A Survey on Quantum Algorithms for Computing Class Groups

Explore a comprehensive survey of quantum algorithms for computing class groups in this 58-minute Fields Number Theory Seminar talk by Armin Jamshidpey from the University of Waterloo. Begin with a brief overview of classical computing results for class group computation in number fields. Gain insights into quantum computing fundamentals before delving into the hidden subgroup problem and its quantum algorithmic solutions. Examine the polynomial-time quantum algorithm for computing ideal class groups, introduced by Biasse and Song in 2016, which operates under the Generalized Riemann Hypothesis. Enhance your understanding of cutting-edge quantum computational techniques in number theory through this informative presentation from the Fields Institute.