Theory of Quantum Annealing of an Ising Spin Glass

Santoro, Giuseppe E.; Martoňák, Roman; Tosatti, Erio; Car, Roberto

doi:10.1126/science.1068774

Theory of Quantum Annealing of an Ising Spin Glass

Giuseppe E. Santoro
(
- SISSA, Trieste
)
,
Roman Martoňák
(
- Zurich, ETH and
- Bratislava, Slovak Tech. U.
)
,
Erio Tosatti
(
- SISSA, Trieste and
- ICTP, Trieste
)
,
Roberto Car
(
- Princeton U.
)

Mar 29, 2002

4 pages

Published in:

Science 295 (2002) 5564, 2427-2430

Published: Mar 29, 2002

DOI:

10.1126/science.1068774

reference search207 citations

Citations per year

Abstract: (American Association for the Advancement of Science)

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power that makes it faster.

References(24)

Figures(0)

[1]

Optimization by Simulated Annealing

- Science 220 (1983) 671-680
•
DOI:
- 10.1126/science.220.4598.671

[2]

Černý V

J. Opt

[3]

Huse D. A.
,
Fisher D. S.

- Phys.Rev.Lett. 57 (1986) 2203

[4]

Quantum Annealing of a Disordered Magnet

- Science 284 (1999) 5415, 779-781
•
DOI:
- 10.1126/science.284.5415.779

[5]

Brooke J.
,
Rosenbaum T. F.
,
Aeppli G.

- Nature 413 (2001) 610

[6]

Quantum annealing: A new method for minimizing multidimensional functions

- Chem.Phys.Lett. 219 (1994) 5-6, 343-348
•
DOI:
- 10.1016/0009-2614(94)00117-0

[7]

Quantum annealing in the transverse Ising model

- Phys.Rev.E 58 (1998) 5, 5355,
- Phys.Rev.E 58 (1998) 5355
•
e-Print:
- cond-mat/9804280
•
DOI:
- 10.1103/PhysRevE.58.5355

[8]

Lee Y. H.
,
Berne B. J.

- J.Phys.Chem.A 104 (2000) 86

[9]

___

- J.Phys.Chem.A 105 (2001) 459

[10]

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

et al.

- Science 292 (2001) 5516, 1057726
•
DOI:
- 10.1126/science.1057726

[11]

Grest G. S.
,
Soukoulis C. M.
,
Levin K.

- Phys.Rev.Lett. 56 (1986) 1148

[12]

Chakrabarti A.
,
Toral R.

- Phys.Rev.B 39 (1989) 542

[13]

Ocampo-Alfaro P.
,
Guo H.

- Phys.Rev.B 53 (1996) 1982

[14]

On the computational complexity of Ising spin glass models

F. Barahona

- J.Phys.A 15 (1982) 10, 3241
•
DOI:
- 10.1088/0305-4470/15/10/028

[15]

For each set of couplings, EGS is calculated using the Spin Glass Ground State Server at

[16]

Ordered Phase of Short-Range Ising Spin-Glasses

Daniel S. Fisher
(
- Bell Labs
)
,
David A. Huse
(
- Bell Labs
)

- Phys.Rev.Lett. 56 (1986) 1601-1604
•
DOI:
- 10.1103/PhysRevLett.56.1601

[17]

Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations

Masuo Suzuki

- Prog.Theor.Phys. 56 (1976) 5, 1454-1469
•
DOI:
- 10.1143/PTP.56.1454

[18]

Supplementary details of the method are available on Science Online at

[19]

Lieb E.
,
Mattis D.

- J.Math.Phys. 3 (1962) 749

[20]

Rieger H.
,
Young A. P.

- Phys.Rev.Lett. 72 (1994) 4141

[21]

Thill M. J.
,
Huse D. A.

- Physica A 214 (1995) 321

[22]

Wu W

Bitko D.
,
Rosenbaum T. F.
,
Aeppli G.

- Phys.Rev.Lett. 71 (1993) 1919

[23]

Quantum Mechanics—Non-Relativistic Theory

L.D. Landau
,
E.M. Lifshitz

[24]

This project was sponsored by the Ministero dell'Istruzione, dell'Università e della Ricerca under project COFIN, by INFM/G, INFM/F, and by INFM's Iniziativa Trasversale Calcolo

Parallelo. R.M.