26 July 2001 Fast quantum nD Fourier and radon transforms
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Fast Classical and quantum algorithms are introduced for a wide class of non-separable nD discrete unitary K- transforms(DKT)KNn. They require a number of 1D DKT Kn smaller than in the Cooley-Tukey radix-p FFT-type approach. The method utilizes a decomposition of the nDK- transform into a product of original nD discrete Radon Transform and of a family parallel/independ 1DK-transforms. If the nDK-transform has a separable kernel, that again in this case our approach leads to decrease of multiplicative complexity by factor of n compared to the tow/column separable Cooley-Tukey p-radix approach.
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Valeri G. Labunets, Valeri G. Labunets, Ekaterina V. Labunets-Rundblad, Ekaterina V. Labunets-Rundblad, Jaakko T. Astola, Jaakko T. Astola, "Fast quantum nD Fourier and radon transforms", Proc. SPIE 4386, Photonic and Quantum Technologies for Aerospace Applications III, (26 July 2001); doi: 10.1117/12.434211; https://doi.org/10.1117/12.434211

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