Preserving qubit coherence by dynamical decoupling

doi:10.1007/s11467-010-0113-8

Front. Phys.

2011, Vol. 6

Issue (1) : 2-14 https://doi.org/10.1007/s11467-010-0113-8

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Preserving qubit coherence by dynamical decoupling

Wen YANG¹, Zhen-Yu WANG², Ren-Bao LIU²(

)

1. Department of Physics, University of California San Diego, La Jolla, CA 92093-0319, USA; 2. Department of Physics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China

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Abstract

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.

Keywords qubit decoherence dynamical decoupling

Corresponding Author(s): LIU Ren-Bao,Email:rbliu@cuhk.edu.hk

Issue Date: 05 March 2011

Cite this article:

Wen YANG,Zhen-Yu WANG,Ren-Bao LIU. Preserving qubit coherence by dynamical decoupling[J]. Front. Phys. , 2011, 6(1): 2-14.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-010-0113-8
https://academic.hep.com.cn/fop/EN/Y2011/V6/I1/2

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 doi: 10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E
3	R. Kubo, J. Phys. Soc. Jpn. , 1954, 9: 935 doi: 10.1143/JPSJ.9.935
4	P. W. Anderson, J. Phys. Soc. Jpn. , 1954, 9: 316 doi: 10.1143/JPSJ.9.316
5	W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. B , 2006, 74: 195301 doi: 10.1103/PhysRevB.74.195301
6	I. A. Merkulov, A. L. Efros, and M. Rosen, Phys. Rev. B , 2002, 65: 205309 doi: 10.1103/PhysRevB.65.205309
7	T. Fujisawa, D. G. Austing, Y. Tokura, Y. Hirayama, and S. Tarucha, Nature , 2002, 419: 278 doi: 10.1038/nature00976
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 doi: 10.1038/nature02693
9	M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Nature , 2004, 432: 81 doi: 10.1038/nature03008
10	Y. G. Semenov and K.W. Kim, Phys. Rev. B , 2003, 67: 073301 doi: 10.1103/PhysRevB.67.073301
11	C. Deng and X. Hu, Phys. Rev. B , 2006, 73: 241303(R) doi: 10.1103/PhysRevB.73.241303
12	N. Shenvi, R. de Sousa, and K. B. Whaley, Phys. Rev. B , 2005, 71: 144419 doi: 10.1103/PhysRevB.71.144419
13	W. M. Witzel and S. Das Sarma, Phys. Rev. B , 2006, 74: 035322 doi: 10.1103/PhysRevB.74.035322
14	W. M. Witzel and S. Das Sarma, Phys. Rev. Lett. , 2007, 98: 077601 doi: 10.1103/PhysRevLett.98.077601
15	S. K. Saikin, W. Yao, and L. J. Sham, Phys. Rev. B , 2007, 75: 125314 doi: 10.1103/PhysRevB.75.125314
16	W. Yang and R. B. Liu, Phys. Rev. B , 2008, 78: 085315 doi: 10.1103/PhysRevB.78.085315
17	W. Yang and R. B. Liu, Phys. Rev. B , 2009, 79: 115320 doi: 10.1103/PhysRevB.79.115320
18	L. M. Duan and G. C. Guo, Phys. Rev. Lett. , 1997, 79: 1953 doi: 10.1103/PhysRevLett.79.1953
19	D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. , 1998, 81: 2594 doi: 10.1103/PhysRevLett.81.2594
20	E. L. Hahn, Phys. Rev. , 1950, 80: 580 doi: 10.1103/PhysRev.80.580
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 doi: 10.1103/PhysRevLett.25.218
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 doi: 10.1103/PhysRevA.58.2733
25	M. Ban, J. Mod. Opt. , 1998, 45: 2315 doi: 10.1080/09500349808231241
26	P. Zanardi, Phys. Lett. A , 1999, 258: 77 doi: 10.1016/S0375-9601(99)00365-5
27	L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. , 1999, 82: 2417 doi: 10.1103/PhysRevLett.82.2417
28	L. Viola and E. Knill, Phys. Rev. Lett. , 2005, 94: 060502 doi: 10.1103/PhysRevLett.94.060502
29	O. Kern and G. Alber, Phys. Rev. Lett. , 2005, 95: 250501 doi: 10.1103/PhysRevLett.95.250501
30	K. Khodjasteh and D. A. Lidar, Phys. Rev. Lett. , 2005, 95: 180501 doi: 10.1103/PhysRevLett.95.180501
31	K. Khodjasteh and D. A. Lidar, Phys. Rev. A , 2007, 75: 062310 doi: 10.1103/PhysRevA.75.062310
32	L. F. Santos and L. Viola, Phys. Rev. Lett. , 2006, 97: 150501 doi: 10.1103/PhysRevLett.97.150501
33	W. Yao, R. B. Liu, and L. J. Sham, Phys. Rev. Lett. , 2007, 98: 077602 doi: 10.1103/PhysRevLett.98.077602
