Quantum Algorithms and the Fourier Transform

Details Quantum Algorithms and the Fourier Transform Quantum Algorithms and the Fourier Transform

1997-07-17

arxiv.org/abs/quant-ph/9707033v1

Physics

Quantum Physics

18 pages Latex. Submitted to Proceedings of Santa Barbara Conference on Quantum Coherence and Decoherence

Scientific paper

10.1098/rspa.1998.0163

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.

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