The quickstart guide is similar to the beginner's guide. The key difference is that the quickstart guide assumes the user already understands what the software intends to do and generally how they would like to use it, and they just need to quickly get spun up on the API. To that end, this document won't provide any scientific background or detailed tutorials/how-tos. It will focus more on installation and usage.
Explain to the user how to install dependencies and the quantum prototype. It is likely best to just link to the installation guide here.
Demonstrate the API usage here. Since the user is assumed to have some background on the software capabilities, more detailed/advanced usage can be provided here than in the beginner's guide.