Colloquium: Quantum annealing and analog quantum computation

Reviews of Modern Physics

Volumn 80, Issue 3, 2008, Pages 1061-1081

  Das, Arnab ^a   Chakrabarti, Bikas K ^a  

^a SAHA INSTITUTE OF NUCLEAR PHYSICS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ANNEALING; ATOMIC PHYSICS; BIOELECTRIC PHENOMENA; CHLORINE COMPOUNDS; COMPUTATIONAL LINGUISTICS; GLASS; QUANTUM COMPUTERS; QUANTUM ELECTRONICS; SPIN DYNAMICS; SPIN FLUCTUATIONS; SPIN GLASS;

ANNEALING BEHAVIOR; CLASSICAL SPIN; COMPLEX SYSTEMS; ENERGY FUNCTIONS; GENERAL FRAMEWORK; HARD PROBLEMS; QUANTUM ANNEALING; QUANTUM COMPUTATIONS; QUANTUM FLUCTUATIONS; QUANTUM SPINS;

QUANTUM THEORY;

EID: 52249083005     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.80.1061     Document Type: Article

References (98)

1. Aeppli, G., and T. F. Rosenbaum, 2005, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg), pp. 159-169.
2. Aharonov, D., W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, 2007, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539705447323 37 166.
3. Alvarez, J. A., and F. Ritort, 1996, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/29/23/006 29, 7355.
4. Amara, P., D. Hsu, and J. E. Straub, 1993, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100127a023 97, 6715.
5. Apolloni, B., C. Carvalho, and D. de Falco, 1989, Stochastic Proc. Appl. STOPB7 0304-4149 10.1016/0304-4149(89)90040-9 33, 233.
6. Apolloni, B., N. Cesa-Bianchi, and D. de Falco, 1990, in Stochastic Processes, Physics and Geometry, edited by, S. Albeverio, (World Scientific, Singapore), p. 97.
7. Barahona, F., 1982, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/15/10/ 028 15, 3241.
8. Battaglia, D. A., G. E. Santoro, and E. Tosatti, 2005, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.066707 71, 066707.
9. Battaglia, D. A., L. Stella, O. Zagordi, G. E. Santoro, and E. Tosatti, 2005, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg), pp. 171-204.
10. Bearwood, J., J. H. Halton, and J. H. Hammersley, 1959, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 55, 299.
11. Bhatt, R. N., 1998, in Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore), pp. 225-249.
12. Binder, K., and A. P. Young, 1986, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.58.801 58, 801.
13. Bray, A. J., and M. A. Moore, 1984, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/18/004 17, L463.
14. Brooke, J., D. Bitko, T. F. Rosenbaum, and G. Aeppli, 1999, Science SCIEAS 0036-8075 10.1126/science.284.5415.779 284, 779.
15. Brooke, J., T. F. Rosenbaum, and G. Aeppli, 2001, Nature (London) NATUAS 0028-0836 10.1038/35098037 413, 610.
16. Calabrese, P., and J. Cardy, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.136801 96, 136801.
17. Chakrabarti, B. K., 1981, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.24.4062 24, 4062.
18. Chakrabarti, B. K., A. Dutta, and P. Sen, 1996, Quantum Ising Phases and Transitions in Transverse Ising Models (Springer-Verlag, Heidelberg).
19. Chakraborti, A., and B. K. Chakrabarti, 2000, Eur. Phys. J. B EPJBFY 1434-6028 16, 667.
20. Childs, A. M., and J. Goldstone, 2004, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022314 70, 022314.
21. Das, A., 2007, unpublished (see also Ph.D. thesis, Jadavpur University, Kolkata, 2008).
22. Das, A., and, B. K. Chakrabarti, 2005, Eds., Quantum Annealing and Related Optimization Methods, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg).
23. Das, A., B. K. Chakrabarti, and R. B. Stinchcombe, 2005, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.026701 72, 026701.
24. Das, A., K. Sengupta, D. Sen, and B. K. Chakrabarti, 2006, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.144423 74, 144423.
25. Dotsenko, V., 2001, Introduction to the Replica Theory of Disordered Statistical Systems (Cambridge University Press, Cambridge, UK).
26. Edwards, S. F., and P. W. Anderson, 1975, J. Phys. F: Met. Phys. JPFMAT 0305-4608 10.1088/0305-4608/5/5/017 5, 965.
27. Ekert, A., and R. Jozsa, 1996, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.733 68, 733.
