I'm trying to become familiar with manipulation of the Dirac notation. I want to be able to compute quickly the final states obtained in a small circuit. Typically, it should include 2 to 5 qubits, and be composed of some 2-qubit controlled gates (essentially CNOT but others would be good too), rotation, hadamard, paulis, and other basic gates. It should not contain too many gates either so I don't spend 4 hours computing it. Once computed the final state I want also to be able to give quickly the results of the measure of one of the qubits, probability and state after measurement.
Do you know any exercises with solutions of the computation of circuits ? Where can I find them ?