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During the past decades, the exploration of new topological material and the study of their novel physical properties have become a hot topic in condensed matter physics. However, it is hard to realize various topological materials and observe their physical properties that have been predicted theoretically due to the limitation of experimental techniques, such as fabrication, parameter control, and measurement. This situation makes quantum simulation a way alternative to simulating large quantum systems. In general, quantum simulation can be implemented by some controllable quantum systems. As a kind of all-solid state device, superconducting quantum circuit is an artificial quantum system that has great advantage in scalability, integration, and controllability, which provides an important scheme to realize the quantum simulator. In this paper, we review our recent results of quantum simulation in the space-time inversion symmetry protected topological semimetal bands, Hopf-link semimetal bands, and topological Maxwell metal bands with superconducting quantum circuits. These results show that the superconducting circuit is a promising system for simulating the quantum many-body system in condensed matter physics.
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Keywords:
- superconducting quantum circuits /
- quantum simulation /
- topological quantum material /
- topological phase transitions
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[1] Feynman R P 1982 Int. J. Theor. Phys. 21 467
[2] Greiner M, Mandel O, Esslinger T, Hänsch T W, Bloch I 2002 Nature 415 39
[3] Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E, Bloch I 2013 Nature Phys. 9 795
[4] Houck A, Tureci H, Koch J 2012 Nature Phys. 8 292
[5] You J, Nori F 2011 Nature 474 589
[6] Paik H, Schuster D I, Bishop L S, Kirchmair G, Catelani G, Sears A P, Johnson B R, Reagor M J, Frunzio L, Glazman L I, Girvin S M, Devoret M H, Schoelkopf R J 2011 Phys. Rev. Lett. 107 240501
[7] Georgescu I, Ashhab S, Nori F 2014 Rev. Mod. Phys. 86 153
[8] Lloyd S 1996 Science 273 1073
[9] Buluta I, Nori F 2009 Science 326 108
[10] Cirac J, Zoller P 2012 Nature Phys. 8 264
[11] Reed M D 2013 Ph. D Dissertation (New Haven: Yale University)
[12] Girvin S M, Devoret M H, Schoelkopf R J 2009 Phys. Scri. T137 014012
[13] Schuster D I 2007 Ph. D Dissertation (New Haven: Yale University)
[14] Reed M D, DiCarlo L, Johnson B R, Sun L, Schuster D I, Frunzio L, Schoelkopf R J 2010 Phys. Rev. Lett. 105 173601
[15] Li J, Paraoanu G S, Cicak K, Altomare F, Park J I, Simonds R W, Sillanpaa M A, Hakonen P J 2012 Sci. Rep. 2 645
[16] Ekert A, Ericsson M, Hayden P, Inamori H, Jones J A, Daniel K L, Vedral V 2000 J. Mod. Optic 47 2501
[17] Aidelsburger M，Lohse M，Schweizer C, Atala M, Barreiro J T, Nascimbene S, Cooper N R, Bloch I, Goldman N 2015 Nature Phys. 11 162
[18] Leek P J, Fink J M, Blais A, Bianchetti R, Göppl M, Gambetta J M, Schuster D I, Frunzio L, Schoelkopf R J 2007 Science 318 1889
[19] Yuan X X, He L, Wang S T, Deng D L, Wang F, Lian W Q, Wang X, Zhang C H, Zhang H L, Chang X Y, Duan M L 2017 Chin. Phys. Lett. 34 060302
[20] Deng D L, Wang S T, Sun K, Duan M L 2018 Chin. Phys. Lett. 35 013701
[21] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[22] Zhao Y X, Schnyder A P, Wang Z D 2016 Phys. Rev. Lett. 116 156402
[23] Tan X S, Zhao Y X, Liu Q, Xue G M, Yu H F, Yu Y 2017 npj Quantum Mater. 2 60
[24] Chen W, Lu H Z, Hou J M 2017 Phys. Rev. B 96 041102
[25] Chang P Y, Yee C H 2017 Phys. Rev. B 96 081114
[26] Tan X S, Li M M, Li D Y, Dai K Z, Yu H F, Yu Y 2018 Appl. Phys. Lett. 112 172601
[27] Yan Z B, Bi R, Shen H T, Lu L, Zhang S C, Wang Z 2017 Phys. Rev. B 96 041103
[28] Abanin D A, Kitagawa T, Bloch I, Demler E 2013 Phys. Rev. Lett. 110 165304
[29] Xiao D, Chang M, Niu Q 2010 Rev. Mod. Phys. 82 1959
[30] Bradlyn B, Cano J, Wang Z J, Vergniory M G, Felser C, Cava R J, Bernevig B A 2016 Science 353 5037
[31] Stone M 2016 Int. J. Mod. Phys. B 30 1550249
[32] Zhu Y Q, Zhang D W, Yan H, Xing D Y, Zhu S L 2018 ArXiv:1610.05993 [cond-mat. quant-gas]
[33] Tan X S, Zhang D W, Liu Q, Xue G M, Yu H F, Zhu Y Q, Yan H, Zhu S L, Yu Y 2018 Phys. Rev. Lett. 120 130503
[34] Gritsev V, Polkovnikov A 2012 Proc. Natl Acad. Sci. USA 109 6457
[35] Roushan P, Neill C, Chen Y, Kolodrubetz M, Quintana C, Leung N, Fang M, Barends R, Campbell B, Chen Z, Chiaro B, Dunsworth A, Jeffrey E, Kelly J, Megrant A, Mutus J, O’Malley P, Sank D, Vainsencher A, Wenner J, White T, Polkovnikov A, Cleland A N, Martinis J M 2014 Nature 515 241
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