Fetching marked items from an unsorted database in NMR ensemble computing

The speedup of an unsorted database search has always been a challenging problem not only in classical computation but also in quantum computation. We propose a fetching algorithm for a Liouville space nuclear magnetic resonance (NMR) ensemble computing to fetch a marked item from an unsorted database directly. This algorithm achieves the absolute optimum in an unsorted database search problem: a single query. In fact, this algorithm also works well for fetching several unknown numbers of marked items. The computer simulation realization of the algorithm in a three-qubit homonuclear spin system is also presented. In addition, a compromised version of the algorithm, which reduces the demand on the structure of the molecules for the NMR experiment, is also devised.