We perform the first quantum computation of parton distribution function (PDF) with a real quantum device by calculating the PDF of the lightest positronium in the Schwinger model with IBM quantum computers. The calculation uses 10 qubits for staggered fermions at five spatial sites and one ancillary qubit. The most critical and challenging step is to reduce the number of two-qubit gate depths to around 500 so that sensible results start to emerge. The resulting lightcone correlators have excellent agreement with the classical simulator result in central values, although the error is still large.  Compared with classical approaches, quantum computation has the advantage of not being limited in the accessible range of parton momentum fraction x due to renormalon ambiguity, and the difficulty of accessing non-valence partons. A PDF calculation with 3+1 dimensional QCD near x=0 or x=1 will be a clear demonstration of the quantum advantage on a problem with great scientific impact.