I have some questions related to superoperators:
What is the differences between quantum operators and superoperators? For instance quantum gates are also unitary operators but can we say quantum operators are superoperators?
Can we write a quantum operator as superoperator?
For instance, I want to write toffoli gate circuit as super operator:
The circuit is here:
And as I asked here before here , I wrote toffoli gate matrix by using one and two qubit gates. But how can I write this circuit as a superoperator? I initially thought that I already wrote the circuit since it is a linear map from H_a to H_b. But I am not sure..