Affleck-Kennedy-Lieb-Tasaki State on a honeycomb lattice is a universal quantum computational resource

Physical Review Letters

Volumn 106, Issue 7, 2011, Pages

  Wei, Tzu Chieh ^a   Affleck, Ian ^a   Raussendorf, Robert ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER STATE; COMPUTATIONAL RESOURCES; HONEYCOMB LATTICES; MEASUREMENT-BASED QUANTUM COMPUTATION; QUANTUM COMPUTATION; QUBIT MEASUREMENT;

COMPUTATIONAL LINGUISTICS; HONEYCOMB STRUCTURES; QUANTUM COMPUTERS;

QUANTUM ENTANGLEMENT;

EID: 79951601920     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.106.070501     Document Type: Article

References (30)

1. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
2. R. Raussendorf and H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001). PRL (Pubitemid 32527770)
3. H.J. Briegel, Nature Phys. 5, 19 (2009). NPAHAX 1745-2473 10.1038/nphys1157
4. D. Gross, S.T. Flammia, and J. Eisert, Phys. Rev. Lett. 102, 190501 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.102.190501
5. M.J. Bremner, C. Mora, and A. Winter, Phys. Rev. Lett. 102, 190502 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.190502
6. H.J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.910 (Pubitemid 32159821)
7. D. Gross and J. Eisert, Phys. Rev. Lett. 98, 220503 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.220503 (Pubitemid 47139735)
8. F. Verstraete and J.I. Cirac, Phys. Rev. A 70, 060302(R) (2004). PLRAAN 1050-2947 10.1103/PhysRevA.70.060302 (Pubitemid 40213784)
9. J.-M. Cai, Phys. Rev. Lett. 103, 050503 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.050503
10. O. Mandel, Nature (London) 425, 937 (2003). NATUAS 0028-0836 10.1038/nature02008 (Pubitemid 37376920)
11. M.A. Nielsen, Rep. Math. Phys. 57, 147 (2006). RMHPBE 0034-4877 10.1016/S0034-4877(06)80014-5 (Pubitemid 43812137)
12. X. Chen, Phys. Rev. Lett. 102, 220501 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.220501
13. J.-M. Cai, A. Miyake, W. Dür, and H.J. Briegel, Phys. Rev. A 82, 052309 (2010). PLRAAN 1050-2947 10.1103/PhysRevA.82.052309
14. I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987); PRLTAO 0031-9007 10.1103/PhysRevLett.59.799
15. I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 115, 477 (1988). 10.1007/BF01218021
16. G.K. Brennen and A. Miyake, Phys. Rev. Lett. 101, 010502 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.010502
17. X. Chen, R. Duan, Z. Ji, and B. Zeng, Phys. Rev. Lett. 105, 020502 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.020502
18. R. Kaltenbaek, Nature Phys. 6, 850 (2010). NPAHAX 1745-2473 10.1038/nphys1777
19. A. Miyake, Phys. Rev. Lett. 105, 040501 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.040501
20. S.D. Bartlett, G.K. Brennen, A. Miyake, and J.M. Renes, Phys. Rev. Lett. 105, 110502 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.110502
21. See the supplementary material at http://link.aps.org/supplemental/10. 1103/PhysRevLett.106.070501 for further discussions.
22. M. Hein, J. Eisert, and H.-J. Briegel, Phys. Rev. A 69, 062311 (2004). PLRAAN 1050-2947 10.1103/PhysRevA.69.062311
23. D. Gottesman, Ph.D. thesis, Caltech, 1997.
24. M. Van den Nest, A. Miyake, W. Dür, and H.J. Briegel, Phys. Rev. Lett. 97, 150504 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.150504 (Pubitemid 44570410)
25. H. Katsura, J. Phys. A 1751-8113 43, 255303 (2010). 10.1088/1751-8113/43/ 25/255303
26. T.-C. Wei, I. Affleck, and R. Raussendorf, arXiv:1009.2840.
27. R. Durrett, Random Graph Dynamics (Cambridge University Press, Cambridge, 2007).
28. D.E. Browne, New J. Phys. 10, 023010 (2008). NJOPFM 1367-2630 10.1088/1367-2630/10/2/023010
29. J. Hoshen and R. Kopelman, Phys. Rev. B PLRBAQ 0556-2805 14, 3438 (1976). 10.1103/PhysRevB.14.3438
30. A. Miyake, arXiv:1009.3491v1.