Experimental Realization of an Order-Finding Algorithm with an NMR   Quantum Computer
  We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques. 
Lieven M.K. Vandersypen (1 and 2), Matthias Steffen (1 and 2), Gregory   Breyta (2), Costantino S. Yannoni (2), Richard Clev...