Computing the unit group and class group of a number field are two of the main tasks in computational algebraic number theory. Factoring integers reduces to solving Pell's equation, which is a special case of computing the unit group, but a reduction in the other direction is not known and appears more difficult. We give polynomial-time quantum algorithms for computing the unit group and class group when the number field has constant degree.
|Original language||English (US)|
|Number of pages||7|
|Journal||Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - Dec 1 2005|
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