# An improved quantum Fourier transform algorithm and applications

@article{Hales2000AnIQ, title={An improved quantum Fourier transform algorithm and applications}, author={Lisa Hales and Sean Hallgren}, journal={Proceedings 41st Annual Symposium on Foundations of Computer Science}, year={2000}, pages={515-525} }

We give an algorithm for approximating the quantum Fourier transform over an arbitrary Z/sub p/ which requires only O(n log n) steps where n=log p to achieve an approximation to within an arbitrary inverse polynomial in n. This improves the method of A.Y. Kitaev (1995) which requires time quadratic in n. This algorithm also leads to a general and efficient Fourier sampling technique which improves upon the quantum Fourier sampling lemma of L. Hales and S. Hallgren (1997). As an application of…

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