Abstract
The idea of quantum annealing (QA) is a late offspring of the celebrated simulated thermal annealing by Kirkpatrick et al. [1]. In simulated annealing, the problem of minimizing a certain cost (or energy) function in a large configuration space is tackled by the introduction of a fictitious temperature, which is slowly lowered in the course of a Monte Carlo or Molecular Dynamics simulation [1]. This device allows an exploration of the configuration space of the problem at hand, effectively avoiding trapping at unfavorable local minima through thermal hopping above energy barriers. It makes for a very robust and effective minimization tool, often much more effective than standard, gradient-based, minimization methods.
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References
S. Kirkpatrick, C.D. Gelatt, Jr., M.P. Vecchi, Science 220, 671 (1983);
A.B. Finnila, M.A. Gomez, C. Sebenik, C. Stenson, J.D. Doll, Chem. Phys. Lett. 219, 343 (1994).
T. Kadowaki, H. Nishimori: Phys. Rev. E 58, 5355 (1998).
J. Brooke, D. Bitko, T.F. Rosenbaum, G. Aeppli: Science 284, 779 (1999).
G. Santoro, R. Martoňák, E. Tosatti, R. Car: Science 295, 2427 (2002).
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, D. Preda: Science 292, 472 (2001).
L. Stella, G. E. Santoro, and E.Tosatti: to appear on Phys. Rev. B; preprint cond-mat/0502129
Y.H. Lee, B.J. Berne: J. Phys. Chem. A 104, 86 (2000).
Y.H. Lee, B.J. Berne: J. Phys. Chem. A 105, 459 (2001).
R. Martoňák, G. Santoro, E. Tosatti: Phys. Rev. B 66, 94203 (2002).
R. Martoňák, G.E. Santoro, E. Tosatti: Phys. Rev. E 70, 057701 (2004).
D. Battaglia, G. Santoro, E. Tosatti: to appear on PRE; preprint cond-mat/0502468.
P.F. Stadler and W. Schnabl: Phys. Lett. A 161, 337 (1992).
L. Stella, G.E. Santoro, and E. Tosatti: in preparation.
N.G. van Kampen: Stochastic processes in physics and chemistry, North-Holland, Amsterdam (1987).
D.A. Huse, D.S. Fisher: Phys. Rev. Lett. 57, 2203 (1986).
L.D. Landau: Phys. Z. Sowjetunion 2, 46 (1932).
C. Zener: Proc. Royal Soc. A 137, 696 (1932).
S. Shinomoto and Y. Kabashima: J. Phys. A 24 L141 (1991); Y. Kabashima and S. Shinomoto: J. Phys. Soc. Japan 60 3993 (1991).
P.A. Lee and T.V. Ramakrishnan: Rev. Mod. Phys. 57, 287 (1985).
M. Suzuki: Prog. Theor. Phys. 56, 1454 (1976).
C.H. Papadimitriou: Combinatorial Optimization: Algorithms and Complexity (Dover, NY 1998).
H. Nishimori: Statistical Physics of Spin Glasses and Information Processing (Oxford University Press, 2001).
Special Issue on NP-hardness and Phase transitions, ed. by O. Dubois, R. Monasson, B. Selman and R. Zecchina, Theor. Comp. Sci. 265, Issue: 1-2 (2001).
J.J. Hopfield and D.W. Tank: Science 233, 625 (1986).
M. Mézard, G. Parisi: Europhys. Lett. 2, 913 (1986)
A.G. Percus, O.C. Martin: Jour. Stat. Phys. 94, 739-758 (1999).
D.S. Dean, D. Lancaster, S.N. Majumdar: J. Stat. Mech. L01001 (2005).
M. Mézard, G. Parisi, R. Zecchina, Science 297, 812 (2002);
M. Mezard, R. Zecchina: Phys. Rev. E 66, 56126 (2002).
S. Mertens: Phys. Rev. Lett. 81, 4281- 4284 (1988).
M. Weigt, A.K. Hartmann: Phys. Rev. Lett. 84, 6118 (2000)
A. Braunstein, R. Mulet, A. Pagnani, M. Weigt, R. Zecchina: Phys. Rev. E 68, 036702 (2003)
G. Parisi, M. Mézard, M.Virasoro: Spin Glass Theory and Beyond (World Scientific, Singapore 1987).
C. H. Papadimitriou, K. Steiglitz: Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, NJ, 1982).
M.R. Garey, D.S. Johnson: Computers and Intractability (Freeman, New York 1979).
