Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition

Details Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition

2010-05-20

arxiv.org/abs/1005.3730v1

Physics

Quantum Physics

12 pages, 1 figure (generated within LaTeX). To appear in Journal of Computational and Applied Mathematics

Scientific paper

We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The Quantum Fourier Transform is one of the most important quantum subroutines known at present, used in most algorithms that have exponential speed up compared to the classical ones. We briefly review Fast Fourier Transform and then make explicit all the steps that led to the quantum formulation of the algorithm, generalizing Coppersmith's work.

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