The heavy ion fusion program is developing single aperture superconducting quadrupoles based on NbTi conductor, for use in the High Current Experiment at Lawrence Berkeley National Laboratory. Following the fabrication and testing of prototypes using two different approaches, a baseline design has been selected and further optimized. A prototype cryostat for a quadrupole doublet, with features to accommodate induction acceleration modules, is being fabricated. The single aperture magnet was derived from a conceptual design of a quadrupole array magnet for multibeam transport. Progress on the development of superconducting quadrupole arrays for future experiments is also reported.