Dynamics and NMR implementation of controlled-NOT gates for quantum computing

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Nuclear Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

1998

Author dc:creator

• Dunlop, Amy E. (Amy Elizabeth), 1973-

Advisor dc:contributor.advisor

• David Cory.

• Nuclear Engineering

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/47660

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/47660