We report the realization of a nuclear magnetic resonance (NMR) quantumcomputer which combines the quantum Fourier transform (QFT) with exponentiatedpermutations, demonstrating a quantum algorithm for order-finding. Thisalgorithm has the same structure as Shor's algorithm and its speed-up overclassical algorithms scales exponentially. The implementation uses aparticularly well-suited five quantum bit molecule and was made possible by anew state initialization procedure and several quantum control techniques.
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