Experimental realization of a continuous version of the Grover algorithm

A continuous, analog version of the Grover algorithm is realized using NMR. The system studied is ²³Na in a liquid-crystal medium. The presence of quadrupolar coupling makes the spin $I=3/2$ nucleus a two-qubit system. Applying a specially designed pulse sequence, the time evolution of the spin-density operator is described in an interaction representation that has no external time-dependent radio-frequency fields. This approach is used to implement one instance of the continuous Grover search for the transform of a uniform state to a target state, and the implementation provides a clear physical interpretation of the algorithm. The experimental results are in good agreement with the theory.