# For Friday, November 10th, 2023:

1. Check out the solutions to the test.  We will do in-person make-ups as usual.  My calendar link is the same (access it from canvas main page).  Written make-up info soon!
2. Consider the qubit state superposition $i|0\rangle + \sqrt{3}|1 \rangle$.
1. Normalize it so that it is length 1 (i.e. $|a|^2 + |b|^2 = 1$).
2. Normalize it further so that it also lies on the Bloch sphere (first entry $a$ should be positive real).
3. Find $\theta$ and $\phi$ giving this state as a point on the Bloch sphere.
4. Draw it on a Bloch sphere.
3. Write $|-\rangle$ as a linear combination of $|0\rangle$ and $|1\rangle$.
4. Write $|i\rangle$ as a linear combination of $|+\rangle$ and $|-\rangle$.
5. Consider the state $|\psi\rangle = \frac{1}{\sqrt{5}} |0\rangle + \frac{2}{\sqrt{5}}|1\rangle$.
1. Measure it in the basis $|0\rangle$, $|1\rangle$.  What are the possible outcomes and their probabilities?
2. Measure it in the basis $|+\rangle$, $|-\rangle$.  What are the possible outcomes and their probabilities?  (To do this, you will first need to write $|\psi\rangle$ as a linear combination of $|+\rangle$ and $|-\rangle$.)
6. Time permitting, here’s an interesting bonus problem concerning phase estimation.