One of the hallmark experiments of quantum transport is the observation of the quantized resistance in a point contact formed with split gates in GaAs/AlGaAs heterostructures. Being carried out on a single material, they represent in an ideal manner equilibrium reservoirs which are connected only through a few electron mode channel with certain transmission coefficients. It has been a long standing goal to achieve similar experimental conditions also in superconductors, only reached in atomic scale mechanically tunable break junctions of conventional superconducting metals, but here the Fermi wavelength is so short that it leads to a mixing of quantum transport with atomic orbital physics. Here we demonstrate for the first time the formation of a superconducting quantum point contact (SQPC) with split gate technology in a superconductor, utilizing the unique gate tunability of the two dimensional superfluid at the LaAlO3/SrTiO3 (LAO/STO) interface. When the constriction is tuned through the action of metallic split gates we identify three regimes of transport: (i) SQPC for which the supercurrent is carried only by a few quantum transport channels. (ii) Superconducting island strongly coupled to the equilibrium reservoirs. (iii) Charge island with a discrete spectrum weakly coupled to the reservoirs. Our experiments demonstrate the feasibility of a new generation of mesoscopic all-superconductor quantum transport devices.