Extracting dynamical equations from experimental data is NP hard

Physical Review Letters

Volumn 108, Issue 12, 2012, Pages

  Cubitt, Toby S ^a   Eisert, Jens ^b   Wolf, Michael M ^c  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL PROBLEMS; DYNAMICAL EQUATION; EMBEDDING PROBLEMS; EXPERIMENTAL DATA; HARD PROBLEMS; NP-HARD; OPEN PROBLEMS; PHYSICAL SYSTEMS; QUANTUM-MECHANICAL SYSTEM;

QUANTUM THEORY;

DYNAMICAL SYSTEMS;

EID: 84859075891     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.108.120503     Document Type: Article

References (23)

1. G. Elfving, Acta Soc. Sci. Fennicae n. Ser. A 2, 1 (1937).
2. S. Cook, www.claymath.org/millennium/P-vs-NP/pvsnp.pdf (2000).
3. L. Ljung, System Identification: Theory for the User (Prentice Hall, Upper Saddle River, NJ, 1999).
4. K. Soutwell Nature (London) NATUAS 0028-0836 453, 1003 (2008). 10.1038/4531003a (Pubitemid 351871698)
5. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
6. M. Nielsen, E. Knill, and R. Laflamme, Nature (London) NATUAS 0028-0836 396, 52 (1998). 10.1038/23891 (Pubitemid 28520443)
7. N. Boulant, T.F. Havel, M.A. Pravia, and D.G. Cory, Phys. Rev. A 67, 042322 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.67.042322
8. M. Riebe, Phys. Rev. Lett. 97, 220407 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.220407 (Pubitemid 44853857)
9. J.L. O'Brien, Phys. Rev. Lett. 93, 080502 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.080502
10. M. Howard, New J. Phys. 8, 33 (2006). NJOPFM 1367-2630 10.1088/1367-2630/8/3/033
11. J.R. Norris, Markov Chains (Cambridge University Press, Cambridge, 1997).
12. G. Lindblad, Commun. Math. Phys. 48, 119 (1976). CMPHAY 0010-3616 10.1007/BF01608499
13. H.J. Carmichael, Statistical Methods in Quantum Optics (Springer, New York, 2003), Vol. 1.
14. V. Gorini, A. Kossakowski, and E.C.G. Sudarshan, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 17, 821 (1976). 10.1063/1.522979
15. M. Howard, New J. Phys. NJOPFM 1367-2630 8, 33 (2006). 10.1088/1367-2630/8/3/033
16. M.M. Wolf and J.I. Cirac, Commun. Math. Phys. 279, 147 (2008). CMPHAY 0010-3616 10.1007/s00220-008-0411-y
17. M.M. Wolf, J. Eisert, T.S. Cubitt, and J.I. Cirac, Phys. Rev. Lett. 101, 150402 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.150402
18. H.-P. Breuer, Phys. Rev. A 75, 022103 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.75.022103
19. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York, 1979).
20. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.108.120503 for more details of the proof.
21. T.S. Cubitt, J. Eisert, and M.M. Wolf, Commun. Math. Phys. CMPHAY 0010-3616 310, 383 (2012). 10.1007/s00220-011-1402-y
22. J.F. C. Kingman, Z. Wahrsch. Verw. Geb. ZWVGAA 0044-3719 1, 14 (1962). 10.1007/BF00531768
23. A. Mukherjea, in Matrix Theory and Applications, edited by, C.R. Johnson, (American Mathematical Society, Providence, RI, 1990).