2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91988Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds given earlier. Exact bounds are given for the number of qubits needed to achieve a desired tolerance, allowing simulation of the algorithm.18 pages. Minor corrections were made, and some new material was added. Particularly, simulation results were added to show output of the algorithm, and to suggest possible improvementsQuantum PhysicsData Structures and Algorithmstext