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超导量子比特的耦合研究进展

赵娜 刘建设 李铁夫 陈炜

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超导量子比特的耦合研究进展

赵娜, 刘建设, 李铁夫, 陈炜

Progress of coupled superconducting qubits

Zhao Na, Liu Jian-She, Li Tie-Fu, Chen Wei
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  • 超导量子比特以其在可控性、低损耗以及可扩展性等方面的优势被认为是最有希望实现量子计算机的固态方式之一. 量子比特之间的相干可控耦合是实现大规模的量子计算的必要条件. 本文介绍了超导量子比特耦合方式的研究进展, 包括利用电容或电感实现量子比特的局域耦合, 着重介绍一维传输线谐振腔作为量子总线实现多个量子比特的可控耦合的电路量子电动力学体系, 并对最新的三维腔与超导量子比特的耦合结构的研究进展进行了论述. 对各种耦合体系的哈密顿量进行了比较详细的分析, 并按照局域性和可控性对不同耦合机制进行了分类.
    Quantum system based on superconducting circuit is considered as one of the most promising schemes to realize quantum computers due to its controllability, low dissipation and scalability. To implement large scale quantum computation, coherent coupling between qubits is crucial for controlling and transferring quantum states. In this review paper, we summarize the progress of coupled superconducting qubits, including local coupling via capacitance or inductance, multiple qubits coherent interaction through one-dimensional resonator as circuit quantum electrodynamics, and superconducting qubits in a three-dimensional waveguide cavity. Hamiltonians of various coupling schemes are analyzed and classification of these coupling structures is summarized based on the coupling range and tunability.
    • 基金项目: 国家重点基础研究发展计划(批准号: 2011CBA00304)和国家自然科学基金(批准号: 60836001)资助的课题.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2011CBA00304) and the National Natural Science Foundation of China (Grant No. 60836001).
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    [2]

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    [3]

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    [4]

    Yu Y, Han S Y, Chu X, Chu S I, Wang Z 2002 Science 296 889

    [5]

    Chiorescu I, Nakamura Y, Harmans C J, Mooij J E 2003 Science 299 1869

    [6]

    Pashkin Y A, Yamamoto T, Astafiev O, Nakamura Y, Averin D V, Tsai J S 2003 Nature 421 823

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    Yamamoto T, Pashkin Y A, Astafiev O, Nakamura Y, Tsai J S 2003 Nature 425 941

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    Berkley A J, Xu H, Ramos R C, Gubrud M A, Strauch F W, Johnson P R, Anderson J R, Dragt A J, Lobb C J, Wellstood F C 2003 Science 300 1548

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    Majer J B, Paauw F G, ter Haar A, Harmans C, Mooij J E 2005 Phys. Rev. Lett. 94 090501

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    Cory D G, Laflamme R, Knill E, Viola L, Havel T F, Boulant N, Boutis G, Fortunato E, Lloyd S, Martinez R, Negrevergne C, Pravia M, Sharf Y, Teklemariam G, Weinstein Y S, Zurek W H 2000 Fortschr. Phys. 48 875

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    Hime T, Reichardt P A, Plourde B L T, Robertson T L, Wu C E, Ustinov A V, Clarke J 2006 Science 314 1427

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    van der Ploeg S H W, Izmalkov A, van den Brink A M, Hubner U, Grajcar M, Ilíchev E, Meyer H G, Zagoskin A M 2007 Phys. Rev. Lett. 98 057004

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    Harris R, Berkley A J, Johnson M W, Bunyk P, Govorkov S, Thom M C, Uchaikin S, Wilson A B, Chung J, Holtham E, Biamonte J D, Smirnov A Yu, Amin M H S, van den Brink A M 2007 Phys. Rev. Lett. 98 177001

    [14]

    Fay A, Hoskinson E, Lecocq F, Levy L P, Hekking F W J, Guichard W, Buisson O 2008 Phys. Rev. Lett. 100 187003

    [15]

    Niskanen A O, Harrabi K, Yoshihara F, Nakamura Y, Lloyd S, Tsai J S 2007 Science 316 723

