NMR quantum computing

Abstract:

It is shown how Cramér-Rao theory may be used to determine the optimal sampling pattern for measuring the NMR spin-spin relaxation time, T2. The results may also be applied to the measurement of any other exponential decay, including some pulse sequences for measuring the spin-lattice relaxation time, T1. The optimal sampling pattern involves placing 22% of the sample points at zero time and the remaining 78% at 1.28 T2, or, more practically and almost as accurately, one point at zero and four at 1.30 T2. These sampling patterns are very different from those commonly used. The Cramér-Rao results are compared with experimental measurements and computer simulations. Some limitations of the method are described, and its extension to the simultaneous measurement of a range of T2 values is addressed. © 1996 Academic Press, Inc.

Abstract:

Various numerical techniques for alleviating crowding in two-dimensional NMR correlation spectra are investigated with a view to facilitating the measurement of spin-spin coupling constants. The following strategy for the analysis of cross sections through COSY cross peaks is developed: The active coupling constant is determined by J doubling (McIntyre and Freeman, J. Magn. Reson.96, 425, 1992). The active splitting is then removed (J deconvolution) by the maximum-entropy method. Estimates of the passive coupling constants are next obtained from the deconvolved spectrum. Finally, the values of all coupling constants are refined, if necessary, by model fitting to the original spectrum. This approach is shown to be successful for complex, congested cross peaks, whose multiplet structures are far from obvious. © 1993 by Academic Press, Inc.