Non-Hermitian quantum annealing in the ferromagnetic Ising model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 87, Issue 4, 2013, Pages

  Nesterov, Alexander I ^a   Zepeda, Juan Carlos Beas ^a   Berman, Gennady P ^b  

^a UNIVERSITY OF GUADALAJARA   (Mexico)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANNEALING TIME; FAST SOLUTIONS; FERROMAGNETIC ISING MODELS; NUMERICAL RESULTS; QUANTUM ALGORITHMS; QUANTUM ANNEALING; QUANTUM OPTIMIZATION;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; FERROMAGNETISM; ISING MODEL; QUANTUM THEORY;

FERROMAGNETIC MATERIALS;

EID: 84877768534     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.87.042332     Document Type: Article

References (51)

1. T. Kadowaki and H. Nishimori, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.58.5355 58, 5355 (1998).
2. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science SCIEAS 0036-8075 10.1126/science.1057726 292, 472 (2001).
3. S. Suzuki and M. Okada, in Quantum Annealing and Related Optimization Methods, edited by, A. Das, and, B. K. Chakrabarti, (Springer, Berlin, Heidelberg, 2005), Vol. 679 of Lecture Notes in Physics, pp. 207-238.
4. A. Das and B. K. Chakrabarti, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.1061 80, 1061 (2008).
5. G. E. Santoro, R. Martonak, E. Tosatti, and R. Car, Science SCIEAS 0036-8075 10.1126/science.1068774 295, 2427 (2002). (Pubitemid 34270251)
6. M. Ohzeki and H. Nishimori, J. Comput. Theor. Nanosci. 1546-1955 10.1166/jctn.2011.1776963 8, 963 (2011).
7. S. Tanaka and R. Tamura, in Lectures on Quantum Computing, Thermodynamics, and Statistical Physics, edited by, M. Nakahara, and, S. Tanaka, (World Scientific, Singapore, 2012), Vol. 8 of Kinki University Series on Quantum Computing, pp. 3-62.
8. L. Stella, G. E. Santoro, and E. Tosatti, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.014303 72, 014303 (2005).
9. S. Suzuki, H. Nishimori, and M. Suzuki, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.051112 75, 051112 (2007). (Pubitemid 47000995)
10. M. H. S. Amin, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.100.130503 100, 130503 (2008). (Pubitemid 351503197)
11. V. N. Smelyanskiy, U. v Toussaint, and D. A. Timucin, arXiv: quant-ph/0202155.
12. T. Jörg, F. Krzakala, J. Kurchan, and A. C. Maggs, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.101.147204 101, 147204 (2008).
13. A. P. Young, S. Knysh, and V. N. Smelyanskiy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.170503 101, 170503 (2008).
14. G. P. Berman and A. I. Nesterov, Int. J. Quantum Inf. 0219-7499 10.1142/S0219749909005961 7, 1469 (2009).
15. A. I. Nesterov and G. P. Berman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.86.052316 86, 052316 (2012).
16. M. V. Berry, Proc. R. Soc. A 1364-5021 10.1098/rspa.1984.0023 392, 45 (1984).
17. M. V. Berry and M. Wilkinson, Proc. R. Soc. A 1364-5021 10.1098/rspa.1984.0022 392, 15 (1984).
18. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
19. A. P. Seyranian, O. N. Kirillov, and A. A. Mailybaev, J. Phys. A: Math. Gen. 1361-6447 10.1088/0305-4470/38/8/009 38, 1723 (2005). (Pubitemid 40306594)
20. O. N. Kirillov, A. A. Mailybaev, and A. P. Seyranian, J. Phys. A 1361-6447 10.1088/0305-4470/38/24/007 38, 5531 (2005). (Pubitemid 40763895)
21. A. A. Mailybaev, O. N. Kirillov, and A. P. Seyranian, Dokl. Math. 1064-5624 10.1134/S1064562406010352 73, 129 (2006).
22. S. Katsura, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.127.1508 127, 1508 (1962).
23. J. Dziarmaga, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 245701 95, 245701 (2005). (Pubitemid 43272890)
24. A. C. M. Carollo and J. K. Pachos, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.157203 95, 157203 (2005). (Pubitemid 41777535)
25. A. I. Nesterov and S. G. Ovchinnikov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.015202 78, 015202 (R) (2008).
26. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(61)90115-4 16, 407 (1961).
27. M. N. Lebedev, Special Functions & Their Applications (Dover, New York, 1972).
28. L. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1958).
29. C. Zener, Proc. R. Soc. A 1364-5021 10.1098/rspa.1932.0165 137, 696 (1932).
30. M. V. Berry, Proc. R. Soc. A 1364-5021 10.1098/rspa.1990.0096 430, 405 (1990).
31. A. Joye, G. Mileti, and C.-E. Pfister, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.4280 44, 4280 (1991).
32. H. K. A. Joye and C. E. Pfister, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(91)90297-L 208, 299 (1991).
33. A. Kvitsinsky and S. Putterman, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.529294 32, 1403 (1991).
34. R. Schilling, M. Vogelsberger, and D. A. Garanin, J. Phys. A 1361-6447 10.1088/0305-4470/39/44/008 39, 13727 (2006).
35. G. Dridi, S. Guérin, H. R. Jauslin, D. Viennot, and G. Jolicard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.022109 82, 022109 (2010).
36. A. M. Dykhne, Sov. Phys. JETP 14, 941 (1962).
37. J. P. Davis and P. Pechukas, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.432648 64, 3129 (1976).
38. J.-T. Hwang and P. Pechukas, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.434630 67, 4640 (1977).
39. S. Suzuki and M. Okada, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.1649 74, 1649 (2005). (Pubitemid 40935156)
40. T. Caneva, R. Fazio, and G. E. Santoro, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.144427 76, 144427 (2007).
41. A. Erdélyi, W. Magnusand, and F. Oberhettinger, Higher Transcendental Functions, Vol. I (McGraw-Hill, New York, 1953).
42. W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.105701 95, 105701 (2005). (Pubitemid 41505777)
43. J. Roland and N. J. Cerf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042308 65, 042308 (2002).
44. M. Ohzeki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105. 050401 105, 050401 (2010).
45. M. Ohzeki and H. Nishimori, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/j.cpc.2010.07.008 182, 257 (2011).
46. F. W. J. Olver, J. Res. Natl. Bur. Stand. B 63B, 131 (1959).
47. N. V. Vitanov and B. M. Garraway, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.4288 53, 4288 (1996).
48. S. R. White and A. E. Feiguin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.076401 93, 076401 (2004).
49. S. Utsunomiya, K. Takata, and Y. Yamamoto, Opt. Express OPEXFF 1094-4087 10.1364/OE.19.018091 19, 18091 (2011).
50. K. Takata, S. Utsunomiya, and Y. Yamamoto, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/14/1/013052 14, 013052 (2012).
51. k ≈ 1 - φ k 2 / 2 leads to omission of corrections to the formula up to O (δ / g).