28. Farhi, E., J. Goldstone, and S. Gutmann, 2002a, e-print arXiv:quant-ph/0201031.
29. Farhi, E., J. Goldstone, and S. Gutmann, 2002b, e-print arXiv:quant-ph/0208135.
30. Farhi, E., J. Goldstone, S. Gutmann, J. Lapan, A. Ludgren, and D. Preda, 2001, Science SCIEAS 0036-8075 10.1126/science.1057726 292, 472.
31. Farhi, E., J. Goldstone, S. Gutmann, and M. Sipser, 2000, e-print arXiv:quant-ph/0001106.
32. Farhi, E., and S. Gutmann, 1998, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.2403 57, 2403.
33. Finnila, A. B., M. A. Gomez, C. Sebenik, C. Stenson, and D. J. Doll, 1994, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/0009-2614(94)00117-0 219, 343.
34. Fisher, D. S., and D. A. Huse, 1986, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1601 56, 1601.
35. Fredrickson, G. H., and H. C. Andersen, 1984, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.1244 53, 1244.
36. Fu, Y., and P. W. Anderson, 1986, J. Phys. A JPHAC5 0305-4470 19, 1620.
37. Galindo, A., and M. A. Martin-Delgado, 2002, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.347 74, 347.
38. Garey, M. R., and D. S. Johnson, 1979, Computers and Intractability: Guide to the Theory of NP-Completeness (Freeman, San Francisco).
39. Gaviro, P. S., J. J. Ruiz-Lorenzo, and A. Tarancon, 2006, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/27/001 39, 8567.
40. Geman, S., and D. Geman, 1984, IEEE Trans. Pattern Anal. Mach. Intell. ITPIDJ 0162-8828 6, 721.
41. Goldschmidt, Y. Y., and P.-Y. Lai, 1990, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.2467 64, 2467.
42. Grover, L. K., 1997, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.325 79, 325.
43. Guo, M., R. N. Bhatt, and D. A. Huse, 1994, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.4137 72, 4137.
44. Hartmann, A., and H. Rieger, 2002, Optimization in Physics (Wiley VCH, Darmstadt).
45. Hatano, N., and M. Suzuki, 2005, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg), pp. 37-67.
46. Huse, D. A., and D. S. Fisher, 1986, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.2203 57, 2203.
47. Inoue, J.-I., 2005, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg), pp. 259-296.
48. Ishii, H., and T. Yamamoto, 1985, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/18/33/013 18, 6225.
49. Jackle, J., and S. Eisinger, 1991, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01453764 84, 115.
50. Kadowaki, T., and H. Nishimori, 1998, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.5355 58, 5355.
51. Kibble, T. W. B., 1976, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/9/ 8/029 9, 1387.
52. Kim, D.-H., and J.-J. Kim, 2002, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.054432 66, 054432.
53. Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi, 1983, Science SCIEAS 0036-8075 10.1126/science.220.4598.671 220, 671.
54. Krzakala, F., J. Houdayer, E. Marinari, O. C. Martin, and G. Parisi, 2001, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.197204 87, 197204.
55. Lancaster, D., and F. Ritort, 1997, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/30/4/001 30, L41.
56. Marinari, E., G. Parisi, J. J. Ruiz-Lorenzo, and F. Zuliani, 1998, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5176 82, 5176.
57. Martoňák, R., G. E. Santoro, and E. Tosatti, 2002, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.094203 66, 094203.
58. Martoňák, R., G. E. Santoro, and E. Tosatti, 2004, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.057701 70, 057701.
59. Mezard, M., G. Parisi, and M. A. Virasoro, 1987, Spin Glass Theory and Beyond, Lecture Note in Physics No. 9 (World Scientific, Singapore), and references therein.
60. Miller, J., and D. A. Huse, 1993, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3147 70, 3147.
61. Mizel, A., D. A. Lidar, and M. Mitchell, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.070502 99, 070502.
62. Monasson, R., R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky, 1999, Nature (London) NATUAS 0028-0836 10.1038/22055 400, 133.
