2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210441We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example. To be specific, we construct a functional braid in a six-anyon Hilbert space that exchanges two neighboring anyons while conserving the encoded quantum information. The leakage error is $\sim$$10^{-10}$ for a braid of $\sim$100 interchanges of anyons. Applying the braid greatly reduces the leakage error in the construction of generic controlled-rotation gates.5 pages, 4 figures, updated, accepeted by Phys. Rev. AMesoscale and Nanoscale PhysicsQuantum Physicstext