Preserving qubit coherence by dynamical decoupling
Wen YANG, Zhen-Yu WANG, Ren-Bao LIU
Preserving qubit coherence by dynamical decoupling
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.
qubit / decoherence / dynamical decoupling
[1] |
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, 2000
|
[2] |
D. DiVincenzo, Fortschr. Phys., 2000, 48: 771
CrossRef
ADS
Google scholar
|
[3] |
R. Kubo, J. Phys. Soc. Jpn., 1954, 9: 935
CrossRef
ADS
Google scholar
|
[4] |
P. W. Anderson, J. Phys. Soc. Jpn., 1954, 9: 316
CrossRef
ADS
Google scholar
|
[5] |
W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. B, 2006, 74: 195301
CrossRef
ADS
Google scholar
|
[6] |
I. A. Merkulov, A. L. Efros, and M. Rosen, Phys. Rev. B, 2002, 65: 205309
CrossRef
ADS
Google scholar
|
[7] |
T. Fujisawa, D. G. Austing, Y. Tokura, Y. Hirayama, and S. Tarucha, Nature, 2002, 419: 278
CrossRef
ADS
Google scholar
|
[8] |
J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, Nature, 2004, 430: 431
CrossRef
ADS
Google scholar
|
[9] |
M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Nature, 2004, 432: 81
CrossRef
ADS
Google scholar
|
[10] |
Y. G. Semenov and K.W. Kim, Phys. Rev. B, 2003, 67: 073301
CrossRef
ADS
Google scholar
|
[11] |
C. Deng and X. Hu, Phys. Rev. B, 2006, 73: 241303(R)
CrossRef
ADS
Google scholar
|
[12] |
N. Shenvi, R. de Sousa, and K. B. Whaley, Phys. Rev. B, 2005, 71: 144419
CrossRef
ADS
Google scholar
|
[13] |
W. M. Witzel and S. Das Sarma, Phys. Rev. B, 2006, 74: 035322
CrossRef
ADS
Google scholar
|
[14] |
W. M. Witzel and S. Das Sarma, Phys. Rev. Lett., 2007, 98: 077601
CrossRef
ADS
Google scholar
|
[15] |
S. K. Saikin, W. Yao, and L. J. Sham, Phys. Rev. B, 2007, 75: 125314
CrossRef
ADS
Google scholar
|
[16] |
W. Yang and R. B. Liu, Phys. Rev. B, 2008, 78: 085315
CrossRef
ADS
Google scholar
|
[17] |
W. Yang and R. B. Liu, Phys. Rev. B, 2009, 79: 115320
CrossRef
ADS
Google scholar
|
[18] |
L. M. Duan and G. C. Guo, Phys. Rev. Lett., 1997, 79: 1953
CrossRef
ADS
Google scholar
|
[19] |
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett., 1998, 81: 2594
CrossRef
ADS
Google scholar
|
[20] |
E. L. Hahn, Phys. Rev., 1950, 80: 580
CrossRef
ADS
Google scholar
|
[21] |
M. Mehring, Principles of High Resolution NMR in Solids, 2nd Ed., Berlin: Spinger-Verleg, 1983
|
[22] |
W. K. Rhim, A. Pines, and J. S. Waugh, Phys. Rev. Lett., 1970, 25: 218
CrossRef
ADS
Google scholar
|
[23] |
U. Haeberlen, High Resolution NMR in Solids: Selective Averaging, New York: Academic Press, 1976
|
[24] |
L. Viola and S. Lloyd, Phys. Rev. A, 1998, 58: 2733
CrossRef
ADS
Google scholar
|
[25] |
M. Ban, J. Mod. Opt., 1998, 45: 2315
CrossRef
ADS
Google scholar
|
[26] |
P. Zanardi, Phys. Lett. A, 1999, 258: 77
CrossRef
ADS
Google scholar
|
[27] |
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett., 1999, 82: 2417
CrossRef
ADS
Google scholar
|
[28] |
L. Viola and E. Knill, Phys. Rev. Lett., 2005, 94: 060502
CrossRef
ADS
Google scholar
|
[29] |
O. Kern and G. Alber, Phys. Rev. Lett., 2005, 95: 250501
CrossRef
ADS
Google scholar
|
[30] |
K. Khodjasteh and D. A. Lidar, Phys. Rev. Lett., 2005, 95: 180501
CrossRef
ADS
Google scholar
|
[31] |
K. Khodjasteh and D. A. Lidar, Phys. Rev. A, 2007, 75: 062310
CrossRef
ADS
Google scholar
|
[32] |
L. F. Santos and L. Viola, Phys. Rev. Lett., 2006, 97: 150501
CrossRef
ADS
Google scholar
|
[33] |
W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. Lett., 2007, 98: 077602
CrossRef
ADS
Google scholar
|
[34] |
R. B. Liu, W. Yao, and L. J. Sham, New J. Phys., 2007, 9: 226
CrossRef
ADS
Google scholar
|
[35] |
W. M. Witzel and S. Das Sarma, Phys. Rev. B, 2007, 76: 241303(R)
CrossRef
ADS
Google scholar
|
[36] |
W. X. Zhang, V. V. Dobrovitski, L. F. Santos, L. Viola, and B. N. Harmon, Phys. Rev. B, 2007, 75: 201302(R)
CrossRef
ADS
Google scholar
|
[37] |
G. S. Uhrig, Phys. Rev. Lett., 2007, 98: 100504
CrossRef
ADS
Google scholar
|
[38] |
