2026-09-20T15:57:36Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/476602021-07-05T14:03:20Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
David Cory.
Dunlop, Amy E. (Amy Elizabeth), 1973-
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
2009-10-01T15:30:14Z
2009-10-01T15:30:14Z
1998
1998
http://hdl.handle.net/1721.1/47660
42138971
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1998.
Includes bibliographical references (leaves 32-33).
NMR experiments implementing two-bit controlled-NOT logic gates on alanine (JAB = 35.1 Hz) and 2,3- dibromothiophene (JAB = 5.6 Hz) were performed. Spectra were collected at a variety of tip angles (angles between the spin and the axis of magnetization) by applying a selective RF pulse of constant power and variable duration. From this collection of spectra, the effective Hamiltonian of the spin system was derived and found to contain an internal Hamiltonian. In a spin system with weak coupling, the internal Hamiltonian contains spin-spin coupling terms. The effective Hamiltonian gives a more complete description than the currently used transition Hamiltonian. Understanding the dynamics of a spin system not only furthers the field of NMR but has application in the subject of quantum computing. NMR pulse sequences for four-, eight- and 16-spin controlled-NOT logic gates were developed. A pattern is evident and the pulse sequence for any number of spins can be derived. Disregarding the differences in the spin-spin coupling constants of different spin systems, these results suggest that the total time to implement a controlled-NOT logic gate in NMR does not increase exponentially with the number of spins in the system.
by aMy e dunlop.
S.M.
33 leaves
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Nuclear Engineering
Dynamics and NMR implementation of controlled-NOT gates for quantum computing
Thesis
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<Abstract>NMR experiments implementing two-bit controlled-NOT logic gates on alanine (JAB = 35.1 Hz) and 2,3- dibromothiophene (JAB = 5.6 Hz) were performed. Spectra were collected at a variety of tip angles (angles between the spin and the axis of magnetization) by applying a selective RF pulse of constant power and variable duration. From this collection of spectra, the effective Hamiltonian of the spin system was derived and found to contain an internal Hamiltonian. In a spin system with weak coupling, the internal Hamiltonian contains spin-spin coupling terms. The effective Hamiltonian gives a more complete description than the currently used transition Hamiltonian. Understanding the dynamics of a spin system not only furthers the field of NMR but has application in the subject of quantum computing. NMR pulse sequences for four-, eight- and 16-spin controlled-NOT logic gates were developed. A pattern is evident and the pulse sequence for any number of spins can be derived. Disregarding the differences in the spin-spin coupling constants of different spin systems, these results suggest that the total time to implement a controlled-NOT logic gate in NMR does not increase exponentially with the number of spins in the system.</Abstract>
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