2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89088We prove that Ω(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons must be made. The previous known lower bound is Ω(n).This paper has been merged with another paper. See quant-ph/0102078Quantum Physicstext