Energy spectrum and exact cover in an extended quantum Ising model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 85, Issue 2, 2012, Pages

  Wakker, G M M ^a   Ockhorst, R ^a   Blaauboer, M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY SPECTRA; EXACT COVERS; EXTENDED VERSIONS; FIRST EXCITED STATE; FLUX QUBITS; LONGITUDINAL FIELDS; LONGITUDINAL MAGNETIC FIELDS; PERTURBATION THEORY;

ISING MODEL; MAGNETIC FIELDS; QUANTUM COMPUTERS;

SPECTROSCOPY;

EID: 84857615133     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.85.022337     Document Type: Article

References (39)

1. P. W. Shor, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539795293172 26, 1484 (1997);
2. L. K. Grover, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79. 325 79, 325 (1997); see also
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
4. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79.1217 79, 1217 (2007). (Pubitemid 47534150)
5. G. Wendin and V. S. Shumeiko, in Handbook of Theoretical and Computational Nanotechnology, edited by, M. Rieth, and, W. Schommers, (American Scientific Publishers, Los Angeles, 2006), Vol. 3.
6. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science SCIEAS 0036-8075 10.1126/science.1057726 292, 472 (2001).
7. V. Murg and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.042320 69, 042320 (2004).
8. M. H. S. Amin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100. 130503 100, 130503 (2008). (Pubitemid 351503197)
9. A. M. Childs, E. Farhi, and J. Preskill, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012322 65, 012322 (2001);
10. M. S. Sarandy and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.250503 95, 250503 (2005); (Pubitemid 41815965)
11. J. Roland and N. J. Cerf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032330 71, 032330 (2005); (Pubitemid 40648445)
12. S. Ashhab, J. R. Johansson, and F. Nori, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.052330 74, 052330 (2006); (Pubitemid 44791113)
13. M. Tiersch and R. Schützhold, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.062313 75, 062313 (2007). (Pubitemid 47014682)
14. M. H. S. Amin, P. J. Love, and C. J. S. Truncik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.060503 100, 060503 (2008); (Pubitemid 351391464)
15. M. H. S. Amin, D. V. Averin, and J. A. Nesteroff, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.022107 79, 022107 (2009);
16. M. H. S. Amin, C.J. S. Truncik, and D. V. Averin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.022303 80, 022303 (2009).
17. S. Lloyd, e-print arXiv: 0805.2757.
18. R. Schützhold and G. Schaller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.060304 74, 060304 (R) (2006). (Pubitemid 46130267)
19. M. H. S. Amin and V. Choi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.062326 80, 062326 (2009).
20. B. Altshuler, H. Krovi, and J. Roland, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1002116107 107, 12446 (2010).
21. A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.170503 101, 170503 (2008);
22. A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.020502 104, 020502 (2010);
23. I. Hen and A. P. Young, Phys. Rev. E 1539-3755 10.1103/PhysRevE.84.061152 84, 061152 (2011).
24. V. Choi, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1018310108 108, E19 (2011); see also the discussion and overview by
25. N. G. Dickson and M. H. S. Amin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.050502 106, 050502 (2011).
26. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(61)90115-4 16, 407 (1961).
27. See, e.g., the flux qubit chains described in F. G. Paauw, Ph.D. thesis, Delft University of Technology, 2009;
28. J. B. Majer, F. G. Paauw, A. C. J. ter Haar, C. J. P. M. Harmans, and J. E. Mooij, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.090501 94, 090501 (2005). (Pubitemid 40620591)
29. M. C. Bañuls, R. Orús, J. I. Latorre, A. Pérez, and P. Ruiz-Femenía, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022344 73, 022344 (2006).
30. A. Fubini, G. Falci, and Andreas Osterloh, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/5/134 9, 134 (2007). (Pubitemid 46804920)
31. A. A. Ovchinnikov, D. V. Dmitriev, V. Ya. Krivnov, and V. O. Cheranovskii, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.214406 68, 214406 (2003).
32. This corresponds to an exactly solvable spin-chain model commonly denoted as the XXZ model; see Ref.[22]. In practice, three-qubit interactions can in principle be realized for, e.g., superconducting qubits by extending the cavity bus coupling method that was pioneered by J. Majer, Nature (London) NATUAS 0028-0836 10.1038/nature06184 449, 443 (2007). (Pubitemid 47509554)
33. S. Suzuki, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(71)90901-7 34, 338 (1971);
34. S. Suzuki, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.46.1337 46, 1337 (1971).
35. P. Pfeuty, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(70)90270- 8 57, 79 (1970).
36. c for which solutions become unique. Although it is beyond the scope of this paper, it would be interesting to investigate the same question for the restricted clauses used in Sec.V. (Pubitemid 40618557)
37. See, e.g., L. DiCarlo, Nature (London) NATUAS 0028-0836 10.1038/nature08121 460, 240 (2009);
38. R. Harris, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.024511 82, 024511 (2010).
39. F. G. Paauw, A. Fedorov, C. J. P. M. Harmans, and J. E. Mooij, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.090501 102, 090501 (2009).