2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174611Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual groups are equivalent. We reformulate this as a statement about categories of B-branes on the quantized moduli spaces of flat connections for these groups. We show that it implies the statement of the Quantum Geometric Langlands duality with a purely imaginary ``quantum parameter'' which is proportional to the inverse of the Planck constant of the gauge theory. The ramified version of the story is also considered.18 pages, AMS latexHigh Energy Physics - TheoryAlgebraic GeometryQuantum Algebratext