63. Moore, M. A., H. Bokil, and B. Drossel, 1998, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4252 81, 4252.
64. Morita, S., 2007, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.76.104001 76, 104001.
65. Morita, S., and H. Nishimori, 2006, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/45/004 39, 13903.
66. Morita, S., and H. Nishimori, 2007, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.76.064002 76, 064002.
67. Mukherjee, V., U. Divakaran, A. Dutta, and D. Sen, 2007, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.174303 76, 174303.
68. Nielsen, M. A., and I. L. Chuang, 2000, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK).
69. Nishimori, H., 2001, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, Oxford).
70. Papadimitriou, C. H., and K. Steiglitz, 1998, Combinatorial Optimization: Algorithm and Complexity (Dover, New York).
71. Parisi, G., 1980, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/3/042 13, 1101.
72. Percus, A., and O. C. Martin, 1996, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1188 76, 1188.
73. Ray, P., B. K. Chakrabarti, and A. Chakrabarti, 1989, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.11828 39, 11828.
74. Rieger, H., 2005, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg), pp. 69-97.
75. Roland, J., and N. J. Cerf, 2001, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042308 65, 042308.
76. Rodriguez-Laguna, J., 2007, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 2007, P05008.
77. Sachdev, S., 1999, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK).
78. Santoro, G. E., R. Martoňák, E. Tosatti, and R. Car, 2002, Science SCIEAS 0036-8075 10.1126/science.1068774 295, 2427.
79. Santoro, G. E., and E. Tosatti, 2006, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/36/R01 39, R393.
80. Santoro, G. E., and E. Tosatti, 2007, Nat. Phys. ZZZZZZ 1745-2473 3, 593.
81. Sarandy, M. S., L.-A. Wu, and D. A. Lidar, 2004, Quantum Inf. Process. QIPUAT 1570-0755 10.1007/s11128-004-7712-7 3, 331.
82. Sarjala, M., V. Petäjä, and M. Alava, 2006, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 2006, PO 1008.
83. Sengupta, K., S. Powell, and S. Sachdev, 2004, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.053616 69, 053616.
84. Sengupta, K., D. Sen, and S. Mondal, 2008, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.077204 100, 077204.
85. Sherrington, D., and S. Kirkpatrick, 1975, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.35.1792 35, 1792.
86. Schechter, M., and N. Laflorencie, 2006, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.137204 97, 137204.
87. Silevitch, D. M., D. Bitko, J. Brooke, S. Ghosh, G. Aeppli, and T. F. Rosenbaum, 2007, Nature (London) NATUAS 0028-0836 10.1038/nature06050 448, 567.
88. Somma, R. D., C. D. Batista, and G. Ortiz, 2007, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.030603 99, 030603.
89. Suzuki, S., H. Nishimori, and M. Suzuki, 2007, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.051112 75, 051112.
90. Suzuki, S., and M. Okada, 2005a, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.1649 74, 1649.
91. Suzuki, S., and M. Okada, 2005b, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, Lecture Notes in Physics No. 679 (Springer-Verlag, Heidelberg).
92. Steffen, M., v. W. Dam, T. Hogg, G. Breyta, and I. Chuang, 2003, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.067903 90, 067903.
93. Stella, L., G. Santoro, and E. A. Tosatti, 2005, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.014303 72, 014303.
94. Thirumalai, D., Q. Li, and T. R. Kirkpatrick, 1989, J. Phys. A JPHAC5 0305-4470 22, 2339.
95. Wu, W., D. Bitko, T. F. Rosenbaum, and G. Aeppli, 1993, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1919 71, 1919.
96. Wu, W., B. Ellman, T. F. Rosenbaum, G. Aeppli, and D. H. Reich, 1991, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.2076 67, 2076.
97. Ye, J., S. Sachdev, and N. Read, 1993, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.4011 70, 4011.
98. Zurek, W. H., 1985, Nature (London) NATUAS 0028-0836 10.1038/317505a0 317, 505.