Experimental realization of order-finding with a quantum computer

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Abstract
Quantum computers offer the potential for efficiently solving certain computational tasks which are too hard for even the fastest conceivable classical computers. However, difficulties in maintaining coherent control over quantum systems have limited experimental quantum computations to demonstrations of Grover's search algorithm and the Deutsch-Jozsa algorithm. Shor's remarkable quantum factoring algorithm has remained beyond the reach of these small-scale realizations. Here we report the experimental implementation of a quantum algorithm which generalizes Shor's algorithm to find the order of a permutation in fewer steps than is possible using a deterministic or probabilistic classical computer. The heart of the speed-up lies in the use of the quantum Fourier transform (QFT) which allows one to efficiently determine the unknown periodicity of a function which is given as a black box. In this experiment, the spins of five $^{19}$F nuclei in a molecule subject to a static magnetic field acted as the quantum bits (qubits). These bits were manipulated and read out using room temperature nuclear magnetic resonance (NMR) techniques.

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