Use FAQ for further questions. This found from FAQ:
Qualis Gems can be found in several places:
-The first Treasure Chest map you acquire from Rane will most likely spawn a Qualis Gem. This may not work on an imported characters, but only a new fresh character
-The first treasure chest from the Red Brotherhood hideout also has a chance to spawn one too. Again, may not work on an imported character
-Most of the time the bulk of the Qualis Gems, however, are acquired through named Unique spawns that spawn throughout the course of the game: Wulfbode, Warlord Zulkar, Eyegrim, Maltise, etc. Once captured by you, you will have as one its option for release, to exchange their Qualis Gem for their freedom.
Note: It’s very important that you initiate the battle first, since if you join an AI friendly lord’s battle against the unique spawn there is a very high chance that the AI Lord will capture that spawn if it’s defeated, thus killing him and then he will never spawn again.