On quantum mean-field models and their quantum annealing

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2012, Issue 6, 2012, Pages

  Bapst, Victor ^a   Semerjian, Guilhem ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

analysis of algorithms; disordered systems (theory); metastable states; quantum phase transitions (theory)

Indexed keywords

EID: 84863300295     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2012/06/P06007     Document Type: Article

References (82)

1. Garey M R and Johnson D S 1979 Computers and Intractability, A Guide to the Theory of NP-Completeness (New York: Freeman)
2. Kirkpatrick S, Gelatt C D Jr and Vecchi M 1983 Science 220 671
3. Apolloni B, Cesa-Bianchi N and de Falco D 1989 Stoc. Proc. Appl. 33 233
4. Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
5. Farhi E et al 2001 Science 292 472
6. Santoro G E and Tosatti E 2006 J. Phys. A: Math. Gen. 39 R393
7. Das A and Chakrabarti B K (ed) 2005 Quantum Annealing and Related Optimization Methods (Berlin: Springer)
8. Messiah A 1976 Quantum Mechanics Vol II (New York: Wiley)
9. Sachdev S 2011 Quantum Phase Transitions (Cambridge: Cambridge University Press)
10. Mitchell D, Selman B and Levesque H 1992 Proc. 10th National Conf. on Artificial Intelligence p459
11. Mézard M and Montanari A 2009 Information, Physics and Computation (New York: Oxford University Press)
12. Biroli G, Monasson R and Weigt M 2000 Eur. Phys. J. B 14 551
13. Mézard M, Parisi G and Zecchina R 2002 Science 297 812 (Pubitemid 34839626)
14. Krzakala F, Montanari A, Ricci-Tersenghi F, Semerjian G and Zdeborova L 2007 Proc. Nat. Acad. Sci. 104 10318 (Pubitemid 47185663)
15. Laumann C, Scardicchio A and Sondhi S L 2008 Phys. Rev. B 78 134424
16. Krzakala F, Rosso A, Semerjian G and Zamponi F 2008 Phys. Rev. B 78 134428
17. Jörg T, Krzakala F, Semerjian G and Zamponi F 2010 Phys. Rev. Lett. 104 207206
18. Young A P, Knysh S and Smelyanskiy V N 2010 Phys. Rev. Lett. 104 020502
19. Goldschmidt Y Y 1990 Phys. Rev. B 41 4858
20. Nieuwenhuizen T M and Ritort F 1998 Physica A 250 8
21. Biroli G and Cugliandolo L F 2001 Phys. Rev. B 64 014206
22. Jörg T, Krzakala F, Kurchan J and Maggs A C 2008 Phys. Rev. Lett. 101 147204
23. Dziarmaga J 2010 Adv. Phys. 59 1063
24. Vazirani V 2010 Approximation Algorithms (Berlin: Springer)
25. Håstad J 2001 J. ACM 48 798
26. Arora S, Lund C, Motwani R, Sudan M and Szegedy M 1998 J. ACM 45 501
27. Aharonov D, Arad I, Landau Z and Vazirani U 2009 Proc. 41st Annual ACM Symp. on Theory of Computing vol 287 p417
28. Hastings M 2012 arXiv:1201.3387
29. Gharibian S and Kempe J 2011 Proc. 26th CCC'11 p178
30. Botet R and Jullien R 1983 Phys. Rev. B 28 3955
31. Vidal J, Mosseri R and Dukelsky J 2004 Phys. Rev. A 69 054101
32. Ribeiro P and Mosseri R 2006 Phys. Rev. A 74 042333 (Pubitemid 44656210)
33. Ribeiro P, Vidal J and Mosseri R 2008 Phys. Rev. E 78 021106
34. Jörg T, Krzakala F, Kurchan J, Maggs A C and Pujos J 2010 Europhys. Lett. 89 40004
35. Filippone M, Dusuel S and Vidal J 2011 Phys. Rev. A 83 022327
36. Seki Y and Nishimori H 2012 Phys. Rev. E 85 051112
37. Caneva T, Fazio R and Santoro G E 2008 Phys. Rev. B 78 104426
38. Solinas P, Ribeiro P and Mosseri R 2008 Phys. Rev. A 78 052329
39. Itin A P and Törmä P 2009 arXiv:0901.4778
40. Itin A P and Törmä P 2009 Phys. Rev. A 79 055602
41. Vidal J, Palacios G and Aslangul C 2004 Phys. Rev. A 70 062304 (Pubitemid 40213808)
42. Das A, Sengupta K, Sen D and Chakrabarti B K 2006 Phys. Rev. B 74 144423 (Pubitemid 44631172)
43. Sciolla B and Biroli G 2011 J. Stat. Mech. P11003
44. Ribeiro P and Paul T 2009 Phys. Rev. A 79 032107
45. Lipkin H, Meshkov N and Glick A 1965 Nucl. Phys. 62 188
46. Chayes L, Crawford N, Ioffe D and Levit A 2008 J. Stat. Phys. 133 131
47. Brout R, Müller K A and Thomas H 1966 Solid State Commun. 4 507
48. Wilms J, Vidal J, Verstraete F and Dusuel S 2012 J. Stat. Mech. P01023
49. Fulton W and Harris J 1991 Representation Theory - A First Course (New York: Springer)
50. Lieb E and Mattis D 1962 J. Math. Phys. 3 749
51. Nachtergaele B, Spitzer W and Starr S 2004 J. Stat. Phys. 116 719 (Pubitemid 39129794)
52. Newman C M and Schulman L S 1977 J. Math. Phys. 18 23
53. Reed M and Simon B 1978 Methods of Modern Mathematical Physics IV: Analysis of Operators (New York: Academic)
54. Ulyanov V V and Zaslavskii O B 1992 Phys. Rep. 216 179
55. Derrida B and Rodgers G J 1993 J. Phys. A: Math. Gen. 26 L457
56. Krzakala F private communication
57. Dusuel S and Vidal J 2005 Phys. Rev. B 71 224420 (Pubitemid 41717918)
58. Landau L D 1932 Phys. Sov. Union 2 46
59. Zener C 1932 Proc. R. Soc. Lond. 137 696
60. Rojo A G 2010 arXiv:1004.2914
61. Wittig C 2005 J. Phys. Chem. B 109 8428 (Pubitemid 40680371)
62. Volkov M V and Ostrovsky V N 2007 Phys. Rev. A 75 022105 (Pubitemid 46294511)
63. Vitanov N V and Garraway B M 1996 Phys. Rev. A 53 4288
64. Vitanov N V 1999 Phys. Rev. A 59 988
65. Santoro G E, Marton R, Tosatti E and Car R 2002 Science 295 2427 (Pubitemid 34270251)
66. Arbenz P, Gander W and Golub G H 1988 Linear Algebr. Appl. 104 75
67. Farhi E, Goldstone J, Gutmann S and Nagaj D 2008 Int. J. Quantum Comput. 6 503
68. Grover L K 1997 Phys. Rev. Lett. 79 325
69. Roland J and Cerf N J 2002 Phys. Rev. A 65 042308
70. Schiró M and Fabrizio M 2010 Phys. Rev. Lett. 105 076401
71. Arnold V, Kozlov V and Neishtadt A 2006 Mathematical Aspects of Classical and Celestial Mechanics 3rd edn (Berlin: Springer)
72. Kevorkian J 1987 SIAM Rev. 29 391
73. Diminnie D C and Haberman R 2000 J. Nonlinear Sci. 10 197
74. Joshi N and Kitaev A V 2001 Stud. Appl. Math. 107 253
75. Boutroux P 1913 Ann. Ecole Norm. 30 265
76. Heiss W D, Scholtz F G and Geyer H B 2005 J. Phys. A: Math. Gen. 38 1843 (Pubitemid 40344829)
77. Zdeborová L and Krzakala F 2010 Phys. Rev. B 81 224205
78. Franz S and Parisi G 1995 J. Physique I 5 1401
79. Farhi E et al 2011 Quantum Inf. Comput. 11 181
80. Laumann C R, Moessner R, Scardicchio A and Sondhi S L 2012 arXiv:1202.3646
81. Huyghebaert J and Raedt H D 1990 J. Phys. A: Math. Gen. 23 5777
82. Poulin D, Quarry A, Somma R and Verstraete F 2011 Phys. Rev. Lett. 106 170501