Dynamics and NMR implementation of controlled-NOT gates for quantum computing
Name
42138971-MIT.pdf
Description
Full printable version
Size
1.31 MB
Format
Adobe PDF
Checksum (MD5)
5f2124b0c87ee67733c55a7f4ff6d46a
Author(s)
Dunlop, Amy E. (Amy Elizabeth), 1973-
Advisor(s)
David Cory.
Date Issued
1998
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1998.
Includes bibliographical references (leaves 32-33).
Subjects
Nuclear Engineering
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
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