Quantum Computing and a Unified Approach to Fast Unitary Transforms

Details Quantum Computing and a Unified Approach to Fast Unitary Transforms Quantum Computing and a Unified Approach to Fast Unitary Transforms

2002-01-26

arxiv.org/abs/quant-ph/0201120v1

Physics

Quantum Physics

11 pages, LaTeX2e, 15 figures, not viewable as dvi. To appear in Image Processing: Algorithms and Systems, Electronic Imaging

Scientific paper

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum algorithms. We present a divide-and-conquer approach to the design of various quantum algorithms. The class of algorithm includes many transforms which are well-known in classical signal processing applications. We show how fast quantum algorithms can be derived for the discrete Fourier transform, the Walsh-Hadamard transform, the Slant transform, and the Hartley transform. All these algorithms use at most O(log^2 N) operations to transform a state vector of a quantum computer of length N.

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