From what I've gathered, there are multiple quantum computational logics. But, I've been having difficulty figuring out whether they subsume quantum logic or how much overlap there may be. I even had difficulty finding the term quantum computational logics.
So, please do share to what degree quantum logic describes the logic of said gates and/or how it is interrelated with different quantum computational logics.
(If there's anything I can do to improve the quality of the question, please let me know.)