Quantum computing and a unified approach to fast unitary transforms

Sos S. Agaian; Andreas Klappenecker

doi:10.1117/12.467967

22 May 2002 Quantum computing and a unified approach to fast unitary transforms

Sos S. Agaian, Andreas Klappenecker

Proceedings Volume 4667, Image Processing: Algorithms and Systems; (2002) https://doi.org/10.1117/12.467967
Event: Electronic Imaging, 2002, San Jose, California, United States

Abstract

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(log² N) operations to transform a state vector of a quantum computer of length N.

Citation Download Citation

Sos S. Agaian and Andreas Klappenecker "Quantum computing and a unified approach to fast unitary transforms", Proc. SPIE 4667, Image Processing: Algorithms and Systems, (22 May 2002); https://doi.org/10.1117/12.467967

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