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

Question

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.

Answer 1

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.