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- W2065276051 abstract "We show how the Quantum Fast Fourier Transform (QFFT) can be made exact for arbitrary orders (first showing it for large primes). Most quantum algorithms only need a good approximation of the quantum Fourier transform of order 2 n to succeed with high probability, and this QFFT can in fact be done exactly. Kitaev 1 showed how to approximate the Fourier transform for any order. Here we show how his construction can be made exact by using the technique known as amplitude amplification. Although unlikely to be of any practical use, this construction allows one to make Shor's discrete logarithm quantum algorithm exact. Thus we have the first example of an exact non black box fast quantum algorithm, thereby giving more evidence that quantum need not be probabilistic. We also show that in a certain sense the family of circuits for the exact QFFT is uniform. Namely, the parameters of the gates can be approximated efficiently." @default.
- W2065276051 created "2016-06-24" @default.
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- W2065276051 date "2004-03-01" @default.
- W2065276051 modified "2023-09-25" @default.
- W2065276051 title "EXACT QUANTUM FOURIER TRANSFORMS AND DISCRETE LOGARITHM ALGORITHMS" @default.
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- W2065276051 doi "https://doi.org/10.1142/s0219749904000109" @default.
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