Experimental quantum deletion in an NMR quantum information processor

We report an NMR experimental realization of a rapid quantum deletion algorithm that deletes marked states in an unsorted database. Unlike classical deletion, where search and deletion are equivalent, quantum deletion can be implemented with only a single query, which achieves exponential speed-up compared to the optimal classical analog. In the experimental realization, the GRAPE algorithm was used to obtain an optimized NMR pulse sequence, and the efficient method of maximum-likelihood has been used to reconstruct the experimental output state.