A survey on quantum algorithms for computing class groups

Armin Jamshidpey, University of Waterloo

Fields Number Theory Seminar

Date and Time: Monday, May 17, 2021 - 12:00pm to 1:00pm

Abstract: Our goal is to review the existing quantum algorithms to compute class groups of number fields. First we briefly survey results for this problem on a standard “classical” computer. After a short introduction to quantum computing, we look at the hidden subgroup problem and quantum algorithms for it, as a fundamental tool. Finally we present the polynomial-time quantum algorithm for computing the ideal class group (under the Generalized Riemann Hypothesis) introduced by Biasse and Song (2016).