Anderson localization makes adiabatic quantum optimization fail

Proceedings of the National Academy of Sciences of the United States of America

Volumn 107, Issue 28, 2010, Pages 12446-12450

  Altshuler, Boris ^a,b   Krovi, Hari ^b   Roland, Jérémie ^b  

^a Department of Earth and Environmental Sciences   (United States)

^b NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADIABATICITY; ALGORITHM; ARTICLE; MONTE CARLO METHOD; PRIORITY JOURNAL; QUANTUM CHEMISTRY; QUANTUM MECHANICS; SIMULATION; STATISTICAL DISTRIBUTION;

ALGORITHMS; PHYSICS; PHYSIOLOGICAL PROCESSES; TIME FACTORS;

EID: 77955454198     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1002116107     Document Type: Article

References (26)

1. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman & Co., New York).
2. Arora S, Barak B (2009) Computational Complexity: A Modern Approach (Cambridge Univ Press, Cambridge, UK).
3. Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26:1484-1509.
4. Farhi E, Goldstone J, Gutmann S, Sipser M (2000) Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106.
5. Farhi E, et al. (2001) A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292:472-475. (Pubitemid 32335943)
6. Messiah A (1959) Mécanique Quantique (Dunod, Paris).
7. Aharonov D, van Dam W, Kempe J, Landau Z, Lloyd S (2007) Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J Comput 37(1): 166-194.
8. Žnidarič M, Horvat M (2006) Exponential complexity of an adiabatic algorithm for an np-complete problem. Phys Rev A 73:022329.
9. Farhi E, Goldstone J, Gutmann S, Nagaj D (2008) How to make the quantum adiabatic algorithm fail. Int J Quantum Inf 6:503-516.
10. Reichardt B (2004) The quantum adiabatic optimization algorithm and local minima. Proceedings of the 36th Annual ACM Symposium on Theory of Computing (IEEE, New York), pp 279-287.
11. van Dam W, Mosca M, Vazirani U (2001) How powerful is adiabatic quantum computation? Proceedings of the 42nd Annual IEEE Symposium on the Foundations of Computer Science (IEEE, New York), pp 279-287.
12. Amin MHS, Choi V (2009) First order quantum phase transition in adiabatic quantum computation. Phys Rev A 80:062326.
13. Hogg T (2003) Adiabatic quantum computing for random satisfiability problems. Phys Rev A 67:022314.
14. Bañuls MC, Orús R, Latorre JI, Pérez A, Ruiz-Femenía P (2006) Simulation of many-qubit quantum computation with matrix product states. Phys Rev A 73:022344.
15. Young AP, Knysh S, Smelyanskiy VN (2008) Size dependence of theminimum excitation gap in the quantum adiabatic algorithm. Phys Rev Lett 101:170503.
16. Jörg T, Krzakala F, Kurchan J, Maggs AC (2008) Simple glass models and their quantum annealing. Phys Rev Lett 101:147204.
17. Jörg T, Krzakala F, Semerjian G, Zamponi F (2009) First-order transitions for random optimization problems in a transverse field. arXiv:0911.3438.
18. Farhi E, et al. (2009) Quantum adiabatic algorithms, small gaps, and different paths. arXiv:0909.4766.
19. von Neumann J, Wigner E (1929) No crossing rule. Z Phys 30:467-470.
20. Anderson PW (1958) Absence of diffusion in certain random lattices. Phys Rev 109:1492-1505.
21. Biroli G, Monasson R, Weigt M (2000) A variational description of the ground state structure in random satisfiability problems. Eur Phys J B 14:551-568.
22. Raymond J, Sportiello A, Zdeborová L (2007) Phase diagram of the 1-in-3 satisfiability problem. Phys Rev E 76:011101. (Pubitemid 47146352)
23. Mayer GE, Goeppert-Mayer M (1948) Statistical Mechanics (Wiley, New York).
24. Anderson PW (1992) Local Moments and Localized States. Nobel Lectures, Physics 1971-1980 (World Scientific, Singapore).
25. Efetov K (1988) Effective-medium approximation in localization theory. J Exp Theor Phys 67:199-205.
26. Abou-Chacra R, Thouless DJ, Anderson PW (1973) A selfconsistent theory of localization. J Phys C 6:1734-1752.