2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141688We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.15 pages, one figure. Two comments added in Secs. 2 and 5Quantum PhysicsBounds for the adiabatic approximation with applications to quantum computationtext