I am getting a bit confused about how to trace through a quantum circuit.
So, for example, if you have the circuit below:
I know that the first gate would split an arbitrary state alpha|0> + beta|1> into an equal superposition of states. (Which I think can be represented by the vector 1/sqrt(2) * [alpha + beta, alpha - beta])
But then, I am starting to get confused about how to apply the sigma_x (0 1; 1 0) gate to the first qubit. (Or is it the second?)