Polynomial time quantum algorithm for the computation of the unit group of a number field

Authors:
Arthur Schmidt;Ulrich Vollmer
Affiliations:
Technische Universität Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt;Technische Universität Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt
Venue:
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Year:
2005

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Abstract

We present a quantum algorithm for the computation of the irrational period lattice of a function on Zn which is periodic in a relaxed sense. This algorithm is applied to compute the unit group of finite extensions of Q. Execution time for fixed field degree over Q is polynomial in the discriminant of the field. Our algorithms generalize and improve upon Hallgren's work [9] for the one-dimensional case corresponding to real-quadratic fields.