Homework 5
1. For the unitary transformation U from Problem 5 of HW 4, find all the vectors |us〉, s =
0, . . . , r − 1, and check that they are eigenvectors of U .
2. Compute explicitly
3. Find the joint quantum state of all t+L qubits right before the measurement blocks in
the quantum circuit from Problem 6 of HW 4 . Recall that in Problem 6 of HW 4 we used
4. Find all possible classical outputs of the measurements with corresponding probabilities.
5. Let N = 21 and x = 3. Find gcd(x,N) and decide whether gcd(x,N) is a nontrivial
factor of N or not.
6. Let N = 21 and x = 5. Find gcd(x,N) and decide whether gcd(x,N) is a nontrivial
factor of N or not.