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.