U1L3m.txt

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So question, how do you describe a rotation of angle theta
around an axis?

Answer, e to the minus i theta sigma x or e--
wait.
There's a 2 in here.
e to the minus i theta sigma y over 2 or e to the minus i
theta sigma z over 2.
Our rotations of theta around the x-axis, the y-axis,
and the z-axis.

Let's worry about sigma z over 2 first.
So sigma z over 2, e to the i theta.
Sigma z over 2 is equal to sigma z was 1 minus 1, so
this is just going to be e to the i theta over 2
e to the minus i--
oh, e to the plus i theta over 2, e to the minus i theta
over 2.
Because we're exponentiating a diagonal matrix, what we do is
we just need to exponentiate the elements
along the diagonal, which is--
I left out a minus sign there--
which gives you an e to the minus i theta over 2 and e
to the plus i theta over 2, which is equivalent
up to global phase.

to 1, 0, 0, e to the i theta.

And we can check this.
I mean, suppose we start with 0 plus 1 over root 2.
And we want to rotate it by 90 degrees.
That's pi over 2.
And if we rotate it 90 degrees, it's
supposed to take this to that.

So we multiply 1, 0, 0 e to the i pi over 4 by 1 over root 2.
We get 1 over root 2 pi over root 2.

So that did it.
So so at least by example, this worked.

The next thing I want to do is figure out
what e to the minus i theta sigma y over 2 is.