Quantum algorithms and the Fourier transform
- 8 January 1998
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 454 (1969) , 323-337
- https://doi.org/10.1098/rspa.1998.0163
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 the 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' algorithm.Keywords
All Related Versions
This publication has 5 references indexed in Scilit:
- Quantum computation and Shor's factoring algorithmReviews of Modern Physics, 1996
- A fast quantum mechanical algorithm for database searchPublished by Association for Computing Machinery (ACM) ,1996
- Quantum complexity theoryPublished by Association for Computing Machinery (ACM) ,1993
- Rapid solution of problems by quantum computationProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Quantum theory, the Church–Turing principle and the universal quantum computerProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1985