Which of the following pairs of quantum gates commute? Select all that apply. (Gates A and B commute if and only if for any input applying A and then B gives the same results as applying B and then A. This is the same as saying that the unitary transformations commute.)
a) I and X
b) X and Z
c) H and X
d) CNOT and X applied to the target
e) qubit Real rotation by 30∘ and real rotation by 45∘
Specify the state of each qubit after we applied the circuit.
First qubit: ... ?
Please :)