2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89826To explore the limitation of a class of quantum algorithms originally proposed for the Hilbert's tenth problem, we consider two further classes of mathematically non-decidable problems, those of a modified version of the Hilbert's tenth problem and of the computation of the Chaitin's $Ω$ number, which is a representation of the Gödel's Incompletness theorem. Some interesting connection to Quantum Field Theory is pointed out.Clarification and new references addedQuantum Physicstext