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- Lisa Hales, Sean Hallgren
- FOCS
- 2000

We give an algorithm for approximating the quantum Fourier transform over an arbitrary Zp which requires only O(n logn) steps where n = log p to achieve an approximation to within an arbitrary inverse polynomial in n. This improves the method of Kitaev [11] which requires time quadratic in n. This algorithm also leads to a general and efficient Fourier… (More)

- Lisa Hales, Sean Hallgren
- STOC
- 1999

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)

The Quantum Fourier Transform and Extensions of the Abelian Hidden Subgroup Problem

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