Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Journal of Magnetic Resonance

Volumn 177, Issue 2, 2005, Pages 285-298

  Mitra, Avik ^a   Ghosh, Arindam ^a   Das, Ranabir ^a,b   Patel, Apoorva ^a   Kumar, Anil ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b NATIONAL CANCER INSTITUTE   (United States)

Author keywords

Deutsch Jozsa algorithm; Grover's search algorithm; Local adiabatic evolution; NMR; Quantum information processing

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; GROUND STATE; HAMILTONIANS; INFORMATION ANALYSIS; NUCLEAR MAGNETIC RESONANCE; PROBLEM SOLVING;

DEUTSCH-JOZSA ALGORITHM; GROVER'S SEARCH ALGORITHM; LOCAL ADIABATIC EVOLUTION; QUANTUM INFORMATION PROCESSING;

QUANTUM THEORY;

EID: 28044466876     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2005.08.004     Document Type: Article

References (39)

1. J. Preskill, Lecture Notes for Physics 229: Quantum Information and Computation. 〈http://theory.caltech.edu/people/preskill 〉.
2. S. Lloyd Universal quantum simulators Science 273 1996 1073
3. D. Deutsch, and R. Jozsa Rapid solutions of problems by quantum computation Proc. R. Soc. Lond. A 439 1992 553
4. L.K. Grover Quantum mechanics helps in searching for a needle in a haystack Phys. Rev. Lett. 79 1997 325
5. P.W. Shor Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer SIAM Rev. 41 1999 303
6. T. Hogg Highly structured searches with quantum computers Phys. Rev. Lett. 80 1998 2473
7. E. Berstein, and U. Vazirani Quantum complexity theory SIAM J. Comput. 26 1997 1411
8. M. Boyer, G. Brassard, P. Hoyer, and A. Tapp Tight bounds on quantum searching Fortschr. Phys. 46 1998 493
9. D. Bouwnmeester A. Ekert A. Zeilinger The Physics of Quantum Information 2000 Springer Berlin
10. D.G. Cory, A.F. Fahmy, and T.F. Havel Ensemble quantum computing by NMR spectroscopy Proc. Natl. Acad. Sci. USA 94 1997 1634
11. N. Gershenfeld, and I.L. Chuang Bulk spin-resonance quantum computation Science 275 1997 350
12. D.G. Cory, M.D. Price, and T.F. Havel Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing Phys. D 120 1998 82
13. I.L. Chuang, L.M.K. Vanderspyen, X. Zhou, D.W. Leung, and S. Llyod Experimental realization of a quantum algorithm Nature 393 1998 143
14. J.A. Jones, and M. Mosca Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer J. Chem. Phys. 109 1998 1648
15. I.L. Chuang, N. Gershenfeld, and M. Kubinec Experimental implementation of fast quantum searching Phys. Rev. Lett. 80 1998 3408
16. J.A. Jones, M. Mosca, and R.H. Hansen Implementation of a quantum search algorithm on a quantum computerm Nature 393 1998 344
17. K. Dorai, T.S. Mahesh, Arvind, and A. Kumar Quantum computation using NMR Curr. Sci. 79 2000 1447
18. K. Dorai, Arvind, and A. Kumar Implementing quantum-logic operations, pseudopure states and the Deutsch-Jozsa algorithm using noncommuting selective pulses in NMR Phys. Rev. A 61 2000 042306
19. N. Sinha, T.S. Mahesh, K.V. Ramanathan, and A. Kumar Toward quantum information processing by nuclear magnetic resonance: pseudopure states and logical operations using selective pulses on an oriented spin 3/2 nucleus J. Chem. Phys. 114 2001 4415
20. L.M.K. Vanderspyen, M. Steffen, G. Breyta, C.S. Yannoni, M.H. Sherwood, and I.L. Chuang Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance Nature 414 2001 883
21. R. Das, and A. Kumar Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm Phys. Rev. A 68 2003 032304
22. R. Das, A. Mitra, S. Vijaykumar, and A. Kumar Quantum information processing by NMR: preparation of pseudopure states and implementation of unitary operations in a single-qutrit system Int. J. Quant. Infor. 1 3 2003 387
23. R. Das, S. Chakraborty, K. Rukmani, and A. Kumar Search for optimum labeling schemes in qubit systems for quantum-information processing by nuclear magnetic resonance Phys. Rev. A 70 2004 012314
24. R. Das, T.S. Mahesh, and A. Kumar Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique Phys. Rev. A. 67 2003 062304
25. E. Farhi, J. Goldstone, S. Guttmann, M. Sipser, Quantum computation by adiabatic evolution. Available from: 〈quant-ph/0001106 〉.
26. A.M. Childs, E. Farhi, and J. Preskill Robustness of adiabatic quantum computation Phys. Rev. A 65 2002 012322
27. E. Farhi, J. Goldstone, S. Guttmann, J. Lapan, A. Lundgren, and D. Preda A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem Science 292 2001 472
28. A.M. Childs, E. Farhi, J. Goldstone, and S. Guttmann Finding cliques by quantum adiabatic evolution Quant. Inform. Comput. 2 2002 181
29. E. Farhi, J. Goldstone, S. Guttmann, A numerical study of the performance of a quantum adiabatic evolution algorithm for satisfiability. Available from: 〈quant-ph/0007071〉.
30. E. Farhi, J. Goldstone, S. Guttmann, Quantum adiabatic evolution algorithms with different paths. Available from: 〈quant-ph/0208135〉.
31. M.R. Garey, D.S. Jhonson, and L. Stockmeyer Some simplified NP-complete graph problems Theor. Comput. Sci. 1 1976 237
32. M. Steffen, W. van Dam, T. Hogg, G. Bryeta, and I. Chuang Experimental implementation of an adiabatic quantum optimization algorithm Phys. Rev. Lett 90 2003 067903
33. J. Roland, and N.J. Cerf Quantum search by local adiabatic evolution Phys. Rev. A 65 2002 042308
34. S. Das, R. Kobes, and G. Kunstatter Adiabatic quantum computation and Deutsch's algorithm Phys. Rev. A 65 2002 062310
35. A. Messiah, Quantum Mechanics, vol. II, Wiley, New York, 1976.
36. Wim van Dam, M. Mosca, U. Vazirani, How powerful is adiabatic quantum computation? in: Proceedings of the 42nd Annual Symposium on Foundations in Coumputer Science, 2001, pp. 279-287.
37. J. Du, P. Zou, M. Shi, L.C. Kwek, J.-W. Pan, C.H. Oh, A. Ekert, D.K.L. Oi, and M. Ericsson Observation of geometric phases for mixed states using NMR interferometry Phys. Rev. Lett. 91 2003 100403
38. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery Numerical Recipies second ed. 1993 Cambridge University Press Cambridge UK
39. R.R. Ernst, G. Bodenhausen, and A. Wokaun Principles of Nuclear Magnetic Resonance in One and Two Dimensions 1994 Clarendon Press Oxford