Quantum factoring, discrete logarithms and the hidden subgroup problem

Details Quantum factoring, discrete logarithms and the hidden subgroup problem Quantum factoring, discrete logarithms and the hidden subgroup problem

2000-12-17

arxiv.org/abs/quant-ph/0012084v1

Physics

Quantum Physics

latex2e, 15 pages. Review article prepared for special issue of "IEEE Computing in Science and Engineering"

Scientific paper

Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential ingredients of these algorithms and draw out the unifying generalization of the so-called abelian hidden subgroup problem. This involves an unexpectedly harmonious alignment of the formalism of quantum physics with the elegant mathematical theory of group representations and fourier transforms on finite groups. Finally we consider the non-abelian hidden subgroup problem mentioning some open questions where future quantum algorithms may be expected to have a substantial impact.

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