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.

Tharrmashastha V · Answer

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.

Answered by Tharrmashastha V on April 11, 2021

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

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