Quantum Computing Using Quadrupolar Spins in Solid State NMR

Nuclear magnetic resonance (NMR) is a successful method for experimental implementation of quantum information processing. Most of the successful NMR quantum processors are small molecules in liquid state. In this case each spin half particle represents a qubit. Another approach is the usage of higher spin particles as multi qubit systems. We present the first solid state virtual 2-Qubit system, represented by the spin-3/2 nucleus Na-23 in a NaNO3 single crystal. For this system we show how to create the pseudo pure states and we derive a set of propagators and logic gates corresponding to the selective excitation of single quantum transitions. With this set, the preparation of an "entangled" state is experimentally verified by state tomography, adjusted to the spin-3/2 system.