In what might not come entirely as a surprise, Damian Conway has been along this road a long while ago: http://search.cpan.org/~dconway/Quantum-Superpositions-1.03/...

Hasn't SymPy done this for a while?

http://docs.sympy.org/0.7.2-py3k/modules/physics/quantum/ind...

It would be great if the functions were documented in a way to show what these gates do and why they exist anyway. Not everybody has some pre education on quantum computing, right?

That presupposes I understand them :-)

My coding followed a specific talk which didn't go at all into why these particular gates are useful.

Once I grok that, I'll improve the code.