Exponential complexity of an adiabatic algorithm for an NP-complete problem

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 2, 2006, Pages

  Žnidarič, Marko ^a,b   Horvat, Martin ^b  

^a UNIVERSITY OF ULM   (Germany)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GROUND STATE; HAMILTONIANS;

EXCITED STATES; EXPONENTIAL COMPLEXITY; QUANTUM ADIABATIC ALGORITHM;

QUANTUM THEORY;

EID: 33144479674     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.022329     Document Type: Article

References (27)

1. P. W. Shor, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by, Shafi Goldwasser, (IEEE Computer Society Press, Los Alamitos, 1994), 124-134.
2. L. K. Grover, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79. 325 79, 325 (1997).
3. Classical algorithms with square-root performance are possible but require exponential memory overhead, see S. Lloyd, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.010301 61 010301 (2000);
4. L. K. Grover and A. M. Sengupta, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032319 65, 032319 (2002).
5. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).
6. S. A. Cook, Millennium Problems (Clay Mathematics Institute, 2000), http://www.claymath.org/millennium;
7. C. Seife, Science SCIEAS 0036-8075 309, 96 (2005).
8. E. Farhi, J. Goldstone, S. Gutman, and M. Sipser, e-print quant-ph/0001106.
9. E. Farhi, J. Goldstone, S. Gutman, J. Lapan, A. Lundgren, and D. Preda, Science SCIEAS 0036-8075 292, 472-476 (2001).
10. V. N. Smelyanskiy, U. V. Toussaint, and D. A. Timucin, e-print quant-ph/0112143.
11. T. Hogg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022314 67, 022314 (2003).
12. M. Žnidarič, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.062305 71, 062305 (2005).
13. W. van Dam, M. Mosca, and U. Vazirani, Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (IEEE, New York, 2001), pp. 279-287.
14. B. W. Reichardt, Proceedings of the 36th Annual ACM Symposium on Theory of Computing (ACM Press, New York, 2004), pp. 502-510.
15. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.2403 57, 2403 (1998).
16. J. Roland and N. J. Cerf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042308 65, 042308 (2002).
17. A. Boulatov and V. N. Smelyanskiy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052309 71, 052309 (2005);
18. D. R. Mitchell, C. Adami, W. Lue, and C. P. Williams, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052324 71, 052324 (2005).
19. M. Žnidarič, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.052336 72, 052336 (2005).
20. G. Schaller, S. Mostame, and R. Schützhold, e-print quant-ph/0510183.
21. R. Monasson and R. Zecchina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3881 76, 3881 (1996).
22. M. Žnidarič, e-print cs.AI/0504101.
23. M. Žnidarič, e-print math.ST/0511226.
24. E. Farhi, J. Goldstone, and S. Gutmann (private communication).
25. E. Farhi, J. Goldstone, and S. Gutmann, e-print quant-ph/0208135.
26. P. W. Shor, Quantum Inf. Process. QIPUAT 1570-0755 10.1007/s11128-004- 3878-2 3, 5 (2004).
27. E. Farhi, J. Goldstone, S. Gutmann, and D. Nagaj, e-print quant-ph/0512159.