    [16]

    You J Q, Tsai J S, Nori F 2002 Phys. Rev. Lett. 89 197902

    [17]

    Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320

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    Schoelkopf R J, Girvin S M 2008 Nature 451 664

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    Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89

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    Haroche S 1992 Fundamental Systems in Quantum Optics (New York: Elsevier) p 767

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    Raimond J, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

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    Schuster D I, Houck A A, Schreier J A, Wallraff A, Gambetta J M, Blais A, Frunzio L, Majer J, Johnson B, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 445 515

    [23]

    Wallraff A, Schuster D I, Blais A, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2005 Phys. Rev. Lett. 95 060501

    [24]

    Brune M, Nussenzveig P, Schmidt K F, Bernardot F, Maali A, Raimond J M, Haroche S 1994 Phys. Rev. Lett. 72 3339

    [25]

    Schuster D I, Wallraff A, Blais A, Frunzio L, Huang R S, Majer J, Girvin S M, Schoelkopf R J 2005 Phys. Rev. Lett. 94 123602

    [26]

    Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162

    [27]

    Braginsky V B, Khalili F Y 1996 Rev. Mod. Phys. 68 1

    [28]

    Abdumalikov A A, Astafiev O, Nakamura Y, Pashkin Y A, Tsai J S 2008 Phys. Rev. B 78 180502

    [29]

    Majer J, Chow J M, Gambetta J M, Koch J, Johnson B R, Schreier J A, Frunzio L, Schuster D I, Houck A A, Wallraff A, Blais A, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 449 443

    [30]

    Blais A, Gambetta J, Wallraff A, Schuster D I, Girvin S M, Devoret M H, Schoelkopf R J 2007 Phys. Rev. A 75 032329

    [31]

    DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240

    [32]

    Sillanpaa M A, Park J I, Simmonds R W 2007 Nature 449 438

    [33]

    DiCarlo L, Reed M D, Sun L, Johnson B R, Chow J M, Gambetta J M, Frunzio L, Girvin S M, Devoret M H, Schoelkopf R J 2010 Nature 467 574

    [34]

    Mariantoni M, Wang H, Bialczak R C, Lenander M, Lucero E, Neeley M, O'Connell A D, Sank D, Weides M, Wenner J, Yamamoto T, Yin Y, Zhao J, Martinis J M, Cleland A N, 2011 Nat. Phys. 7 287

    [35]

    Wang H, Hofheinz M, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Cleland A N, Martinis J M 2008 Phys. Rev. Lett. 101 240401

    [36]

    Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M, Cleland A N 2009 Nature 459 546

    [37]

    Gao J S, Zmuidzinas J, Mazin B A, LeDuc H G, Day P K 2007 Appl. Phys. Lett. 90 102507

    [38]

    Chen W, Bennett D A, Patel V, Lukens J E 2008 Supercond. Sci. Technol. 21 075013

    [39]

    Wang H, Hofheinz M, Wenner J, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, O'Connell A D, Sank D, Weides M, Cleland A N, Martinis J M 2009 Appl. Phys. Lett. 95 233508

    [40]

    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

    [41]

    Gao J S, Daal M, Vayonakis A, Kumar S, Zmuidzinas J, Sadoulet B, Mazin B A, Day P K, Leduc H G 2008 Appl. Phys. Lett. 92 152505

    [42]

    O'Connell A D, Ansmann M, Bialczak R C, Hofheinz M, Katz N, Lucero E, McKenney C, Neeley M, Wang H, Weig E M, Cleland A N, Martinis J M 2008 Appl. Phys. Lett. 92 112903

    [43]

    Rigetti C, Poletto S, Gambetta J M, Plourde B, Chow J M, Corcoles A D, Smolin J A, Merkel S T, Rozen J R, Keefe G A, Rothwell M B, Ketchen M B, Steffen M 2012 arXiv: 1202. 5533v1 [quant-ph]

    [44]

    Riste D, Leeuwen J, Ku H S, Lehnert K W, DiCarlo L 2012 arXiv:1204. 2479v1 [cond-mat. mes-hall]

