Non-Abelian Berry connections for quantum computation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 1, 2000, Pages 103051-103054

  Pachos, Jiannis ^a   Zanardi, Paolo ^a,b   Rasetti, Mario ^a,b  

^a ISI FOUNDATION   (Italy)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347949096     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. For reviews, see D.P. DiVincenzo, Science 270, 255 (1995); A. Steane, Rep. Prog. Phys. 61, 117 (1998).
2. For reviews, see D.P. DiVincenzo, Science 270, 255 (1995); A. Steane, Rep. Prog. Phys. 61, 117 (1998).
3. P. Zanardi and M. Rasetti, Phys. Lett. A (to be published).
4. T.T. Wu and C.N. Yang, Phys. Rev. D 12, 3845 (1975); R. Jackiw, in Relativity Groups and Topology, Les Houches 1983, edited by B.S. DeWitt and R. Stora (North-Holland, Amsterdam, 1984), p. 154.
5. T.T. Wu and C.N. Yang, Phys. Rev. D 12, 3845 (1975); R. Jackiw, in Relativity Groups and Topology, Les Houches 1983, edited by B.S. DeWitt and R. Stora (North-Holland, Amsterdam, 1984), p. 154.
6. For a review see, Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989).
7. A. Kitaev, e-print archive quant-ph/9707021.
8. J. Preskill, in Introduction to Quantum Computation and Information, edited by Hoi-Kwong Lo, S. Popescu, and T. Spiller (World Scientific, Singapore, 1999).
9. F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
10. M. Nakahara, Geometry, Topology and Physics (IOP Publishing Ltd., Bristol, 1990).
11. We thank H. Barnum for pointing out this possibility.
12. j) means that X has nontrivial action only on the jth factor of H.
13. When the system geometry is given, one can restrict to "local" gates without loss of efficiency.
14. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); D.P. Di Vincenzo, Phys. Rev. A 51, 1015 (1995).
15. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); D.P. Di Vincenzo, Phys. Rev. A 51, 1015 (1995).
16. N+1).
17. P. Zanardi, Phys. Lett. A 258, 77 (1999).
18. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).