Quantum Algorithms and the Fourier Transform
Quantum Physics
2009-10-30 v1
Abstract
The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a unified way of understanding the efficacy of these algorithms. Finally we describe an efficient quantum factoring algorithm based on a general formalism of Kitaev and contrast its structure to the ingredients of Shor's algorithm.
Cite
@article{arxiv.quant-ph/9707033,
title = {Quantum Algorithms and the Fourier Transform},
author = {Richard Jozsa},
journal= {arXiv preprint arXiv:quant-ph/9707033},
year = {2009}
}
Comments
18 pages Latex. Submitted to Proceedings of Santa Barbara Conference on Quantum Coherence and Decoherence