I am getting a bit confused about how to trace through a quantum circuit.

So, for example, if you have the circuit below:

Hadamard, sigmax, hadamard

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?)

  • $\begingroup$ you need to understand tensor products to understand the answer. $\endgroup$
    – psitae
    Apr 21 at 20:47
  • $\begingroup$ Hi Emily. Welcome to PhysicsStackExchange. It would be better if you write the mathematical parts of your post using MathJax. FMI, see this: physics.stackexchange.com/help/notation $\endgroup$
    – SG8
    Apr 21 at 21:02