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

@inproceedings{Hallgren2005FastQA, title={Fast quantum algorithms for computing the unit group and class group of a number field}, author={Sean Hallgren}, booktitle={STOC}, year={2005} }

- Published 2005 in STOC
DOI:10.1145/1060590.1060660

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.Â

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