Abstract
Strong, fast pulses, called “bang–bang” controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, provide a geometric picture for evaluating errors due to imperfect bang–bang controls and give conditions for the compatibility of BB operations with other controlling operations. This will provide additional support for the usefulness of such controls as a means for providing more reliable quantum information processing.
PACS: 0.365.Yz, 03.67.Lx, 03.67-a
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. Viola and S. Lloyd, Phys. Rev. A 58, 2733 (1998).
D. Vitali and P. Tombesi, Phys. Rev. A 59, 4178 (1999), eprint quant-ph/9802033.
P. Zanardi, Phys. Lett. A 258, 77 (1999), eprint quant-ph/9809064.
L.-M. Duan and G. Guo Phys. Lett. A 261, 139 (1999), eprint quant-ph/9807072.
Velimir Jurdjevic, Geometric Control Theory (Cambridge University Press, 1997).
D. Vitali and P. Tombesi, Phys. Rev. A 65, 012305 (2002), LANL eprint quant-ph/0108007.
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 83, 4888 (1999), eeprint quant-ph/ 9906094.
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 85, 3520 (2000), eprint quant-ph/0002072.
P. W. Shor, Phys. Rev. A 52, 2493 (1995).
A. M. Steane, Phys. Rev. Lett. 77, 793 (1996).
A. M. Steane, in Introduction to Quantum Computation and Information, H. K. Lo, S. Popescu, and T.P. Spiller, eds. (World Scientific, Singapore, 1999), p. 184.
P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997), eprint quant-ph/9705044.
L.-M. Duan and G.-C. Guo, Phys. Rev. A 57, 737 (1998).
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998), eprint quant-ph/9807004.
E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000), eprint quant-ph/ 9908066.
J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A 63, 042307 (2001), eprint quant-ph/0004064.
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
P. Zanardi, Phys. Rev. A 63, 012301 (2001), eprint quant-ph/9910016.
G. Mahler and V. A. Weberruss. Quantum Networks: Dynamics of Open Nanostructures, 2nd ed. (Springer Verlag, Berlin, 1998).
Michael Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill Book Company, 1964).
M. S. Byrd and D. A. Lidar, in Proceedings of the 1st International Conference on Quantum Information, ICQI01 (Rochester, NY, 2001).
M. S. Byrd, J. Math. Phys. 39(11), 6125 (1998).
M.S. Byrd, J. Math. Phys. 41, 1026 (2000).
T. Tilma, M. S. Byrd, and E. C. G. Sudarshan (2001), LANL eprint math-ph/0202002.
D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998), eprint quant-ph/9701055.
D.A. Lidar and L.-A. Wu, Phys. Rev. Lett. 88, 017905 (2002), eprint quant-ph/0109021.
M. S. Byrd and D. A. Lidar (2001), LANL eprint quant-ph/0112054.
Lorenza Viola (2001), LANL ePrint quant-ph/0111167.
Evan M. Fortunato, et al. (2001), LANL eprint quant-ph/0111166.
L.-A. Wu and D.A. Lidar, Phys. Rev. Lett. 88, 207902 (2002), LANL eprint quant-ph/ 0112144.
L.-A. Wu, M.S. Byrd, and D.A. Lidar (2002), LANL eprint quant-ph/0202168.
A. Hanany and Y.-H. He, JHEP 0102, 27 (2001).
W.M. Fairbanks, T. Fulton, and W. H. Klink, J. Math. Phys. 5, 1038 (1964).
D. Anselmi, M. Bill, P. Fr, L. Girardello, and A. Zaffaroni, Int. J. Mod. Phys. A9, 3007 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Byrd, M.S., Lidar, D.A. Bang–Bang Operations from a Geometric Perspective. Quantum Information Processing 1, 19–34 (2002). https://doi.org/10.1023/A:1019697017584
Issue Date:
DOI: https://doi.org/10.1023/A:1019697017584