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A quantum computer directly manipulates information stored in the state ofquantum mechanical systems. The available operations have many attractivefeatures but also underly severe restrictions, which complicate the design ofquantum algorithms. We present a divide-and-conquer approach to the design ofvarious quantum algorithms. The class of algorithm includes many transformswhich are well-known in classical signal processing applications. We show howfast quantum algorithms can be derived for the discrete Fourier transform, theWalsh-Hadamard transform, the Slant transform, and the Hartley transform. Allthese algorithms use at most O(log^2 N) operations to transform a state vectorof a quantum computer of length N.Comment: 11 pages, LaTeX2e, 15 figures, not viewable as dvi. To appear in  Image Processing: Algorithms and Systems, Electronic Imaging 2002, San Jose,  SPIE, 2002. Odd title beyond our contro

<title>Quantum computing and a unified approach to fast unitary transforms</title>