Qubit-qubit interaction in quantum computers. II. Adder algorithm with diagonal and off-diagonal interactions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 60, Issue 1, 1999, Pages 185-193

  Gea Banacloche, Julio ^a  

^a UNIVERSITY OF ARKANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243644069     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.60.185     Document Type: Article

References (20)

1. See, for example, the recent review article by A. Steane, Rep. Prog. Phys. 61, 117 (1998).
2. These have been studied in many cases for many different systems. For ion-chain systems without error correction, see the work by M. B. Plenio and P. L. Knight, Phys. Rev. A 53, 2986 (1996)
3. M. B. PlenioP. L. KnightProc. R. Soc. London, Ser. A 453, 2017 (1997)
4. see also A. Garg, Phys. Rev. Lett. 77, 964 (1996), where the “environment” is the zero-point oscillations of the ion chain.
5. J. Gea-Banacloche, Phys. Rev. A 57, R1 (1998).
6. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
7. For a description of the QFT, see, for instance, A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
8. J. Gea-Banacloche, in Photonic Quantum Computing II, edited by Steven P. Hotaling and Andrew R. Pirich, special issue of Proc. SPIE 3385, 64 (1998).
9. R. J. Hughes, D. F. V. James, E. H. Knill, R. Laflamme, and A. G. Petschek, Phys. Rev. Lett. 77, 3240 (1996).
10. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
11. D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998)
12. see also D. Wineland, C. Monroe, W. Itano, B. King, D. Leibfried, D. Meekhof, C. Myatt, and C. Wood, Fortschr. Phys. 46, 363 (1998).
13. J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985).
14. Actually, the form given here is only the asymptotic form of these states for infinitely strong applied field. For a finite field, the hyperfine interaction would result in a small amount of coupling to (mixing with) other states with different values of (Formula presented) in fact, it is this coupling that must cancel the energy dependence on the nuclear spin for the special value of B at which near field independence is achieved. However, it follows from this that the magnitude of the coupling (the amplitude of other states in the mix) must be as small as the ratio of the nuclear to the electronic dipole, and thus the effective value of δ in the direct electron-electron magnetic interaction would also be correspondingly reduced.
15. V. Vedral, A. Barenco, and A. Ekert, Phys. Rev. A 54, 147 (1996).
16. T. Pellizzari, S. A. Gardiner, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 75, 3788 (1995).
17. M. Chapman, L. You, and T. A. B. Kennedy (unpublished).
18. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
19. A. M. Steane, Fortschr. Phys. 46, 443 (1998).
20. See, e.g., E. Knill, R. Laflamme, and W. H. Zurek, Science 279, 342 (1998), and references therein.