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We give an algorithm for approximating the quantum Fourier transform over an arbitrary Ô which requires only Ç´Ò ÐÓÓ Òµ steps where Ò ÐÓÓ Ô to achieve an approximation to within an arbitrary inverse polynomial in Ò. This improves the method of Kitaev [11] which requires time quadratic in Ò. This algorithm also leads to a general and efficient Fourier… (More)

We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over Zp can be efficiently approximated by transforming over Z, for any q in a large range. Our result places no restrictions on the… (More)

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