Generalized methods for the development of quantum logic gates for an NMR quantum information processor

Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natu ral extension of such gates would necessarily operate on one quantum bit (q ubit) conditional on the state of the remaining qubits in the system. We sh ow that such selective gates, termed (controlled)(n)-NOT gates, or c(n)-NOT gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometr ic algebra. These methods yield equivalent NMR pulse sequences for the gene ration of cn-NOT gates for any number of control spins. In this work, a cat alog of c(n)-NOT gates for systems of as many as 16 spins is provided along with an experimental implementation of a c(3)-NOT gate on a four spin syst em, C-13 alanine. [S1050-2947(99)0621 0-1].