Our research group is part of a consortium to develop a quantum software stack funded by the German Federal Ministry of Economic Affairs and Climate Action. A quantum algorithm is expressible as a parallel and sequential composition of morphisms in a specific dagger compact closed category H. one among several categorical doctrines supported by the software project CAP, actively developed by our research group. Part of the project is the development of a domain specfic compiler for category theory that can compile away the entire abstraction introduced by the categorical language. The remaining optimization in the specific category H will be performed using the ZX-calculus introduced by Bob Coecke and Ross Duncan in 2008 and further developed by them and several other scientists.