    [45]

    Houck A A, Schuster D I, Gambetta J M, Schreier J A, Johnson B R, Chow J M, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 449 328

    [46]

    Fragner A, Göppl M, Fink J M, Baur M, Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Science 322 1357

    [47]

    Fink J M, Göppl M, Baur M, Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Nature 454 315

    [48]

    Johnson B R, Reed M D, Houck A A, Schuster D I, Bishop L S, Ginossar E, Gambetta J M, DiCarlo L, Frunzio L, Girvin S M, Schoelkopf R J 2010 Nat. Phys. 6 663

  • [1]

    Nielsen M A, Chuang I L 2002 Quantum Computation and Quantum Information (Cambridge: Cambridge Univ. Press) p 1

    [2]

    Josephson B D 1962 Phys. Lett. 1 251

    [3]

    Nakamura Y, Pashkin Y A, Tsai J S 1999 Nature 398 786

    [4]

    Yu Y, Han S Y, Chu X, Chu S I, Wang Z 2002 Science 296 889

    [5]

    Chiorescu I, Nakamura Y, Harmans C J, Mooij J E 2003 Science 299 1869

    [6]

    Pashkin Y A, Yamamoto T, Astafiev O, Nakamura Y, Averin D V, Tsai J S 2003 Nature 421 823

    [7]

    Yamamoto T, Pashkin Y A, Astafiev O, Nakamura Y, Tsai J S 2003 Nature 425 941

    [8]

    Berkley A J, Xu H, Ramos R C, Gubrud M A, Strauch F W, Johnson P R, Anderson J R, Dragt A J, Lobb C J, Wellstood F C 2003 Science 300 1548

    [9]

    Majer J B, Paauw F G, ter Haar A, Harmans C, Mooij J E 2005 Phys. Rev. Lett. 94 090501

    [10]

    Cory D G, Laflamme R, Knill E, Viola L, Havel T F, Boulant N, Boutis G, Fortunato E, Lloyd S, Martinez R, Negrevergne C, Pravia M, Sharf Y, Teklemariam G, Weinstein Y S, Zurek W H 2000 Fortschr. Phys. 48 875

    [11]

    Hime T, Reichardt P A, Plourde B L T, Robertson T L, Wu C E, Ustinov A V, Clarke J 2006 Science 314 1427

    [12]

    van der Ploeg S H W, Izmalkov A, van den Brink A M, Hubner U, Grajcar M, Ilíchev E, Meyer H G, Zagoskin A M 2007 Phys. Rev. Lett. 98 057004

    [13]

    Harris R, Berkley A J, Johnson M W, Bunyk P, Govorkov S, Thom M C, Uchaikin S, Wilson A B, Chung J, Holtham E, Biamonte J D, Smirnov A Yu, Amin M H S, van den Brink A M 2007 Phys. Rev. Lett. 98 177001

    [14]

    Fay A, Hoskinson E, Lecocq F, Levy L P, Hekking F W J, Guichard W, Buisson O 2008 Phys. Rev. Lett. 100 187003

    [15]

    Niskanen A O, Harrabi K, Yoshihara F, Nakamura Y, Lloyd S, Tsai J S 2007 Science 316 723

    [16]

    You J Q, Tsai J S, Nori F 2002 Phys. Rev. Lett. 89 197902

    [17]

    Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320

    [18]

    Schoelkopf R J, Girvin S M 2008 Nature 451 664

    [19]

    Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89

    [20]

    Haroche S 1992 Fundamental Systems in Quantum Optics (New York: Elsevier) p 767

    [21]

    Raimond J, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [22]

    Schuster D I, Houck A A, Schreier J A, Wallraff A, Gambetta J M, Blais A, Frunzio L, Majer J, Johnson B, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 445 515

    [23]

    Wallraff A, Schuster D I, Blais A, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2005 Phys. Rev. Lett. 95 060501

    [24]

    Brune M, Nussenzveig P, Schmidt K F, Bernardot F, Maali A, Raimond J M, Haroche S 1994 Phys. Rev. Lett. 72 3339

