Abstract
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Chuang and M. A. Nielsen, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).
N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A 63, 032308 (2001).
J. Botina, H. Rabitz, and N. Rahman, J. Chem. Phys. 104, 4031 (1996).
P. W. Shor, Phys. Rev. A 52, 2493 (1995).
A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996).
P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 17 (1997).
L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 79, 1953 (1997).
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
U. Haeberlen, High Resolution NMR in Solids: Selective Averaging (Academic Press, New York, 1976).
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
L. Viola and E. Knill, Phys. Rev. Lett. 90, 037901 (2003).
K. Khodjasteh and D. A. Lidar, Phys. Rev. Lett. 95, 180 501 (2005).
E. Fortunato et al., J. Chem. Phys. 116, 7599 (2002).
M. A. Pravia et al., J. Chem. Phys. 119, 9993 (2003).
L. Viola, E. Knill, and R. Laflamme, J. Phys. A 34, 7076 (2001).
E. Fortunato, L. Viola, J. Hodges, et al., New J. Phys 4, 5 (2002).
L. Tian and S. Lloyd, Phys. Rev. A 62, 050301 (2000).
L.-A. Wu, M. S. Byrd, and D. A. Lidar, Phys. Rev. Lett. 89, 127901 (2002).
E. Hahn, Phys. Rev. 80, 580 (1950).
M. Levitt, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
N. Khaneja, T. Reiss, C. Kehlet, et al., J. Magn. Res. 172, 296 (2005).
R. Ghose, Conc. Magn. Res. 12, 152 (2000).
Y. C. Cheng and R. J. Silbey, Phys. Rev. A 69, 052325 (2004).
P. Cappellaro, J. Hodges, T. Havel, and D. Cory, J. Chem. Phys. 125, 44514 (2006).
M. Nielsen, Phys. Lett. A 303, 249 (2002).
Author information
Authors and Affiliations
Additional information
Original Text © Astro, Ltd., 2007.
Rights and permissions
About this article
Cite this article
Cappellaro, P., Hodges, J.S., Havel, T.F. et al. Control of qubits encoded in decoherence-free subspaces. Laser Phys. 17, 545–551 (2007). https://doi.org/10.1134/S1054660X0704038X
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1054660X0704038X