Human growth hormone (HGH) is popular amongst some athletes who use it for performance enhancement. A significant amount of HGH is secreted at night when asleep. Sleep deprivation can reduce HGH levels. HGH levels also naturally decrease with age. HGH can be used to treat certain medical conditions, like Prader-Willi Syndrome, which can cause sleep problems. I've not seen it used however in otherwise healthy people to improve sleep quality.
This study did just that - subjects took HGH at bedtime and reported significant improvement in time to fall asleep. They also had less time awake in the middle of the night and woke more rested in the morning. No reason for why HGH may improve sleep quality is given. Perhaps scientists will discover a novel mechanism of action to help those with reduced sleep quality.