2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101496It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the Quantum Yang--Baxter equation via Yang--Baxterization and constructs the Hamiltonian responsible for the time-evolution of the unitary braiding operator.v1, 11 pages; v2, 11 pages; v3, 12 pages, additional comments; v4, 10 pages; v5, published versionQuantum PhysicsHigh Energy Physics - TheoryMathematical Physicstext