34	R. B. Liu, W. Yao, and L. J. Sham, New J. Phys. , 2007, 9: 226 doi: 10.1088/1367-2630/9/7/226
35	W. M. Witzel and S. Das Sarma, Phys. Rev. B , 2007, 76: 241303(R) doi: 10.1103/PhysRevB.76.241303
36	W. X. Zhang, V. V. Dobrovitski, L. F. Santos, L. Viola, and B. N. Harmon, Phys. Rev. B , 2007, 75: 201302(R) doi: 10.1103/PhysRevB.75.201302
37	G. S. Uhrig, Phys. Rev. Lett. , 2007, 98: 100504 doi: 10.1103/PhysRevLett.98.100504
38	L. Cywiński, R.M. Lutchyn, C. P. Nave, and S. Das Sarma, Phys. Rev. B , 2008, 77: 174509 doi: 10.1103/PhysRevB.77.174509
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 doi: 10.1038/nphys192
40	M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Nature , 2009, 458: 996 doi: 10.1038/nature07951
41	J. F. Du, X. Rong, N. Zhao, Y. Wang, J. H. Yang, and R. B. Liu, Nature , 2009, 461: 1265 doi: 10.1038/nature08470
42	K. Khodjasteh and D. A. Lidar, Phys. Rev. A , 2008, 78: 012355 doi: 10.1103/PhysRevA.78.012355
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 doi: 10.1103/PhysRev.94.630
46	S. Meiboom and D. Gill, Rev. Sci. Instrum. , 1958, 29: 688 doi: 10.1063/1.1716296
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 doi: 10.1103/PhysRevLett.100.160505
49	G. S. Uhrig, New J. Phys. , 2008, 10: 083024 doi: 10.1088/1367-2630/10/8/083024
50	W. Yang and R. B. Liu, Phys. Rev. Lett. , 2008, 101: 180403 doi: 10.1103/PhysRevLett.101.180403
51	D. Dhar, L. K. Grover, and S. M. Roy, Phys. Rev. Lett. , 2006, 96: 100405 doi: 10.1103/PhysRevLett.96.100405
52	G. S. Uhrig and D. A. Lidar, Phys. Rev. A , 2010, 82: 012301 doi: 10.1103/PhysRevA.82.012301
53	S. Pasini and G. S. Uhrig, Phys. Rev. A , 2010, 81: 012309 doi: 10.1103/PhysRevA.81.012309
54	W. M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys. , 1990, 62: 867 doi: 10.1103/RevModPhys.62.867
55	S. Pasini and G. S. Uhrig, J. Phys. A: Math. Theor. , 2010, 43: 132001 doi: 10.1088/1751-8113/43/13/132001
56	S. Pasini, T. Fischer, P. Karbach, and G. S. Uhrig, Phys. Rev. A , 2008, 77: 032315 doi: 10.1103/PhysRevA.77.032315
57	S. Pasini and G. S. Uhrig, J. Phys. A: Math. Theor. , 2008, 41: 312005 doi: 10.1088/1751-8113/41/31/312005
58	G. S. Uhrig and S. Pasini, New J. Phys. , 2010, 12: 045001 doi: 10.1088/1367-2630/12/4/045001
59	K. Khodjasteh, D. A. Lidar, and L. Viola, Phys. Rev. Lett. , 2010, 104: 090501 doi: 10.1103/PhysRevLett.104.090501
60	T. E. Hodgson, L. Viola, and I. D’Amico, Phys. Rev. A , 2010, 81: 062321 doi: 10.1103/PhysRevA.81.062321
61	M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Phys. Rev. A , 2009, 79: 062324 doi: 10.1103/PhysRevA.79.062324
62	H. Uys, M. J. Biercuk, and J. J. Bollinger, Phys. Rev. Lett. , 2009, 103: 040501 doi: 10.1103/PhysRevLett.103.040501
63	G. S. Uhrig, Phys. Rev. Lett. , 2009, 102: 120502 doi: 10.1103/PhysRevLett.102.120502
64	J. R. West, B. H. Fong, and D. A. Lidar, Phys. Rev. Lett. , 2010, 104: 130501 doi: 10.1103/PhysRevLett.104.130501
65	Z. Y. Wang, unpublished
66	M. Mukhtar, T. B. Saw, W. T. Soh, and J. Gong, Phys. Rev. A , 2010, 81: 012331 doi: 10.1103/PhysRevA.81.012331
67	E. R. Jenista, A. M. Stokes, R. T. Branca, and S. Warren, J. Chem. Phys. , 2009, 131: 204510 doi: 10.1063/1.3263196
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. R?tteler, D. Janzing, and T. Beth, Phys. Rev. A , 2002, 65: 042309 doi: 10.1103/PhysRevA.65.042309
71	G. Gordon, G. Kurizki, and D. A. Lidar, Phys. Rev. Lett. , 2008, 101: 010403 doi: 10.1103/PhysRevLett.101.010403
72	P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, and F. K. Wilhelm, Phys. Rev. Lett. , 2009, 102: 090401 doi: 10.1103/PhysRevLett.102.090401
73	K. Khodjasteh and L. Viola, Phys. Rev. Lett. , 2009, 102: 080501 doi: 10.1103/PhysRevLett.102.080501
74	J. Clausen, G. Bensky, and G. Kurizki, Phys. Rev. Lett. , 2010, 104: 040401 doi: 10.1103/PhysRevLett.104.040401

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