(Solved): 2. Using n=3 qubits such that N=2n, a. Compute the entries in the QFT matrix and then compute Q3 ...

2. Using $n=3$ qubits such that $N=2^n$, a. Compute the entries in the QFT matrix and then compute $Q|3⟩=|\tilde{3}⟩$ b. use Equation (33) or Equation (37) in the Module 4 paper '2021 Sakk QFT final final.pdf' in order to compute $Q|3⟩=|\tilde{3}⟩$ c. Using the Module 4 Python notebook 'QFTintro1.ipynb' in Google Colab, verify your answer in part a by doing the following: i. Include an image of the histogram generated by your code. ii. Use your wave function $|\tilde{3}⟩$ to verify the probabilities.