    [25]

    Schuster D I, Wallraff A, Blais A, Frunzio L, Huang R S, Majer J, Girvin S M, Schoelkopf R J 2005 Phys. Rev. Lett. 94 123602

    [26]

    Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162

    [27]

    Braginsky V B, Khalili F Y 1996 Rev. Mod. Phys. 68 1

    [28]

    Abdumalikov A A, Astafiev O, Nakamura Y, Pashkin Y A, Tsai J S 2008 Phys. Rev. B 78 180502

    [29]

    Majer J, Chow J M, Gambetta J M, Koch J, Johnson B R, Schreier J A, Frunzio L, Schuster D I, Houck A A, Wallraff A, Blais A, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 449 443

    [30]

    Blais A, Gambetta J, Wallraff A, Schuster D I, Girvin S M, Devoret M H, Schoelkopf R J 2007 Phys. Rev. A 75 032329

    [31]

    DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240

    [32]

    Sillanpaa M A, Park J I, Simmonds R W 2007 Nature 449 438

    [33]

    DiCarlo L, Reed M D, Sun L, Johnson B R, Chow J M, Gambetta J M, Frunzio L, Girvin S M, Devoret M H, Schoelkopf R J 2010 Nature 467 574

    [34]

    Mariantoni M, Wang H, Bialczak R C, Lenander M, Lucero E, Neeley M, O'Connell A D, Sank D, Weides M, Wenner J, Yamamoto T, Yin Y, Zhao J, Martinis J M, Cleland A N, 2011 Nat. Phys. 7 287

    [35]

    Wang H, Hofheinz M, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Cleland A N, Martinis J M 2008 Phys. Rev. Lett. 101 240401

    [36]

    Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M, Cleland A N 2009 Nature 459 546

    [37]

    Gao J S, Zmuidzinas J, Mazin B A, LeDuc H G, Day P K 2007 Appl. Phys. Lett. 90 102507

    [38]

    Chen W, Bennett D A, Patel V, Lukens J E 2008 Supercond. Sci. Technol. 21 075013

    [39]

    Wang H, Hofheinz M, Wenner J, Ansmann M, Bialczak R C, Lenander M, Lucero E, Neeley M, O'Connell A D, Sank D, Weides M, Cleland A N, Martinis J M 2009 Appl. Phys. Lett. 95 233508

    [40]

    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

    [41]

    Gao J S, Daal M, Vayonakis A, Kumar S, Zmuidzinas J, Sadoulet B, Mazin B A, Day P K, Leduc H G 2008 Appl. Phys. Lett. 92 152505

    [42]

    O'Connell A D, Ansmann M, Bialczak R C, Hofheinz M, Katz N, Lucero E, McKenney C, Neeley M, Wang H, Weig E M, Cleland A N, Martinis J M 2008 Appl. Phys. Lett. 92 112903

    [43]

    Rigetti C, Poletto S, Gambetta J M, Plourde B, Chow J M, Corcoles A D, Smolin J A, Merkel S T, Rozen J R, Keefe G A, Rothwell M B, Ketchen M B, Steffen M 2012 arXiv: 1202. 5533v1 [quant-ph]

    [44]

    Riste D, Leeuwen J, Ku H S, Lehnert K W, DiCarlo L 2012 arXiv:1204. 2479v1 [cond-mat. mes-hall]

    [45]

    Houck A A, Schuster D I, Gambetta J M, Schreier J A, Johnson B R, Chow J M, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 449 328

    [46]

    Fragner A, Göppl M, Fink J M, Baur M, Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Science 322 1357

    [47]

    Fink J M, Göppl M, Baur M, Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Nature 454 315

    [48]

    Johnson B R, Reed M D, Houck A A, Schuster D I, Bishop L S, Ginossar E, Gambetta J M, DiCarlo L, Frunzio L, Girvin S M, Schoelkopf R J 2010 Nat. Phys. 6 663

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出版历程
  • 收稿日期:  2012-05-15
  • 修回日期:  2012-07-30
  • 刊出日期:  2013-01-05

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