Quantum dot solar cells are promising for next-generation photovoltaics owing to their potential for improved device efficiency related to bandgap tailoring and quantum confinement of charge carriers. Yet implementing effective photon management to increase the absorptivity of the quantum dots is instrumental. To this end, the performance of thin-film InAs/GaAs quantum dot solar cells with planar and structured back reflectors is reported. The experimental thin-film solar cells with planar reflectors exhibited a bandgap-voltage offset of 0.3 V with an open circuit voltage of 0.884 V, which is one of the highest values reported for quantum dot solar cells grown by molecular beam epitaxy to our knowledge. Using measured external quantum efficiency and current-voltage characteristics, we parametrize a simulation model that was used to design an advanced reflector with diffractive pyramidal gratings revealing a 12-fold increase of the photocurrent generation in the quantum dot layers.