An update for Grassmannian.info: 2 big exceptional quantum spectra
A little while ago I let my computer waste some electricity on computing the quantum spectra of two exceptional Grassmannians. For more on the quantum spectrum, see this blogpost for more information.
The exceptional Grassmannians are:
I believe slightly larger Grassmannians should also within reach, but the calculation, which by no means was optimized, did not finish on time. Below you can see the largest quantum spectrum currently available on Grassmannian.info: