Quantum Computation using Two Component Bose-Einstein Condensates

Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two qubit gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per qubit. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.


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References:
[1] M. H. Anderson et al., Science 269, 198 (1995).
[2] J. R. Anglin and W. Ketterle, Nature 416, 211 (2002).
[3] H. Deng, H. Haug, Y. Yamamoto, Rev. Mod. Phys. 82, 1489 (2010).
[4] S. O. Demokritov et al., Nature 443, 430 (2006).
[5] J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[6] J. Fort'agh, C. Zimmermann, Rev. Mod. Phys. 79, 235 (2007).
[7] A. S├©rensen, L.-M. Duan, J. I. Cirac, P. Zoller, Nature 409, 63 (2000).
[8] I. Buluta, F. Nori, Science 326, 108 (2009).
[9] M. Riedel et al., Nature 464, 1170 (2010).
[10] P. B¨ohi et al., Nature Phys. 5, 592 (2009).
[11] P. Treutlein et al., Fortschr. Phys. 54, 702 (2006).
[12] T. Hecht, Diploma Thesis, Technische Universit¨at M¨unchen Max-
Planck-Institut f¨ur Quantenoptik (2004).
[13] D. Press, T. Ladd, B. Zhang, Y. Yamamoto, Nature 456, 218 (2008).
[14] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, D. Awschalom, Science 320, 349 (2008).
[15] D. Press et al. Nature Photonics 4, 367 (2010).
[16] Y. Li, P. Treutlein, J. Reichel, A. Sinatra, Eur. Phys. J. B 68, 365 (2009).
[17] E. Brion, K. M├©lmer, M. Saffman, Phys. Rev. Lett. 99, 260501 (2007).
[18] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I.
Cirac, P. Zoller, Phys. Rev. Lett. 87, 037901 (2001).
[19] P. Rabl et al. Phys. Rev. Lett. 97, 033003 (2006).
[20] M. Nielsen, I. & Chuang, Quantum computation and quantum information
(Cambridge University Press, 2000).
[21] S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
[22] S. Braunstein and P. van Loock, Rev. Mod Phys. 77, 513 (2005).
[23] J. Altepeter,D. James, P. Kwiat, Lect. Notes Phys. 649, 113 (2004).
[24] T. Pellizzari, S. A. Gardiner, J. I. Cirac, P. Zoller, Phys. Rev. Lett. 75,
3788 (1995).
[25] Y. Colombe et al., Nature 450, 272 (2007).
[26] K. Henschel, J. Majer, J. Schmiedmayer, H. Ritsch, Phys. Rev. A 82,
033810 (2010).
[27] T. P. Purdy, D. M. Stamper-Kurn, Appl. Phys. B 90, 401 (2008).
[28] S. B. Zheng and G. C. Guo, Phys. Rev. Lett. 85, 2392 (2000).
[29] T. Ladd et al., Nature 464, 45 (2010).