dorsal/arxiv
View SchemaQuantum factoring, discrete logarithms and the hidden subgroup problem
| Authors | Richard Jozsa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012084 |
| URL | https://arxiv.org/abs/quant-ph/0012084 |
| DOI | 10.1109/5992.909000 |
Abstract
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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"abstract": "Amongst the most remarkable successes of quantum computation are Shor\u0027s\nefficient quantum algorithms for the computational tasks of integer\nfactorisation and the evaluation of discrete logarithms. In this article we\nreview the essential ingredients of these algorithms and draw out the unifying\ngeneralization of the so-called abelian hidden subgroup problem. This involves\nan unexpectedly harmonious alignment of the formalism of quantum physics with\nthe elegant mathematical theory of group representations and fourier transforms\non finite groups. Finally we consider the non-abelian hidden subgroup problem\nmentioning some open questions where future quantum algorithms may be expected\nto have a substantial impact.",
"arxiv_id": "quant-ph/0012084",
"authors": [
"Richard Jozsa"
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"quant-ph"
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"doi": "10.1109/5992.909000",
"title": "Quantum factoring, discrete logarithms and the hidden subgroup problem",
"url": "https://arxiv.org/abs/quant-ph/0012084"
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