Simulating More Complicated Quantum Circuits

  1. (20 pts.; 2 pts. each) In your own words (and only words, not equations or code), describe the following algorithms or concepts:

    • Bernstein-Varirani Algorithm
    • Computational Efficiency
    • Query Method
    • Oracle
    • Phase Kickback
    • Discrete Fourier Transform
    • Quantum Fourier Transform

  2. (10 pts.; 5 pts. each) Compute the following entangled states or gate calculations in terms of the \(|\uparrow\rangle\) and \(|\downarrow\rangle\) basis. For full credit, show every step and write a few words explaining the process for each step. \[|\uparrow+\downarrow\rangle\] \[C_X|++\rangle\]

  3. (10 pts.) Compute the DFT matrices for N = 2, N = 3, and N = 4. Show that the matrices are unitary. Feel free to use Numpy/Wolfram Alpha/insert your favorite linear algebra solver here.

  4. (10 pts.) Draw a three qubit circuit where all qubits start off in the \(|\uparrow\rangle\) state. Show two different circuits where a phase can be added to the second qubit by applying a phase angle of \(\frac{\pi}{3}\).