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 r−1 |us⟩.
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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 t = 4.
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.
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