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Fast quantum algorithms for computing the unit group and class group of a number field

Published: 22 May 2005 Publication History

Abstract

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.

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  1. Fast quantum algorithms for computing the unit group and class group of a number field

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    cover image ACM Conferences
    STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
    May 2005
    778 pages
    ISBN:1581139608
    DOI:10.1145/1060590
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    Publication History

    Published: 22 May 2005

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    Author Tags

    1. class group
    2. computational algebraic number theory
    3. quantum algorithms
    4. unit group

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    May 22 - 24, 2005
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