2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149645In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case polynomial time. We also give a quantum algorithm which solves claw problem with certainty in a worst-case polynomial time.This paper was withdrawn because of gaps in this paperQuantum Physicstext