What are the possible gates that I can use to vary input states before CNOT?

We know that the noise of the $$\text{CNOT}$$ gate varies depending on the input state before it.

What are the gates that I can put in the place of the 4 identity gates above to change the input state that goes to $$\text{CNOT}$$? For example, if I just place a Hadamard gate then $$|+\rangle$$ state is the input to $$\text{CNOT}$$ and this might be noisier than other states. What are the possible gates that I can put before $$\text{CNOT}$$ to vary the input state? I know that $$S$$, $$T$$, $$S^\dagger$$, $$T^\dagger$$, $$X$$, $$Y$$, and $$Z$$ gates do not change the $$|+\rangle$$ state if I put them. and if I use a general u3 gate then Qiskit divides it into multiple gate operations and that can be even noisier to start with.

• First I need to say that $\hat Z|+\rangle=|-\rangle$. Then, your question is about analyzing the noise of a quantum operation, but what your further statement shows is quite different from that. Qiskit has a particular package when dealing with the noisy, Qiskit Ignis. – Yitian Wang Dec 21 '20 at 1:11

Contrary to what you have mentioned in the question, when you use a $$u_3$$ gate, Qiskit does not break it up into multiple gates. In fact $$u_3$$ gate is one of the basis gates for all Qiskit backends and all the single qubit gates are ultimately implemented as $$u_1, u_2$$ or $$u_3$$ gates (You can check more about those gates here). Since $$u_3$$ gate is the most generalized single qubit gate, using $$u_3$$ gates in place of the $$I$$ gates will give you more freedom to vary you input to the $$CNOT$$ gate.