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Quantum Computation 4x4 Unitary Matrix for Circuit

  1. Oct 19, 2012 #1
    1. The problem statement, all variables and given/known data
    What is the 4x4 unitary matrix for the circuit in the computational basis.
    LrTZi.png

    2. Relevant equations

    We were given the following relationship in our notes: 8yAOT.png .

    By letting [itex] A = H [/itex] and [itex]B = I[/itex], the answer is supposedly supposed to be: 8yN69.png simply by inspection (where H is the Hadarmard gate and I is the identity matrix).

    3. The attempt at a solution

    Unfortunately, I found a different result. By running the basis states through the circuit, I came up with the following:
    [itex]\left| 00 \right\rangle \rightarrow H(\left|0\right\rangle)\left|0\right\rangle = ( \frac{1}{\sqrt{2}} \left|0\right\rangle + \frac{1}{\sqrt{2}} \left|1\right\rangle ) \left|0\right\rangle = \frac{1}{\sqrt{2}}\left|00\right\rangle + \frac{1}{\sqrt{2}}\left|10\right\rangle[/itex]

    Using this method for each computational basis, I was able to generate the following matrix by inspection:
    lE0SE.png

    Why are the answers so vastly different? What is the correct one?

    Thanks in advance.
     
  2. jcsd
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