D. Mitchell, B. Selman, H. Levesque: Hard and Easy Distribution of SAT Problems. In: Proc. of the Tenth National Conference on Artificial Intelligence, (AAAI-Press, 1992), p. 459.
M. Mezard, F. Ricci-Tersenghi, R. Zecchina: J. Stat. Phys 111, 505 (2003).
F. Barahona: J. Phys. A 15, 3241 (1982).
C. De Simone et al.: J. Stat. Phys. 80, 487 (1995).
D.S. Johnson and L.A. McGeoch: In Local Search in Combinatorial Optimization, ed. E.H.L. Aarts and J.K. Lenstra (J. Wiley and Sons, London, 1997, pp. 215-310).
P. F. Stadler: Towards a Theory of Landscapes. In: Complex Systems and Binary Networks, ed. by R. Lopez-Pena, R. Capovilla, R. Garca-Pelayo, H. Waelbroeck, and F. Zertuche (Springer Verlag, Berlin, New York 1995), pp. 77-163.
See http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95
See http://www.intellektik.informatik.tu-darmstadt.de/SATLIB/
D. Battaglia, M. Kolář, R. Zecchina: Phys. Rev. E 70, 036107 (2004).
A. Montanari, G. Parisi, and F. Ricci-Tersenghi: J. Phys. A 37, 2073 (2004).
Z. Michalewicz: Genetic algorithms + data structures = evolution programs, 3rd ed. (Springer-Verlag, Berlin 1996).
J.R. Koza: Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge MA, 1992).
J.H. Holland: Proc. Int. Un. Physiol. Soc. 3, 330 (1962).
J.H. Holland: Processing and Processors for schemata. In: Associative Information Processing (American Elsevier, New York 1971).
J.P. Bouchaud, V. Dupuis, J. Hammann, E. Vincent: Phys. Rev. B 65, 24439 (2001).
A. Montanari and R. Zecchina: Phys. Rev. Lett. 88, 178701 (2002).
M. Takahashi and M. Imada: J. Phys. Soc. Jpn. 53, 3765 (1984).
D. M. Ceperley: Rev. Mod. Phys. 67, 275 (1995).
J.W. Negele and H. Orland: Quantum Many-Particle Systems (Addison-Wesley, 1988)
B. Selman, H. Kautz and B. Cohen: In: Proc. AAAI-94 (AAAI Press, Seattle WA 1994), pp. 337-343.
S. Seitz, P. Orponen: An efficient local search method for random 3-satisfiability. In: Proc. LICS'03 Workshop on Typical Case Complexity and Phase Transitions (Ottawa, Canada, 2003); Electronic Notes in Discrete Mathematics Vol. 16 (Elsevier, Amsterdam, 2003).
S. Boettcher, A. Percus: Phys. Rev. Lett. 86, 5211 (2001).
N. Trivedi and D. M. Ceperley: Phys. Rev. B 41, 4552 (1990).
G. Santoro, S. Sorella, L. Guidoni, A. Parola, and E. Tosatti: Phys. Rev. Lett. 83, 3065 (1999).
L. Onsager: J. Am. Chem. Soc. 58, 1486 (1936).
A. Braunstein, M. Mézard, R. Zecchina: Survey propagation: an algorithm for satisfiability. To appear in Random Structures and Algorithms; preprint cs.CC/0212002
D. Battaglia, A. Braunstein, J. Chavas, R. Zecchina: Source coding by efficient selection of ground states clusters, preprint cond-mat/0412652.
J.S. Yedidia, W.T. Freeman and Y. Weiss: Generalized Belief Propagation. In: Advances in Neural Information Processing Systems 13 (MIT press 2001), pp. 689-695.
F. R. Kschischang, B. J. Frey, and H.-A. Loeliger: IEEE Trans. Inf. Theory 47, 498 (2002).
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Battaglia, D., Stella, L., Zagordi, O., E. Santoro, G., Tosatti, E. Deterministic and Stochastic Quantum Annealing Approaches. In: Das, A., K. Chakrabarti, B. (eds) Quantum Annealing and Other Optimization Methods. Lecture Notes in Physics, vol 679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526216_7
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