Experimental realization of an order-finding algorithm with an NMR quantumcomputer

We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutation s, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speedup over classical algor ithms scales exponentially. The implementation uses a particularly well-sui ted five quantum bit molecule and was made possible by a new state initiali zation procedure and several quantum control techniques.