakov S V, Troyer M 2015 Science 348 215
[44]	Broome M A, Fedrizzi A, Rahimi-Keshari S, Dove J, Aaronson S, Ralph T C, White A G 2013 Science 339 794
[45]	Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G R, Walmsley I A 2013 Science 339 798
[46]	Tillmann M, Dakić B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photon. 7 540
[47]	Wang H, He Y, Li Y H, Su Z E, Li B, Huang H L, Ding X, Chen M C, Liu C, Qin J, Li J P, He Y M, Schneider C, Kamp M, Peng C Z, Hfling S, Lu C Y, Pan J W 2017 Nat. Photon. 11 361
[48]	OriginQC, www.qubitonline.cn
[49]	Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y, Sandvik A W 2017 Phys. Rev. X 7 041072
[50]	Liao H J, Xie Z Y, Chen J, Liu Z Y, Xie H D, Huang R Z, Normand B, Xiang T 2017 Phys. Rev. Lett. 118 137202
[51]	Chong F T, Franklin D, Martonosi M 2017 Nature 549 180
[52]	Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S 2017 Nature 549 195
[53]	Lloyd S 2000 Phys. Rev. A 62 022108

[1]	Yang Xiao-Kun, Li Wei, Huang Yong-Chang. Quantum game— “PQ” problem. Acta Physica Sinica, 2024, 73(3): 030301. doi: 10.7498/aps.73.20230592
[2]	Jiang Da, Yu Dong-Yang, Zheng Zhan, Cao Xiao-Chao, Lin Qiang, Liu Wu-Ming. Research progress of material, physics, and device of topological superconductors for quantum computing. Acta Physica Sinica, 2022, 71(16): 160302. doi: 10.7498/aps.71.20220596
[3]	Wang Mei-Hong, Hao Shu-Hong, Qin Zhong-Zhong, Su Xiao-Long. Research advances in continuous-variable quantum computation and quantum error correction. Acta Physica Sinica, 2022, 71(16): 160305. doi: 10.7498/aps.71.20220635
[4]	Zhou Zong-Quan. “Quantum memory” quantum computers and noiseless phton echoes. Acta Physica Sinica, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
[5]	Wang Ning, Wang Bao-Chuan, Guo Guo-Ping. New progress of silicon-based semiconductor quantum computation. Acta Physica Sinica, 2022, 71(23): 230301. doi: 10.7498/aps.71.20221900
[6]	Xu Da, Wang Yi-Pu, Li Tie-Fu, You Jian-Qiang. Coherent coupling in a driven qubit-magnon hybrid quantum system. Acta Physica Sinica, 2022, 71(15): 150302. doi: 10.7498/aps.71.20220260
[7]	Gao Xue-Er, Li Dai-Li, Liu Zhi-Hang, Zheng Chao. Recent progress of quantum simulation of non-Hermitian systems. Acta Physica Sinica, 2022, 71(24): 240303. doi: 10.7498/aps.71.20221825
[8]	Luo Yu-Chen, Li Xiao-Peng. Quantum simulation of interacting fermions. Acta Physica Sinica, 2022, 71(22): 226701. doi: 10.7498/aps.71.20221756
[9]	Chen Yang, Zhang Tian-Yang, Guo Guang-Can, Ren Xi-Feng. Research progress of integrated photonic quantum simulation. Acta Physica Sinica, 2022, 71(24): 244207. doi: 10.7498/aps.71.20221938
[10]	Wang Chen-Xu, He Ran, Li Rui-Rui, Chen Yan, Fang Ding, Cui Jin-Ming, Huang Yun-Feng, Li Chuan-Feng, Guo Guang-Can. Advances in the study of ion trap structures in quantum computation and simulation. Acta Physica Sinica, 2022, 71(13): 133701. doi: 10.7498/aps.71.20220224
[11]	Zhang Jie-Yin, Gao Fei, Zhang Jian-Jun. Research progress of silicon and germanium quantum computing materials. Acta Physica Sinica, 2021, 70(21): 217802. doi: 10.7498/aps.70.20211492
[12]	Zhang Shi-Hao, Zhang Xiang-Dong, Li Lü-Zhou. Research progress of measurement-based quantum computation. Acta Physica Sinica, 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
[13]	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
[14]	He Ying-Ping, Hong Jian-Song, Liu Xiong-Jun. Non-abelian statistics of Majorana modes and the applications to topological quantum computation. Acta Physica Sinica, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[15]	Shen Yu-Tian, Meng Sheng. Water photosplitting: Atomistic mechanism and quantum dynamics. Acta Physica Sinica, 2019, 68(1): 018202. doi: 10.7498/aps.68.20181312
[16]	Yu Xiang-Min, Tan Xin-Sheng, Yu Hai-Feng, Yu Yang. Topological quantum material simulated with superconducting quantum circuits. Acta Physica Sinica, 2018, 67(22): 220302. doi: 10.7498/aps.67.20181857
[17]	Kong Xiang-Yu, Zhu Yuan-Ye, Wen Jing-Wei, Xin Tao, Li Ke-Ren, Long Gui-Lu. New research progress of nuclear magnetic resonance quantum information processing. Acta Physica Sinica, 2018, 67(22): 220301. doi: 10.7498/aps.67.20180754
[18]	Zhao Shi-Ping, Liu Yu-Xi, Zheng Dong-Ning. Novel superconducting qubits and quantum physics. Acta Physica Sinica, 2018, 67(22): 228501. doi: 10.7498/aps.67.20180845
[19]	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
[20]	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

Catalog

Vol. 67, Issue 12 - 2018-06-20

Metrics

Abstract views: 22064
PDF Downloads: 2285
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