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基于超导传输线和超导量子比特相互耦合的电路量子电动力学 (quantum electrodynamics, QED)系统, 是研究固态量子信息和量子测量与控制的理想实验平台. 本文在已有工作(单比特电路QED)基础上, 进一步研究多比特电路QED系统. 具体通过对两比特系统的量子测量和量子控制动力学的模拟, 检验了"绝热消除"和"极化子变换"两种消除微腔光子自由度方法的适用条件. 和单比特情况不同, 我们特别检验了两比特系统Bell纠缠态的"确定性"制备问题. 在量子路径水平上模拟发现, 由于反馈操作引起量子比特状态翻转, 使得极化子变换方法失效,它所导出的"有效测量算符" (其中含有非平庸的"宇称项")此时也将变得没有意义.Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.
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Keywords:
- circuit-QED /
- adiabatic elimination /
- polaron transformation /
- feedback operating
[1] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
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[4] 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
[5] Houck A A, Schuster D I, Gambetta J, 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
[6] Hofheinz M, Weig E M, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Wang H, Martinis J M, Cleland A N 2008 Nature 454 310
[7] Leek P J, Fink J M, Blais A, Bianchetti R, Gppl M, Gambetta J M, Schuster D I, Frunzio L, Schoelkopf R J, Wallraff A 2007 Science 318 1889
[8] Astafiev O, Inomata K, Niskanen A O, Yamamoto T, Pashkin Y A, Nakamura Y, Tsai J S 2007 Nature 449 588
[9] 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
[10] Gambetta J, Blais A, Schuster D I, Wallraff A, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2006 Phys. Rev. A 74 042318
[11] 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
[12] Sarovar M, Goan H S, Spiller T P, Milburn G J 2005 Phys. Rev. A 72 062327
[13] Liu Z, Kuang L, Hu K, Xu L, Wei S, Guo L, Li X Q 2010 Phys. Rev. A 82 032335
[14] Feng W, Wang P, Ding X, Xu L, Li X Q 2011 Phys. Rev. A 83 042313
[15] Wiseman H M, Milburn G J 1993 Phys. Rev. A 47 642
[16] Gambetta J M, Blais A, Boissonneault M, Houck A A, Schuster D I, Girvin S M 2008 Phys. Rev. A 77 012112
[17] Hutchison C L, Gambetta J M, Blais A, Wilhelm, F K 2009 Can. J. Phys. 87 225
[18] Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89
[19] Tavis M, Cummings F W 1968 Phys. Rev. 170 379
[20] Wiseman H M, Milburn G J 2010 Quantum Measurement and Control, Cambridge University Press, Cambridge, England
[21] Lalumiere K, Gambetta J M, Blais A 2010 Phys. Rev. A 81 040301(R)
[22] Ruskov R, Korotkov A N 2002 Phys. Rev. B 66 041401(R)
[23] Jin J S, Li X Q, Yan Y J 2006 Phys. Rev. B 73 23330
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[1] Blais A, Huang R S, Wallraff A, Girvin S M, Schoelkopf R J 2004 Phys. Rev. A 69 062320
[2] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature (London) 431 162
[3] Haroche S, Kleppner D 1989 Phys. Today 24
[4] 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
[5] Houck A A, Schuster D I, Gambetta J, 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
[6] Hofheinz M, Weig E M, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Wang H, Martinis J M, Cleland A N 2008 Nature 454 310
[7] Leek P J, Fink J M, Blais A, Bianchetti R, Gppl M, Gambetta J M, Schuster D I, Frunzio L, Schoelkopf R J, Wallraff A 2007 Science 318 1889
[8] Astafiev O, Inomata K, Niskanen A O, Yamamoto T, Pashkin Y A, Nakamura Y, Tsai J S 2007 Nature 449 588
[9] 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
[10] Gambetta J, Blais A, Schuster D I, Wallraff A, Frunzio L, Majer J, Devoret M H, Girvin S M, Schoelkopf R J 2006 Phys. Rev. A 74 042318
[11] 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
[12] Sarovar M, Goan H S, Spiller T P, Milburn G J 2005 Phys. Rev. A 72 062327
[13] Liu Z, Kuang L, Hu K, Xu L, Wei S, Guo L, Li X Q 2010 Phys. Rev. A 82 032335
[14] Feng W, Wang P, Ding X, Xu L, Li X Q 2011 Phys. Rev. A 83 042313
[15] Wiseman H M, Milburn G J 1993 Phys. Rev. A 47 642
[16] Gambetta J M, Blais A, Boissonneault M, Houck A A, Schuster D I, Girvin S M 2008 Phys. Rev. A 77 012112
[17] Hutchison C L, Gambetta J M, Blais A, Wilhelm, F K 2009 Can. J. Phys. 87 225
[18] Jaynes E T, Cummings F W 1963 Proc. IEEE 51 89
[19] Tavis M, Cummings F W 1968 Phys. Rev. 170 379
[20] Wiseman H M, Milburn G J 2010 Quantum Measurement and Control, Cambridge University Press, Cambridge, England
[21] Lalumiere K, Gambetta J M, Blais A 2010 Phys. Rev. A 81 040301(R)
[22] Ruskov R, Korotkov A N 2002 Phys. Rev. B 66 041401(R)
[23] Jin J S, Li X Q, Yan Y J 2006 Phys. Rev. B 73 23330
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