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Colloidal quantum dot (CQD) films allow large-area solution processing and bandgap tuning through the quantum size effect. However, the high ratio of surface area to volume makes CQD films prone to high trap state densities if surfaces are imperfectly passivated, promoting recombination of charge carriers that is detrimental to device performance. Recent advances have replaced the long insulating ligands that enable colloidal stability following synthesis with shorter organic linkers or halide anions, leading to improved passivation and higher packing densities. Although this substitution has been performed using solid-state ligand exchange, a solution-based approach is preferable because it enables increased control over the balance of charges on the surface of the quantum dot, which is essential for eliminating midgap trap states. Furthermore, the solution-based approach leverages recent progress in metal:chalcogen chemistry in the liquid phase. Here, we quantify the density of midgap trap states in CQD solids and show that the performance of CQD-based photovoltaics is now limited by electron-hole recombination due to these states. Next, using density functional theory and optoelectronic device modelling, we show that to improve this performance it is essential to bind a suitable ligand to each potential trap site on the surface of the quantum dot. We then develop a robust hybrid passivation scheme that involves introducing halide anions during the end stages of the synthesis process, which can passivate trap sites that are inaccessible to much larger organic ligands. An organic crosslinking strategy is then used to form the film. Finally, we use our hybrid passivated CQD solid to fabricate a solar cell with a certified efficiency of 7.0%, which is a record for a CQD photovoltaic device.