We have the tri fold mattress kind of murphy bed.
I bought a queen size mattress topper and actually put it under the mattress, so I guess it's no longer a topper. A bottomer?
Comfy.
Anyway, the whole thing folds up fine and fits in the space.
This is what I bought.
https://www.amazon.com/Cr-Gel-Infuse.../dp/B01NBFBFBM