L. Cywiński, R.M. Lutchyn, C. P. Nave, and S. Das Sarma, Phys. Rev. B, 2008, 77: 174509
CrossRef
ADS
Google scholar
|
[39] |
J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, S. C. Benjamin, K. Porfyrakis, S. A. Lyon, and G. A. D. Briggs, Nature Phys., 2006, 2: 40
CrossRef
ADS
Google scholar
|
[40] |
M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Nature, 2009, 458: 996
CrossRef
ADS
Google scholar
|
[41] |
J. F. Du, X. Rong, N. Zhao, Y. Wang, J. H. Yang, and R. B. Liu, Nature, 2009, 461: 1265
CrossRef
ADS
Google scholar
|
[42] |
K. Khodjasteh and D. A. Lidar, Phys. Rev. A, 2008, 78: 012355
CrossRef
ADS
Google scholar
|
[43] |
J. R. West, D. A. Lidar, B. H. Fong, M. F. Gyure, X. Peng, and D. Suter, arXiv: 0911.2398, 2009
|
[44] |
H. K. Ng, D. A. Lidar, and J. Preskill, arXiv: 0911.3202, 2009
|
[45] |
H. Carr and E. M. Purcell, Phys. Rev., 1954, 94: 630
CrossRef
ADS
Google scholar
|
[46] |
S. Meiboom and D. Gill, Rev. Sci. Instrum., 1958, 29: 688
CrossRef
ADS
Google scholar
|
[47] |
M. S. Byrd and D. A. Lidar, Quant. Info. Proc., 2002, 1: 19
|
[48] |
B. Lee,W. M. Witzel, and S. Das Sarma, Phys. Rev. Lett., 2008, 100: 160505
CrossRef
ADS
Google scholar
|
[49] |
G. S. Uhrig, New J. Phys., 2008, 10: 083024
CrossRef
ADS
Google scholar
|
[50] |
W. Yang and R. B. Liu, Phys. Rev. Lett., 2008, 101: 180403
CrossRef
ADS
Google scholar
|
[51] |
D. Dhar, L. K. Grover, and S. M. Roy, Phys. Rev. Lett., 2006, 96: 100405
CrossRef
ADS
Google scholar
|
[52] |
G. S. Uhrig and D. A. Lidar, Phys. Rev. A, 2010, 82: 012301
CrossRef
ADS
Google scholar
|
[53] |
S. Pasini and G. S. Uhrig, Phys. Rev. A, 2010, 81: 012309
CrossRef
ADS
Google scholar
|
[54] |
W. M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys., 1990, 62: 867
CrossRef
ADS
Google scholar
|
[55] |
S. Pasini and G. S. Uhrig, J. Phys. A: Math. Theor., 2010, 43: 132001
CrossRef
ADS
Google scholar
|
[56] |
S. Pasini, T. Fischer, P. Karbach, and G. S. Uhrig, Phys. Rev. A, 2008, 77: 032315
CrossRef
ADS
Google scholar
|
[57] |
S. Pasini and G. S. Uhrig, J. Phys. A: Math. Theor., 2008, 41: 312005
CrossRef
ADS
Google scholar
|
[58] |
G. S. Uhrig and S. Pasini, New J. Phys., 2010, 12: 045001
CrossRef
ADS
Google scholar
|
[59] |
K. Khodjasteh, D. A. Lidar, and L. Viola, Phys. Rev. Lett., 2010, 104: 090501
CrossRef
ADS
Google scholar
|
[60] |
T. E. Hodgson, L. Viola, and I. D’Amico, Phys. Rev. A, 2010, 81: 062321
CrossRef
ADS
Google scholar
|
[61] |
M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Phys. Rev. A, 2009, 79: 062324
CrossRef
ADS
Google scholar
|
[62] |
H. Uys, M. J. Biercuk, and J. J. Bollinger, Phys. Rev. Lett., 2009, 103: 040501
CrossRef
ADS
Google scholar
|
[63] |
G. S. Uhrig, Phys. Rev. Lett., 2009, 102: 120502
CrossRef
ADS
Google scholar
|
[64] |
J. R. West, B. H. Fong, and D. A. Lidar, Phys. Rev. Lett., 2010, 104: 130501
CrossRef
ADS
Google scholar
|
[65] |
Z. Y. Wang, unpublished
|
[66] |
M. Mukhtar, T. B. Saw, W. T. Soh, and J. Gong, Phys. Rev. A, 2010, 81: 012331
CrossRef
ADS
Google scholar
|
[67] |
E. R. Jenista, A. M. Stokes, R. T. Branca, and S. Warren, J. Chem. Phys., 2009, 131: 204510
CrossRef
ADS
Google scholar
|
[68] |
N. Zhao, J. L. Hu, S.W. Ho, J. T. K. Wan, and R. B. Liu, arXiv: 1003.4320, 2010
|
[69] |
K. Khodjasteh and D. A. Lidar, Phys. Rev. A, 2003, 68: 022322; Erratum: Phys. Rev. A, 2005, 72: 029905(E)
|
[70] |
P. Wocjan, M. Rötteler, D. Janzing, and T. Beth, Phys. Rev. A, 2002, 65: 042309
CrossRef
ADS
Google scholar
|
[71] |
G. Gordon, G. Kurizki, and D. A. Lidar, Phys. Rev. Lett., 2008, 101: 010403
CrossRef
ADS
Google scholar
|
[72] |
P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, and F. K. Wilhelm, Phys. Rev. Lett., 2009, 102: 090401
CrossRef
ADS
Google scholar
|
[73] |
K. Khodjasteh and L. Viola, Phys. Rev. Lett., 2009, 102: 080501
CrossRef
ADS
Google scholar
|
[74] |
J. Clausen, G. Bensky, and G. Kurizki, Phys. Rev. Lett., 2010, 104: 040401
CrossRef
ADS
Google scholar
|
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